Markus Schulze wrote:
Hallo,
Eric Maskin, a Nobel laureate, is currently very
active in promoting the Black method. The Black
method says: If there is a Condorcet winner, then
the Condorcet winner should win; if there is no
Condorcet winner, then the Borda winner should win.
(...)
Maskin's argumentation doesn't work because
of the following reason: Whether an election
method is good or bad depends on which criteria
it satisfies. Most criteria say how the result
should change when the profile changes. Now it
can happen that the original profile and the
new profile are in different domains. This
means that, to satisfy some criterion, election
method X for domain X and election method Y for
domain Y must not be chosen independent from
each other.
I find it strange for a Nobel laureate (and within mechanism design at
that!) to not notice this. I've mentioned my concept of "discontinuity"
before, and it seems quite obvious that if you stitch together two
methods, you can't just look at how one method behaves and how the other
does, but also the boundary between the two. To my knowledge the
Participation and LNH incompatibility proofs against Condorcet work this
way: they show that no matter how you smooth the transition between the
Condorcet domain and the non-Condorcet domain, there will be sudden
transitions ("discontinuities") and you can't line them all up at the
same time.
Moreover, I agree with you that Borda doesn't seem to be very good.
Well, it works when there's no strategy (and it gets respectable regret
in such cases), but strategy is very obvious and can backfire horribly
(as by Warren's NEC example where the mediocre candidates win because of
massive burial).
The burial strategy may be obvious enough that voters would engage in it
even if they thought there would be a CW. They would think that "perhaps
there won't be a CW and in that case I should maximize the effect of my
vote", similar to how FPC could encourage compromising in a
Nader/Bush/Gore scenario.
Finally, if one accepts that the Condorcet criterion makes sense, and to
comply with it is best when there is a CW, why not expand? Why not limit
oneself to the Smith set, or to uncovered candidates? The decision to be
Condorcet compliant but to go no further in the Condorcet direction
seems rather arbitrary.
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