<div dir="ltr"><div><div><div>My version of Symmetric ICT had a problem. It might have been that it no longer avoided chicken dilemma. So I withdrew my Symmetric ICT proposal, and went back to advocating ordinary ICT.<br><br></div>Your version isn't simple, but it will be interesting to study. <br><br></div>This is just a preliminary note.<br><br></div><div>One thing that I'd like to add about 3-Slot MDDTR:<br><br></div><div>Another advantage that it has over 3-Slot ICT is that 3-Slot MDDTR has a much simpler definition:<br><br></div><div>The winner is the most favorite candidate who isn't majority-beaten.<br><br></div><div>That's a brief enough definition to be proposable, even as a first reform from Plurality. But admittedly it lacks use-precedent.<br><br></div><div>Michael Ossipoff<br><br></div><div><br></div><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Nov 10, 2016 at 4:47 PM, Forest Simmons <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</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><div><div><div><div>Here's my reformulation of Symmetric ICT:<br><br></div>Ballots are ranked preference style with equal rankings allowed, especially at top and bottom, with bottom as default.<br><br></div>Let the notation [phi(X,Y)] mean the number of ballots on which the formula phi(X,Y) is satisfied, so that, for example, [X=Y=Top] is the number of ballots on which X and Y are ranked equal Top.<br><br></div>Definition:<br>X strongly beats Y<br></div> if and only if<br></div>[X>Y] - [Y>X] > max(0, [X=Y=Top] - [X=Y=Bottom])<br><div><div><div><div><div><div><div><div class="gmail_extra"><br></div><div class="gmail_extra">Step 1. Eliminate all strongly beaten candidates unless that would eliminate all candidates.<br></div><div class="gmail_extra">Step 2. Among the candidates remaining after step 1, elect the candidate ranked Top on the greatest number of ballots.<br><br></div><div class="gmail_extra">Is that an accurate restatement of Symmetric ICT?<br><br></div><div class="gmail_extra">If it is I would like to make one suggestion to make it even more symmetrical, namely ...<br><br></div><div class="gmail_extra">Step 2'. Among the candidates remaining after step 1, elect the candidate X with the greatest value of [X=Top] - [X=Bottom].<br><br></div><div class="gmail_extra">I don't think it will worsen the Later-no-help failure.<br><br></div><div class="gmail_extra">Of course, then we would have to change the name to something like<br><br></div><div class="gmail_extra">IC(TmB), Improved Condorcet (Top minus Bottom).<br><br></div><div class="gmail_extra">Does this comply with CD?<br><br></div><div class="gmail_extra">45 C<br></div><div class="gmail_extra">30 A>B<br></div><div class="gmail_extra">25 B>A<br><br></div><div class="gmail_extra">Candidate A is elected as the only unbeaten candidate.<br><br></div><div class="gmail_extra">If the B>A faction defects by truncating A ...<br></div><div class="gmail_extra"><br><div class="gmail_extra">45 C<br></div><div class="gmail_extra">30 A>B<br></div>25 B<br><br></div><div class="gmail_extra">then no candidate is unbeaten. The respective Top minus Bottom scores for the respective candidates A, B, and C, are<br><br>30 - 70 = -40<br></div><div class="gmail_extra">25 - 45 = -20, and<br>45 - 55 = -10, <br><br></div><div class="gmail_extra">so C is elected.<br><br></div><div class="gmail_extra">However, if we reduce C's faction slightly and increase B's faction, we can produce a CD failure:<br><br></div><div class="gmail_extra">41 C<br></div><div class="gmail_extra">30 A>B<br></div><div class="gmail_extra">29 B<br><br></div><div class="gmail_extra">The Top - Bottom scores are<br>30 - 70 = -40<br>29 - 41 = -12<br>41 - 59 = -18,<br></div><div class="gmail_extra">so the B faction benefits from its defection.<br><br></div><div class="gmail_extra">So the ICT version appears to be better even though it is not quite as symmetrical in its definition as IC(T-B).<br><br></div><br><div class="gmail_extra"><br></div></div></div></div></div></div></div></div></div>
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