2011/2/20 Kristofer Munsterhjelm <[email protected]> > James Green-Armytage wrote: > >> >> >> Dear election methods fans, >> >> >> 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. >> >> Here?s a definition: >> 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. >> > To me, the term "burial" implies burying under something. So, I'd propose: 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.
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. > >> 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. >> > > 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. > > > 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. >> >> 4: A>B>C >> 3: B>A>C >> 2: C>A>B >> The initial winner is A, but if the B>A>C voters switch to B>C>A, the >> winner changes to B. >> > > 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. 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. 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. > > > 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: >> >> 40: A>B>C >> 41: B>A>C >> 10: C>A>B >> The initial winner is B, but if the A>B>C voters switch to A>C>B, the >> winner changes to A. >> > > 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. Interesting. > > > 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. >> > > 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 :-) > > 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. 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. JQ > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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