In order to have optimum Bayesian Regret, a voting system should be able to not elect a Weak Condorcet Winner (WCW), that is, a CW whose utility is lower than the other candidates. Consider the following payout matrices:<div>
<div style="background-color:transparent"><span id="internal-source-marker_0.977759484667331"><div style="font-weight:bold"><table style="border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;border-width:initial;border-color:initial;border-collapse:collapse">
<tbody><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap"><br></span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">Group</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">size</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
can</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
did</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
ate<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Scenario 1 (zero sum)</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">A</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">B</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">C</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">a</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">1</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">b</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">c</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Total payout</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Scenario 2 (positive sum)</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">A</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">B</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">C</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">a</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">1</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">b</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">1.5</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">c</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Total payout</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">12</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">12</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Scenario 3 (negative sum)</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">A</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">B</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">C</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">a</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0.5</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">b</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">c</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">1</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Total payout</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">11</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td></tr></tbody></table><br></div><div>All three scenarios consist of 3 groups of voters: groups a, b, and c, with 4, 2, and 3 voters respectively, for a total of 9 voters. All scenarios have 3 candidates: A, B, and C, who favor their respective groups. And in all three scenarios, candidate B is the CW, because the preference matrix is always</div>
<div><br></div><div>4: A>B</div><div>2: B>C</div><div>3: C>B</div><div><br></div><div>But in scenario 1, the utilities of the three candidates are balanced; in scenario 2, B has the highest utility; and in scenario 3, A and C have the highest utilities.</div>
<div><br></div><div>Obviously, any purely preferential system will tend to give the same result in all three scenarios. This might not be 100% true if strategy propensity depended on the utility payoff of a strategy; but the strategic possibilities would have to be just right for a method to "get it right" for this reason.</div>
<div><br></div><div>It's easy to see how Range could "get it right" in scenarios 2 and 3. With just a bit of strategy, it's also easy to see how it could successfully find the CW in scenario 1.</div><div>
<br></div><div>You can also construct plausible stories of how Approval or MJ could "get it right" in all 3 scenarios, although it probably involves adding some random noise to voting patterns rather than assuming pure "honest" votes.</div>
<div><br></div><div>But what about SODA? As a primarily preferential system, it seems that it should give the same result in all three scenarios. If candidates all rationally pursue the interests of their primary constituency, then A will approve B to prevent B from having to approve C, leaving a win for B.</div>
<div><br></div><div>But if candidate A decides to make an ultimatum, things could go differently. A says to B: "Make some promise that transfers 0.5 point of utility to each member of group a, or I will not approve you." Assume that B can make a promise to transfer utility from one group to another at 80% efficiency; and that such promises are not strictly enforceable. Thus, if A gets too greedy, B can simply promise the moon and not keep the promise; but if A asks for something reasonable, B will see honesty as worth it.</div>
<div><br></div><div>B could promise to transfer 0.5 point of utility from groups b and c to group a. Since utility transfers are assumed to be only 80% efficient, that transfer of 2.5 utility points would result in a net loss of 0.5. So the payoffs would be:</div>
<div><br><div><div style="background-color:transparent"><span id="internal-source-marker_0.977759484667331"><div style="font-weight:bold"><table style="border-top-style:none;border-right-style:none;border-bottom-style:none;border-left-style:none;border-width:initial;border-color:initial;border-collapse:collapse">
<tbody><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap"><br></span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">Group</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">size</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
can</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
did</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
ate<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Scenario 1 (zero sum)</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">A</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">B</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">C</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">a</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">1.5</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">b</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">2.5</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">c</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">1.5</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Total payout</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">15.5</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Scenario 2 (positive sum)</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">A</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">B</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">C</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">a</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">1.5</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">b</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><font class="Apple-style-span" face="Arial"><span class="Apple-style-span" style="white-space:pre-wrap">2.5</span></font></p></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">1.5</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">c</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">1.5</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Total payout</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">12</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">15.5</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">12</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Scenario 3 (negative sum)</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:top;padding-top:7px;padding-right:7px;padding-bottom:7px;padding-left:7px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">A</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">B</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(239,239,239);padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;text-decoration:none;vertical-align:baseline;white-space:pre-wrap">C</span><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">a</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">1</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">b</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2.5</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">2</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">c</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">3</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">0.5</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">4</span></p>
</td></tr><tr style="height:0px"><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;background-color:rgb(200,200,200);padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">Total payout</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">10.5</span></p>
</td><td style="border-top-width:1px;border-right-width:1px;border-bottom-width:1px;border-left-width:1px;border-top-style:dotted;border-right-style:dotted;border-bottom-style:dotted;border-left-style:dotted;border-top-color:rgb(170,170,170);border-right-color:rgb(170,170,170);border-bottom-color:rgb(170,170,170);border-left-color:rgb(170,170,170);vertical-align:bottom;padding-top:0px;padding-right:3px;padding-bottom:0px;padding-left:3px">
<p dir="ltr" style="text-align:center;margin-top:0pt;margin-bottom:0pt"><span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap">16</span></p>
<span style="font-size:13px;font-family:Arial;background-color:rgb(255,255,255);text-decoration:none;vertical-align:baseline;white-space:pre-wrap"></span></td></tr></tbody></table><br></div><div>Note that in scenarios 1 and 2, this utility transfer has left B giving the same utility to groups a and c, while in scenario 3, B has switched from favoring group c over group a, to favoring group a over group c. Also, note that in scenario 2, group b still gets a full point of advantage with candidate B versus what they would get with candidate C, whereas in the other two scenarios, group b only gets half a point of advantage there. If group b demands a full point of advantage, then B could only meet the ultimatum in scenario 1 by taking all the utility from group c, which would leave c with less utility than a.</div>
<div><br></div><div>I believe that these factors tend to make it more likely that B would meet the ultimatum in scenario 2 than in the other scenarios. Of course, C could realize this, and simply not attempt to make the ultimatum in scenarios 1 and 3; and then B would still win. But C's utility payouts show that they honestly have no preference between groups b and c, so I think that it is not unreasonable to imagine that they'd make the ultimatum in all three cases.</div>
<div><br></div><div>The upshot is, there is a plausible (though perhaps not too likely) mechanism for SODA to avoid electing a CW specifically in cases where that CW is intrinsically weak. And that's with perfect information; I'd argue that the mechanism would work even better in cases where B's strength were illusory; that is, where groups a and c were overestimating their payoff from candidate B because of the A/C rivalry. Candidate A, realizing that they were choosing between B and C, would be more careful about assessing the relative payoffs between those candidates than group a, distracted by the A/C rivalry, had been.</div>
<div><br></div><div>Thoughts?</div><div><br></div><div>Jameson</div><div>All three scena</div></span></div></div></div></span></div></div>