<div dir="ltr"><div class="gmail_extra">Interesting two criteria. For the first one, would the magnitude of a change be measured by the total number of half-reversals of candidate-order (the matter of which is voted over which), where a half-reversal is a move from voting X over Y, to voting nether over the other?</div>
<div class="gmail_extra"> </div><div class="gmail_extra">The 2nd one, as you said, seems closely-related to FBC. Having just now read of it, I don't now know how it differs.You say it's somewhat weaker. Then it could be useful for comparing methods that don't meet the more demanding FBC. </div>
<div class="gmail_extra"> </div><div class="gmail_extra">Do you know how MAM, Benham, Woodall, MMLV(erw)M and your sequence based on covering and approval do, by those two new criteria?</div><div class="gmail_extra"> </div>
<div class="gmail_extra">Michael Ossipoff<br><br></div><div class="gmail_quote">On Wed, May 14, 2014 at 8:11 PM, Forest Simmons <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>></span> wrote:<br>
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<div><div><div><div><div><div><div><div><div><div><div><div><div><div><div>Every reasonable method that takes ranked ballots has the following problem: not every sincere ballot set represents a strategic equilibrium.<br>
<br></div>In other words, no matter the method there is some scenario where a loser can change to winner through unilateral insincere voting.<br><br></div>For example, consider the following two sincere scenarios:<br><br>
</div>34 A>B<br></div>31 B>A<br></div>35 C<br><br></div>and <br><br></div>34 X>Y<br></div>31 Y<br></div>35 Z>Y<br><br></div>All of the methods that we currently consider reasonable (except perhaps IRV) , make A win in the ABC scenario, and make Y win in the XYZ, scenario.<br>
<br></div>Now suppose that the B supporters unilaterally truncate A in the first scenario, and the Z supporters unilaterally truncate Y in the second scenario. The resulting insincere ballot sets are<br><br>34 A>B<br>
31 B<br>35 C<br><br></div>and<br><br>34 X>Y<br>31 Y<br>35 Z .<br><br></div>By neutrality, if our method must pick corresponding winners in the two scenarios, i.e. either A and X, or B and Y, or C and Z.<br><br></div>But plurality rules out A and X, while the chicken dilemma criterion rules out B and Y. Therefore our method must pick C and Z.<br>
<br></div>That's fine for the first scenario; it means that sincere votes in that scenario could well be a strategic equilibrium. But making z the winner in the second scenario means that sincere ballots were not a strategic equilibrium position. The unilateral defection of the Z faction was rewarded by the election of Z.<br>
<br></div>The purpose of this example is to illustrate why sincere votes cannot always be a strategic equilibrium position.<br><br></div>Sometimes a faction can take advantage of this problem by making a move (away from sincere ballots) that (if not countered) would improve the outcome from their point of view. Let's call such a move an offensive move. Any move by another faction that would make an offensive move unrewarding can be called a defensive move.<br>
<br></div>Now here's the criterion:<br><br></div>A method satisfies the Economical Defense Criterion (EDC) if and only if every potential unilateral offensive move away from sincere ballots can be deterred by a smaller unilateral defensive move.<br>
<br></div>How should we measure the size of a move?<br><br></div>It should be by the total number of order changes over all changed ballots. An order reversal of the type X>Y to Y>X should count significantly more than a collapse of the type X>Y to X=Y or the reverse process from X=Y to X>Y.<br>
<br></div>Here's another criterion:<br><br></div>A method satisfies the Semi-Sincere Criterion if and only if each sincere ballot set can be modified without any order reversals into a strategic equilibrium ballot set that preserves the sincere winner.<br>
<br></div>This SSC criterion is similar to the FBC, but easier to satisfy. I think it is just as good as the FBC for practical purposes, since rational voters will always aim at strategic equilibria.<br><div><div><div><div>
<div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><br><br></div><div>Gotta Go!<span class="HOEnZb"><font color="#888888"><br><br></font></span></div><span class="HOEnZb"><font color="#888888"><div>
Forest<br></div><div><div><div><div><div><div><div><div><div><div><div><div><div class="gmail_extra">
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