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<pre>Forrest--<br><br>I'm assuming "approval bad example" is typified by the implicit approval order in the scenario<br><br>49 C<br>27 A>B<br>24 B<br><br>Yes, A majority prefer A and B to C. They're the voters to whom A is favorite and the voters to whom B is favorite.<br><br>Knowing that the more-numerous A voters will vote for B, the B voters can win by defection.<br><br>You continued:<br><br>It seems to me that IF we (1) want to respect the Plurality Criterion, (2) discourage "chicken" strategy, <br>(3) stick with determinism, and (4) not take advantage of proxy ideas, then our method must allow <br>equal-rank-top and elect C in the above scenario<br><br>[endquote]<br><br>...when A voters and B voters vote only for their favorites.<br><br>If the B voters (in 3-slot balloting) rate B above bottom, and C at bottom, shouldn't the method<br>defeat C and elect A or B?<br><br>You continued:<br><br>, but elect B when B is advanced to top equal with A [by the A voters].<br><br>Sure. But what if the A voters vote A top, B middle, and C bottom?<br><br>C should lose. Should A lose too, even though they're more numerous, and even though A pairbeats B,<br>just because the A voters were the ones who were co-operative and responsible enough to <br>rate B above bottom, to defeat C?<br><br>You wrote:<br><br>in <br>the middle faction:<br><br>[endquote]<br><br>But it isn't a matter of one faction in the middle. The A-preferring voters and the B-preferring voters<br>all prefer A and B to C. The A and B voters share one end, rather than either being in the middle.<br><br><br><br><br>You continued:<br><br>49 C<br>27 A=B<br>24 B<br><br>Then if sincere preferences are<br><br>49 C<br>27 A>B<br>24 B>A,<br><br>the B faction will be deterred from truncating A.<br><br>[endquote]<br><br>Is that attainable in a method meeting FBC and Participation?<br><br>...or in a method meeting those plus 1CM and 3P?<br><br>You continued:<br><br> While if the B supporters are sincerely indifferent <br>between A and C<br><br>[endquote]<br><br>Ok, but, to me, an essential element of the example is that the A supporters and the B supporters<br>all prefer A and B to C.<br><br>You continued:<br><br>, the A supporters can vote approval style (A=B) to get B elected.<br><br>Do we <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-November/028988.html#" id="_GPLITA_0" title="Powerd by Text-Enhance">agree</a> on this?<br><br>[endquote]<br><br>Wait a minute...If the A supporters were indifferent between B and C, then they'd have<br>no motive to suppport B against C, unless it would elect A. In some methods their A>B>C<br>ballot would achieve that. MDD,TR is such a method.<br><br>You continued:<br><br>Note that IRV (=whole) satisfies this, but now the question remains ... is there a method that satisfies <br>this which also satisfies the FBC?<br><br>Chris mentioned something that should have been obvious to me: MDD,TR passes in the Approval<br>bad example.<br><br>Here's the definition of MDD,TR:<br><br>3-slot method: Top, Middle, Bottom (unmarked)<br><br>Disqualify any candidate(s) having a majority pairwise defeat.<br><br>The winner is the un-disqualified candidate with the most top ratings.<br><br>[end of MDD,TR definition]<br><br>MDD,TR avoids electing B in the Approval bad example (ABE). In fact, it elects A, which<br>seems the fairest outcome, allowing the A voters to defeat C by giving hir a majority<br>defeat via B. And by not penalizing the A voters by rewarding the B voters for defection.<br><br>Additionally (unless I'm mistaken), MDD,TR meets FBC and SFC.<br><br>Regrettably it fails 1CM and 3P.<br><br>MTA better protects a group of factions with similar policy-proposals against other groups.<br><br>MDD,TR doesn't do that as well, but it better protects that group of similar factions against eachother.<br><br>In our electoral system, there is great mutual antagonism among factions and parties with similar<br>policy proposals, and so maybe MDD,TR would be better for our elections, as compared to MTA.<br><br>Of course both of those methods fail Participation. It has been pointed out to me that Participation<br>failure, while only an "aesthetic embarrassment criterion", might be used by reform-opponents to<br>defeat MTA, MDD,TR, MDDA or MDD,ER-Bucklin(whole).<br><br>Mike Ossipoff<br><br><br></pre> </div></body>
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