Kathy Dopp wrote:
I can't help wondering why anyone would think it beneficial to have
either later-no-harm or burial prevention in a voting method. Here is
why:
1. later-no-harm prevents finding compromise candidates, and thus is
not a desirable feature of a voting method, and
2. if a voter tries to bury a candidate, then logically it can only be
(unless the voter is acting against his own interests) because he
would rather have any other candidate more than the candidate he tries
to bury. Allowing a voter to express which candidate he would like
least is a good feature, not a bad one. All the talk about a voter
preferring in truth a candidate 2nd and then burying that candidate
below other candidates he prefers less, and thus giving those other
candidates he prefers even less a better chance, well is simply
illogical drivel.
Not necessarily. Because of the Gibbard-Satterthwaite theorem, no
(ranked, deterministic, non-dictatorial) voting method is immune to
strategy. Therefore, it may sometimes pay off to lie about one's
preferences, particularly if the opposition isn't.
For an extreme example, consider a method that gives -1 point to the
candidate ranked last on a ballot, and 0 points to every other, and
whoever has the most point wins. Then, if you're voting third party, you
would face a similar "lesser evil" problem: do you vote the most hated
mainstream party's candidate last, or the most hated party candidate, in
general, last? It would seem logical that most people who compromise in
Plurality would also bury the most hated mainstream party by moving it
to last place, since the method is at least as vulnerable to burial as
Plurality is to compromising.
Most methods aren't that extreme, but they have some vulnerability to
burial. I suppose it's more accurate to say that Plurality is special in
that it doesn't have burial incentive -- simply because it doesn't care
about what happens on any rank other than first.
So why all the talk of trying to invent voting methods that have two
very bad traits - later-no-harm and disallowing burial? I don't see
why anyone would want to spend the time trying to devise such a flawed
voting method as to prohibit finding compromise candidates that more
voters like and to prohibit a voter from ability to contribute to
preventing his least favorite choice from winning.
For me, at least, it's to try to understand what makes a method
vulnerable to burial, and thus how to make a method that would work even
when most of the electorate treats the voting method like a game rather
than a way of expressing their honest opinion, or when parties encourage
voters to vote according to a preset strategy.
I don't value the LNHs (Harm or Help) on their own, but in this case, it
seems that methods that have both LNHarm and LNHelp are immune to
burial. That's interesting from an abstract point of view, but Woodall's
impossibility proof (regarding mutual majority, LNH, and monotonicity)
seriously limits the practical application of that.
There might also be a trade-off. If you have a certain election where a
candidate wins, that election might be made up of honest ballots (in
which case it's good that the candidate wins), or of strategic ballots
(in which a metod that resists strategy should elect another candidate);
but the method can't know which is the case because all it's got are the
ballots themselves, free of any context. Looking at the structure of
election methods may let us know more about where that trade-off
actually resides, though, or in simpler terms: how strategy-resistant a
method can be and still be a good method.
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