<html><head></head><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:13px"><div><span></span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6749" dir="ltr">I think Chiastic Approval would fail participation, assuming I've done this right. Take the following ballots with scores out of 100:</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6634"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6661">2 voters: A=50, B=40</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6662">1 voter: A=50, B=60</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6663"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6693" dir="ltr">A would have a score of 50. B would have a score of 40. Everyone gives B a score of at least 40, and only a third give B a score higher. Now imagine there are two extra voters and we have these ballots:</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6726" dir="ltr"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6733" dir="ltr">2 voters: A=50, B=40</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6744" dir="ltr">1 voter: A=50, B=60</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6745" dir="ltr">2 voters: A=100, B=60</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6757" dir="ltr"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1477659719414_6758" dir="ltr">A still has a score of 50, but B now has a score of 60. So these two ballots cause B to overtake A despite them both preferring A to B.<br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1477659719414_6567" style="display: block;"> <blockquote id="yui_3_16_0_ym19_1_1477659719414_6566" style="padding-left: 5px; margin-top: 5px; margin-left: 5px; border-left-color: rgb(16, 16, 255); border-left-width: 2px; border-left-style: solid;"> <div id="yui_3_16_0_ym19_1_1477659719414_6565" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px;"> <div id="yui_3_16_0_ym19_1_1477659719414_6564" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div id="yui_3_16_0_ym19_1_1477659719414_6563" dir="ltr"> <font id="yui_3_16_0_ym19_1_1477659719414_6562" face="Arial" size="2"> <hr size="1"> <b><span style="font-weight: bold;">From:</span></b> Forest Simmons <fsimmons@pcc.edu><br> </font></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1477659719414_6574"><div id="yiv9852368392"><div id="yui_3_16_0_ym19_1_1477659719414_6575" dir="ltr"><div class="yiv9852368392gmail_quote" id="yui_3_16_0_ym19_1_1477659719414_6578"><div id="yui_3_16_0_ym19_1_1477659719414_6577" dir="ltr"><div class="yiv9852368392MsoNormal" id="yui_3_16_0_ym19_1_1477659719414_6588"><br></div><div class="yiv9852368392MsoNormal" id="yui_3_16_0_ym19_1_1477659719414_6587">Does it satisfy Participation?</div><div class="yiv9852368392MsoNormal" id="yui_3_16_0_ym19_1_1477659719414_6586"><br></div></div></div></div></div><br></div> </div> </div> </blockquote> </div></div></body></html>