Jonathan Lundell wrote:
On Feb 21, 2011, at 4:06 PM, Kristofer Munsterhjelm wrote:
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.
On a related note, one of the problems with burial-prone methods is
that burial is a simple, intuitive and attractive strategy that can
be easily employed by relatively naive voters. It's a perverse
incentive precisely because of KM's point above: the method is faced
with an unknown mix of sincere and strategic ballots. GIGO.
By contrast, non-monotonicity is relatively benign (in this sense),
in that it's very hard for a voter to come up with a practical voting
strategy to take advantage of it. Among other things, voters don't
have enough information about the detailed preferences (and
strategies) of the other voters to successfully strategize
themselves; there's little to be gained by voting other than
sincerely.
I'd say they are different sorts of properties. Burial resistance is
something that makes it less tempting to try a certain strategy,
(preferably) because it won't work, because it won't work any better
than less distorting strategies, or (less preferably) because it will
almost always backfire. There may be other strategy resistance
properties, like compromising resistance or the favorite betrayal criterion.
Monotonicity, however, is a property whose failure implies that the
method is confused about itself and that there's something suspect about
its value system. Raising a candidate shouldn't make him lose, because
all other things equal, if a candidate gets a a higher rank, that should
be evidence he's doing better. To put it another way, if you have a pair
of ballot sets, the latter of which raises a candidate in the former,
and the method decides to award that candidate the win in the first case
but not in the second, that seems like implying the method is wrong
about one of the two ballot sets. Either the candidate should not have
won in the first case, or he should also have won in the second.
I would put criteria like Plurality and reversal symmetry in this
category, too -- or Pareto, for that matter.
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