[EM] Eric Maskin promotes the Black method

[Peter Zbornik]

Dear all,

Why not write an open letter to him (i.e. publish the letter on this
list) and invite him to further discuss on this list?
I found Maskin's email: maskin at ias.edu in his CV, which is online.
If hybrid methods is the way to go, then the forthcoming paper in
Voting matters which Kristofer linked to seems to be better than his
Condorcet-Borda:
http://www.votingmatters.org.uk/FORTHCOMING/I29P1f.pdf

Peter

On Tue, Jun 21, 2011 at 1:56 PM, Markus Schulze
<markus.schulze at alumni.tu-berlin.de> 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.
>
> See e.g.:
>
> 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268
> 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww
>
> Maskin argues as follows:
>
>   If election method X is the best possible
>   election method in domain X and if election
>   method Y is the best possible election method
>   in domain Y and if domain X and domain Y are
>   disjoint and if domain X and domain Y together
>   cover all possible situations, then the best
>   possible election method is to use election
>   method X in domain X and election method Y in
>   domain Y.
>
> Maskin argues: "domain X" = "situations with a
> Condorcet winner"; "election method X" = "any
> Condorcet method"; "domain Y" = "situations
> without a Condorcet winner"; "election method Y"
> = "Borda method".
>
> ***********************************
>
> That method, that uses election method X in
> domain X and election method Y in domain Y,
> will be called "election method Z".
>
> ***********************************
>
> 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.
>
> Example:
>
> The participation criterion says that adding
> some ballots, that rank candidate A above
> candidate B, must not change the winner from
> candidate A to candidate B.
>
> Election method X satisfies the participation
> criterion in domain X. Reason: If candidate A
> was the winner in the original profile and if
> the original profile was in domain X, then this
> means that candidate A was the Condorcet winner
> and, therefore, that candidate A pairwise beat
> candidate B. If candidate B is the winner in
> the new profile and if the new profile is in
> domain X, then this means that candidate B
> is the Condorcet winner and, therefore, that
> candidate B pairwise beats candidate A. If
> candidate A pairwise beat candidate B in the
> original profile and if candidate B pairwise
> beats candidate A in the new profile, then
> this means that the added ballots rank
> candidate B above candidate A.
>
> Election method Y satisfies the participation
> criterion in domain Y, because the Borda method
> satisfies the participation criterion in general.
>
> However, election method Z doesn't satisfy the
> participation criterion since the Condorcet
> criterion and the participation criterion are
> incompatible.
>
> In short: Even if election method X satisfies
> criterion A in domain X and election method Y
> satisfies criterion A in domain Y, it doesn't
> mean that election method Z satisfies
> criterion A. Therefore, Maskin's argumentation
> doesn't work.
>
> ***********************************
>
> I also question the claim that the Borda
> method is the best possible election method
> in situations without a Condorcet winner.
>
> Markus Schulze
>
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