Arrow and Gibbard-Satterthwaite
Markus Schulze
schulze at sol.physik.tu-berlin.de
Fri Sep 19 05:26:57 PDT 1997
Dear David,
the usual definition of Pareto looks like that:
A method meets Pareto if & only if:
Option B must not be chosen, if there is an option A,
such that every voter prefers A to B.
Your definition of Pareto ("An Option A can be eliminated,
only if there is an option B remaining, such that a simple
majority of the voters prefers B to A.") is identical to
Hallett's version of the "Smith Criterion":
Suppose, the "Smith set" is the smallest set of options
such that every option of this set beats every option
outside this set in a pairwise comparison. Then the
winning option is chosen from the options of the Smith
set.
Use my definition of Pareto and you will understand my
last e-mail.
[By the way, I didn't say, that Pareto is
unachievable. For example: Smith//Condorcet[EM] without
the subcycle rule meets Pareto.]
Markus Schulze (schulze at sol.physik.tu-berlin.de)
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