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<pre><br>Hi Forest--<br><br>Thanks for answering my question about MTA vs MCA. Your argument on that question is convincing, and<br>answers my question about the strategy difference between those two methods.<br><br>Certainly, electing C in the ABE avoids the ABE problem. I'd been hoping that the election of C can be attained<br>without diverging from Plurality's results enough to upset some people, as MMPO and MDDTR seem to<br>do.<br><br>So the method that you describe might avoid the public relations (non)problems of methods that elect<br>A.<br><br>I have a few questions about the method that you describe:<br><br>1. What name do you give to it? In this post I'll call it "Range till cover-winner" or RCW<br><br><br>2. The covering relation doesn't look at pairwise ties?<br><br>3. Does the ballot ask the voter for cardinal ratings of the candidates, or is the range score<br>calculated a la Borda? <br><br>4. How does it do by FBC? And by the criteria that bother some people here about MMPO (Kevin's<br>MMPO bad-example) and MDDTR (Mono-Add-Plump)? <br><br>There's much hope that, by electing C instead of A, RCW can avoid those criticisms.<br><br>I'm also interested in how it does by 1CM and 3P, but I'll look at that, instead<br>of asking you to do everything for me, especially since I'm the one promoting those<br>two criteria.<br><br>Mike<br><br><br><br><br>Here’s my current favorite deterministic proposal: Ballots are Range Style, say three slot for simplicity.<br><br>When the ballots are collected, the pairwise win/loss/tie relations are<br>determined among the candidates.<br><br>The covering relations are also determined. Candidate X covers candidate Y if X<br>beats Y as well as every candidate that Y beats. In other words row X of the<br>win/loss/tie matrix dominates row Y.<br><br>Then starting with the candidates with the lowest Range scores, they are<br>disqualified one by one until one of the remaining candidates X covers any other<br>candidates that might remain. Elect X.<br><br>For practical purposes this method is the same as Smith//Range. Where they<br>differ, the member of Smith with the highest range score is covered by some<br>other Smith member with a range score not far behind.<br><br>This method resolves the ABE (approval bad example) in the following way:<br>Suppose that the ballots are<br><br>49 C<br>27 A(top)>B(middle)<br>24 B<br><br>No candidate covers any other candidate. The range order is C>B>A. Both A and<br>B are removed before reaching candidate C, which is not covered by any<br>remaining candidate. So the Smith//Range candidate C wins.<br><br>If the ballots are sincere, then nobody can say that the Range winner was a<br>horrible choice. But more to the point, if the ballots are sincere, the A<br>supporters have a way of rescuing B: just rate hir equal top with A.<br><br>Suppose, on the other hand that the B supporters like A better than C and the A supporters know this. Then the threat of C being elected will deter B faction defection, and they will rationally vote A in the middle:<br><br>49 C<br>27 A(top)>B(middle)<br>24 B(top)>A(middle)<br><br>Now A covers both other candidates, so no matter the Range score order A wins.<br><br>This completely resolves the ABE to my satisfaction.<br><br>The method also allows for easy defense against burial of the CW.<br><br>In the case<br><br>40 A>B (sincere A>C>B)<br>30 B>C<br>30 C>A<br><br>where C is the sincere CW, the C supporters can defend C's win by truncating A. Then the Nash equilibrium is<br><br>40 A<br>30 B>C<br>30 C<br><br>in which C is the ballot CW, and so is elected.<br><br><br>Now for another topic...<br><br><br>MTA vs. MCA<br><br>I like MTA better than MCA because in the case where they differ (two or more<br>candidates with majorities of top preferences) the MCA decision is made only by<br>the voters whose ballots already had the effect of getting the ”finalists” into<br>the final round, while the MTA decision reaches for broader <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-November/029061.html#" id="_GPLITA_1" title="Powered by Text-Enhance">support</a>.<br>Because of this, in MTA there is less incentive to top rate a lesser evil. If<br>you don’t believe the fake polls about how hot the lesser evil is, you can take<br>a wait and see attitude by voting her in the middle slot. If it turns out that<br>she did end up as a finalist (against the greater evil) then your ballot will<br>give her full support in the final round.<br></pre> </div></body>
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