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.
If you want to be generous, you could read the argument as "all methods
fail one of Arrow's criteria; monotonicity failure is a result of this,
and if a method doesn't fail monotonicity, it'll fail something else".
That's still odd, though, because you can turn the argument around and
say "well, then if you think Arrow failure makes all methods equal,
there's no disadvantage to using Condorcet, but if you think some
criteria are more important than others, then there's an advantage to
using Condorcet, therefore in any case there's no disadvantage to using
Condorcet".
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