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<pre>Chris Benham wrote:<br><br>It isn't possible for a method to both meet Mono-add-Top and fail <br>Mono-add-Plump. <br><br>[endquote]<br><br><br>I hope that I didn't say that ABucklin fails Mono-Add-Plump. If I did, it was an error<br>and I retract the statement. In the subject-line, I said that ABucklin passes <br>Mono-Add-Plump.<br><br>So yes, that was a typo. I meant what I said in the subject-line: ABucklin doesn't meet<br>Mono-Add-Top, but it meets Mono-Add-Plump.<br><br>You (Chris) said:<br><br>(Just before posting this I've noticed that your quoted text isn't <br>consistent with your <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-November/029017.html#" id="_GPLITA_2" title="Powered by Text-Enhance">Subject</a> line)<br><br>[endquote]<br><br>Yes, there was a typo in my message, regarding that.<br><br>I'd said:<br><br>><i> MDDTR and Mono-Add-Plump:<br></i>><i><br></i>><i> Say the method is MDDTR, and your favorite candidate is F. F doesn't <br></i>><i> have a <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-November/029017.html#" id="_GPLITA_0" title="Powered by Text-Enhance">winning</a> approval (top + middle) score,<br></i>><i> because x has significantly more approvals. But x is disqualified by <br></i>><i> having a (bare) majority voting y over hir.<br></i>><i> With x disqualified, F wins with the most approvals of any <br></i>><i> undisqualified candidate. F isn't close to having a top-rating<br></i>><i> majority.<br></i>><i><br></i>><i> Then you and a few other people show up, and plump for F. (You top <br></i>><i> rate F, and don't rate anyone else).<br></i>><i><br></i>><i> Now your presence in the election increases the requirement for a <br></i>><i> majority, with the result that x<br></i>><i> no longer has a majority ranking y over hir.<br></i>><i><br></i>><i> Now, x wins instead of F, because x has significantly more approvals <br></i>><i> (F was behind x in approvals by more than<br></i>><i> the number of newly-arrived voters.<br></i>><i><br></i>><i> By plumping for F, you and the other newly-arrived voters have made F <br></i>><i> lose.<br></i><br>You wrote:<br><br>Mike, I'd like to see an example election of what you are talking about. <br>If this way of MDD,TR failing Mono-add-Plump<br>is possible it isn't the one I know about. <br><br>[endquote]<br><br>I admit, not assert, that MDDTR fails Mono-Add-Plump. We agree that it does.<br><br>But I'll post and example of that particular kind of Mono-Add-Plump failure within<br>the next few days.<br><br>You continued:<br><br>(Also it looks like you have <br>some other method in mind<br><br>[endquote]<br><br>How so? As I said, I'm referring to MDDTR.<br><br>Here's my definition of MDDTR:<br><br>3-slot method: top, middle, and bottom (unrated)<br><br>Disqualify every candidate who has another candidate voted over hir by a majority.<br><br>The winner is the undisqualified candidate with the most top ratings.<br><br>[end of MDDTR definition]<br><br>That is the method that I was referring to when I said "MDDTR".<br><br>You wrote:<br><br>25: A>B<br>26: B>C<br>23: C>A<br>04: F<br><br>(78 ballots) B>C 51-27, C>A 53-25, A>B 48-26 <br><br>TR scores: C27, B26, A25. Approval scores: C53, B51, A48.<br><br>All candidates have a majority-strength pairwise defeat, so no candidate <br>is disqualified. MDD,TR and MDD,A and<br>MDD,ABucklin (as you call it) all elect C.<br><br>Now say we add 22 ballots which plump for C.<br><br>25: A>B<br>26: B>C<br>23: C>A<br>26: C<br><br>(100 ballots) B>C 51-49, C>A 75-25, A>B 48-26<br><br>TR scores: C49, B26, A25. Approval scores: C75, B51, A48.<br><br>Now there is one candidate (B) without a majority-strength pairwise <br>defeat, so all except B are disqualified and B wins.<br><br>[endquote]<br><br>Thank you for that example showing the MDDTR Mono-Add-Plump scenario that I described. No, your<br>example is not different from my scenario. It's a numerical example of my scenario. The plump-ballots <br>took away B's majority defeat, allowing B to win. The only difference was that, my scenario, B beat C by<br>higher Approval score, whereas, in your example, B wins by being the only undisqualified candidate. Unimportant<br>difference. In both stories, the plump-ballots take away B's majority defeat by raising the requirement for<br>a majority.<br><br>You wrote:<br><br>BTW, unrelated to the Mono-add-Plump issue, C in both elections is <br>uncovered and positionally dominant so I think<br>a method needs a much better excuse for not electing C in both cases <br>than any that the MDD methods can offer.<br><br>[endquote]<br><br>Cetainly, if uncoveredness and positional dominance can be shown to have great practical<br>importance, as opposed to aesthetic appeal.<br><br>Any method will fail many aesthetic criteria. We choose a method based on what we want or need from it. We need<br>compliance with criteria that are of practical importance.<br><br>I'd said:<br><br>><i> So you storm into the Department of Elections office, to complain <br></i>><i> about that.<br></i>><i><br></i>><i> The person at the counter says, "Excuse me, but do you think that the <br></i>><i> election was a Plurality election?"<br></i>><i><br></i>><i> You see, in Plurality, 1st choice votes are what decide the election. <br></i>><i> Rank methods look at more than that. They<br></i>><i> look at your other preferences too. Maybe it's tempting to want 1st <br></i>><i> choice ratings to decide the election in rank methods<br></i>><i> too. But they're rank methods, and rank methods needn't <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-November/029017.html#" id="_GPLITA_3" title="Powered by Text-Enhance">act</a> like <br></i>><i> Plurality.<br></i><br>You wrote:<br><br>This explanation might be acceptable if we were just talking about a <br>failure of Mono-add-Top where the complainers provided<br>some extra information that the voting-method algorithm might have <br>reasonably construed as strengthening not just their favourite<br>but also the <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-November/029017.html#" id="_GPLITA_1" title="Powered by Text-Enhance">winner</a><br><br>[endquote]<br><br>They did. Their ballots proclaimed "I am indifferent between everyone but my favorite!"<br><br>Either they were indifferent, or they just were too lazy to vote otherwise. In either case, they<br>have only themselves to blame. Their indifference regarding everyone but their favorite meant that<br>someone who previously had a majority defeat no longer has a majority defeat.<br><br>The fallacy of Mono-Add-Plump is that a plump-ballot says nothing other than who the voter's favorite is.<br><br>You wrote:<br><br>, or even just extra information that might have <br>caused the algorithm to be (perhaps) forgivably "confused."<br><br>[endquote]<br><br>The algorithm wasn't confused, forgivably or otherwise. It looked for majority defeats, and<br>didn't find one for the candidate who beat your favorite. It had a good reason for looking<br>for majority defeats--doing so allows it to meet CD, LNHa, and SFC.<br><br><br>I'd said:<br><br>><i> Yes, it's aesthetically nice if the win is monotonically related to <br></i>><i> addition of 1st choice ballots, but there is no reason why it should<br></i>><i> or must be. Rank methods aren't Plurality.<br></i><br>You wrote:<br><br>Here again it sounds more like you are talking about Mono-add-Top <br>instead of Mono-add-Plump.<br><br>[endquote]<br><br>I was talking about what I said I was talking about: MDDTR, as I define it,<br>and Mono-Add-Plump.<br><br>A plump-ballot contains information other than only the voter's favorite. It expresses<br>indifference among the other candidates. That indifference can obviously make the difference<br>regarding whether or not some particular candidate has a majority defeat.<br><br>We're used to Plurality. There's therefore a tendency to judge methods' results in terms of Plurality, and to <br>interpret ballots in terms of Plurality.<br><br>Mike Ossipoff<br><br><br><br><br></pre> </div></body>
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