[EM] Eric Maskin promotes the Black method

[Kristofer Munsterhjelm]

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.