[EM] Why care about later-no-harm or prohibiting candidate burial?

[Kristofer Munsterhjelm]

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.