Arrow and Gibbard-Satterthwaite

Markus Schulze schulze at
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

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

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