<br><br><div class="gmail_quote">2011/2/20 Kristofer Munsterhjelm <span dir="ltr"><<a href="mailto:km-elmet@broadpark.no">km-elmet@broadpark.no</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div class="im">James Green-Armytage wrote:<br>
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Dear election methods fans,<br>
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After reading the last few messages on this topic, my feeling is that immunity to burying should be its own criterion. I?m not quite sure what the relationship is to later-no-help and later-no-harm, but it doesn?t seem like it?s quite equivalent to either of them.<br>
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Here?s a definition:<br>
If w is winner when votes are sincere, and voters who prefer q to w change their ballots only by giving w an inferior rating or ranking, then w must still be the winner.<br></blockquote></div></blockquote><div><br></div>
<div>To me, the term "burial" implies burying under something. So, I'd propose:</div><div><meta http-equiv="content-type" content="text/html; charset=utf-8">If w is winner when votes are sincere, and voters who prefer q to w change their ballots only by giving w an inferior ranking, or by improving the rating of x, then the winner cannot change fro w to q.</div>
<div><br></div><div>Why is this better than the first definition, why bring x into it? There is nothing a priori wrong with reducing w's rating leading to w not winning. The problem is when you start using third parties to game the system - because of the inherent risk of misfired strategy leading to unqualified x winning.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div class="im"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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The methods that I know of that pass this are things like plurality, runoff, and IRV. They pass it because q needs to be eliminated before any later preferences matter.<br>
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Those methods pass both LNHelp and LNHarm. Do you think those criteria, in combination, imply immunity to burial? I'm pretty sure they do, but I'll think about it a bit more.<div class="im"><br>
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Bucklin definitely fails this criterion. Here?s a simple example, which I think applies to most Bucklin variants as well, though you can correct me if I?m wrong about this.<br>
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4: A>B>C<br>
3: B>A>C<br>
2: C>A>B<br>
The initial winner is A, but if the B>A>C voters switch to B>C>A, the winner changes to B.<br>
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Bucklin advocates might say that you could just vote B > (empty) > A > C, or for that matter, truncate. But if we limit ourselves to ordinary rank ballots (i.e. no empties), and ties are broken by excess (how much above majority each candidate is), then that example shows burial works.</blockquote>
<div><br></div><div>First off, I don't call myself a Bucklin advocate, for precisely this reason; the limited version of Bucklin you propose is silly. That's why I say MCA - aside from being more descriptive, the Majority Choice Approval name clearly does not refer to your limited Bucklin.</div>
<div><br></div><div>Second, both of those arguments are true, and are what I think voters would do in reality. But under my criterion definition, they're irrelevant - nonblack noncrows. The relevant move would be for B>A>C voters to move to B>A=C, which does not change the winner. (Or, if you add an empty second rank to all ballots, such that the original vote is B>...>A>C, the same can be said of B>C>A>...). So that's why I'd argue that MCA does pass (my definition of) burial immunity, or at least that I think it does and no counterexample has been given.</div>
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Descending solid coalitions (DSC) fails this criterion as well, assuming that I understand the method correctly. I wasn?t familiar with it, so I looked it up on electowiki (thank you for posting the definition there!), and eventually resorted to writing a computer program to generate burying vulnerability examples. Here?s a modified version of the first example it came up with:<br>
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40: A>B>C<br>
41: B>A>C<br>
10: C>A>B<br>
The initial winner is B, but if the A>B>C voters switch to A>C>B, the winner changes to A.<br>
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That's interesting, because DAC and DSC are equal when there's no partial or equal rank. Therefore, your example works both for DAC (which passes LNHelp) and DSC (which passes LNHarm), showing that either by itself isn't enough. That's kind of what you're saying, but this makes it very clear.</blockquote>
<div><br></div><div>Interesting. </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div class="im"><br>
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By the way, immunity to compromising should be its own criterion as well. (Instead of ?giving w an inferior ranking or rating?, write ?giving q a superior ranking or rating? in the definition above.) The methods that I know of that pass this are things like anti-plurality, and Coombs... basically, the mirror images of plurality and IRV. I?ve found that these methods are highly vulnerable to burying, and more vulnerable to strategy overall than their counterparts.<br>
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Doing a Smith constraint seems to limit compromising pretty well, even though the method isn't immune. That's why I was focused on burial rather than compromising :-)<br>
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Quite some time ago, Kevin Venzke talked about criteria called "earlier-no-help" and "earlier-no-harm". If it turns out that having both LNHelp and LNHarm immunizes a method against burial, perhaps the same thing is the case for ENHelp and ENHarm with respect to compromising.</blockquote>
<div><br></div><div>I'd use a symmetrical modification of the definition for compromising immunity. I haven't worked this out at all, but initially, I don't see why MCA wouldn't meet that criterion. </div>
<div><br></div><div>JQ</div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div><div></div><div class="h5"><br>
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