<div dir="ltr"><div><div><div>I'm hopeful that some of our recent proposals including both of Benham's methods might satisfy these two criteria; I haven't any proof, but I have no counter example either.<br><br>
</div>I can show that IRV fails Economical Defense:<br><br></div>Sincere ballots:<br>34 X>Y<br>31 Y<br>35 Z>Y<br></div><div>The sincere IRV winner is Z.<br><br></div><div>Offensive Threat by the X faction to support Y which they prefer over the sincere winner Z:<br>
<br></div><div>34 Y>X<br></div><div>31 Y<br>35 Z>Y<br></div><br><div>The Z supporters have no deterrent at all, let alone an economical one.<br><br><br></div><div>Now here's an example of Benham employing an economical defense:<br>
<br><br>Same sincere scenario:<br>34 X>Y<br>31 Y<br>35 Z>Y<br><br></div><div>The Benham winner is Y.<br><br></div><div>The Z faction threatens to truncate Y, which would get Z elected under Benham:<br><br>34 X>Y<br>
31 Y<br>35 Z<br><br></div><div>But the X faction defends the sincere CW by raising Y:<br><br>34 X=Y<br>31 Y<br>35 Z<br><br></div><div>Now the threat is empty.<br><br></div><div>The threat involved truncating Y on 35 ballots. The deterrence involved raising Y on 34 ballots. The defense involved fewer (half) reversals than the threat. The defense was indeed economical.<br>
<br></div><div>Here's another example involving Enhance Majority (equal top minus equal bottom):<br><br>Sincere<br>34 A>B<br>31 B>A<br>35 C<br><br></div><div>The B faction threatens truncation of A on all 31 ballots, which if unopposed, would change the winner from A to B.<br>
<br></div><div>In turn the A faction announces that they intend to vote as in the nearest strategic equilibrium: they will truncate B on 28 ballots (all except 6).<br><br></div><div>28 A<br></div><div> 6 A>B<br></div>
<div><br></div><div>As long as two B voters refuse to truncate A, the sincere winner A will be saved. Otherwise, C wins.<br><br></div><div>Since the threat involves at least 30 truncations, and the deterrent involves only 26 truncations, the defense is economical.<br>
<br></div><div>The rationale for this defense criterion is that in general it is easier to convince 28 voters than to convince 30 voters to do a semi-sincere truncation.<br></div><div><br></div><div>Note that in these examples (except for the case of IRV) semi-sincere modifications were sufficient to reach the nearest strategic equilibrium position.<br>
<br></div><div>FBC is much stronger because it is an unconditional guarantee (regardless of strategic equilibria) that raising your favorite to equal top must change the winner to your favorite unless the winner doesn't change at all.<br>
</div><div><br></div><div>The semi-sincere criterion entails that you never have to lower your favorite below another candidate in order to reach the strategic equilibrium<br></div><div><div><div class="gmail_extra"><br><br>
<div class="gmail_quote">On Thu, May 15, 2014 at 8:12 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:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<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"><div><div class="h5">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>
</div></div><blockquote style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left:1px solid rgb(204,204,204)" class="gmail_quote"><div><div class="h5"><div dir="ltr"><div><div><div><div><div><div><div><div><div>
<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><font color="#888888"><br><br></font></span></div><span><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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