<div dir="ltr"><div>Yes, you have succinctly summarized the intent of the criterion. Now it remains to be seen which methods (if any) comply. <br><br> I have a feeling that both of Benham's methods comply, and perhaps even an equal ranking version of IRV, at least in the case of three candidates, but so far no general proof.<br>
<br></div>Some random simulations would be nice, but finding the Nash equilibria automatically might be challenging.<br><br><br></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Tue, May 20, 2014 at 8:31 AM, Michael Ossipoff <span dir="ltr"><<a href="mailto:email9648742@gmail.com" target="_blank">email9648742@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>Then, with a complying method, it's always possible to get, without using revesal, a result that's a Nash equilibrium, and--as the MAM winner--is an ideal majoritarian result.</div>
<div> </div><div>
So,even though, to meet CD, it's necessary to give up SDSC and SFC, a group of voters can, without reversal, achieve, at equilibrium ,an ideal majoritarian result.</div><span class="HOEnZb"><font color="#888888"><div>
</div><div>Michael Ossipoff</div><div> </div>
<div> </div></font></span></div><div class="gmail_extra"><br><br><div class="gmail_quote"><div><div class="h5">On Mon, May 19, 2014 at 3:15 PM, Forest Simmons <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>></span> wrote:<br>
</div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5"><div dir="ltr"><div><div>Chris and Mike,<br><br></div>your combined comments gave me an idea for a more practical version of semi-sincerity:<br>
<br></div><div>A method satisfies Semi-Sincerity Relative to MAM or SS(MAM) if and only if a semi-sincere modification of the sincere preferences leads to a strategic equilibrium ballot set from which the method elects the the sincere MAM winner.<br>
<br></div><div>This criterion recognizes the superiority of MAM under ideal conditions while allowing the method in question to comply with CD, for example.<br><br></div><div>Suppose our method is Benham, and sincere votes are<br>
</div><div><div><br></div><div></div><div>34 A>B<br></div><div>31 B<br></div><div>35 C<br><br></div></div><div>A semi-sincere ballot modification results in a Nash equilibrium for Benham that elects B, the MAM winner of the sincere ballot set (not to mention the modified set).<br>
<br></div><div class="gmail_extra"><div>34 A=B<br></div><div>31 B<br></div>35 C<br><br></div><div class="gmail_extra">Forest<br></div><div class="gmail_extra"><br><div class="gmail_quote"><br><blockquote style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid" class="gmail_quote">
Date: Sun, 18 May 2014 14:46:30 -0400<br>
From: Michael Ossipoff <<a href="mailto:email9648742@gmail.com" target="_blank">email9648742@gmail.com</a>><br>
To: <a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>, "<a href="mailto:election-methods@electorama.com" target="_blank">election-methods@electorama.com</a>"<br>
<<a href="mailto:election-methods@electorama.com" target="_blank">election-methods@electorama.com</a>><div><br>
Subject: Re: [EM] New Criterion<br>
Message-ID:<br></div>
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<br>
Chris--<br>
<br>
One comment that I can make right away is that FBC is almost surely<br>
incompatible with CD + MMC. ...just as FBC is incompatible with Condorcet.<br>
So, in Green scenario or ideal majoritarian conditions, FBC would be too<br></div>
costly. So, if the 2nd of Forest's criteria, too, is incompatible with the<div><br>
criteria desirable for the Green scenario, that's favorable to a likening<br>
of that criterion to FBC. Sure, the differences are great too..<br>
<br>
Of course you have a point about the desirability of sacrificing one's<br>
favorite in order to save the winner under sincere voting.<br>
<br>
It could be argued that the thing being measured for is the _possibiity_ of<br>
easily (without reversal) preserving the sincere winner, whether or not<br>
it's always desirable, and that that's a matter of interest, just because<br>
it _could_ be desirable.<br>
<br>
Mike<br></div>
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