[EM] Eric Maskin promotes the Black method

[Markus Schulze]

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".

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That method, that uses election method X in
domain X and election method Y in domain Y,
will be called "election method Z".

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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.

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I also question the claim that the Borda
method is the best possible election method
in situations without a Condorcet winner.

Markus Schulze