On Oct 8, 2008, at 2:28 AM, Markus Schulze wrote:
Dear Jonathan Lundell,
I wrote (7 Oct 2008):
Well, the second paper is more general. Here they use
Arrow's Theorem to argue why monotonicity has to be
sacrificed.
You wrote (7 Oct 2008):
Or at least that something has to be sacrificed. Do
you see that as a problem?
Well, monotonicity is actually not needed in Arrow's
Theorem. Therefore, Arrow's Theorem is frequently
stated as saying that no single-winner election
method can satisfy (1) universal admissibility,
(2) Pareto, (3) nondictatorship, and (4) independence
from irrelevant alternatives.
Therefore, using Arrow's Theorem to argue that
monotonicity should be sacrificed to get
compatibility with the other criteria seems
to be odd.
Markus Schulze
If I were writing the argument, I think I'd focus on manipulation
instead of Arrow per se, non-monotonicity being a manipulability
concern.
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