[EM] Re: [Fwd: Election-methods digest, Vol 1 #520 - 13 msgs]

[Markus Schulze]

Hallo,

my favorite formulation of Arrow's Theorem is Pattanaik and Peleg's
formulation (Prasanta K. Pattanaik, Bezalel Peleg, "Distribution of
Power Under Stochastic Social Choice Rules," Econometrica, vol. 54,
p. 909-921, 1986). In their formulation, this theorem says that
there is no rank method that is non-dictatorial and satisfies Pareto
and regularity. "Regularity" says that adding candidate Z should
not increase the probability that candidate A (with A <> Z) is
elected.

Ken Johnson wrote (29 Feb 2004):
> I wish someone would put this issue to rest once and for all: Is CR
> (or Approval) an "ideal" voting method according to Arrow's criteria
> or is it not? If it is, then the "Arrow proved ..." assertion is
> patently false and should be recognized as such. Although Arrow
> limited his analysis to ranked preference methods, it certainly
> makes sense to ask the question in the broader context of CR and
> Approval, and I'd like to see some clarification on this issue.

There are many possible interpretations of Arrow's Theorem. A possible
interpretation is: Arrow restricts his considerations to paretian
non-dictatorial rank methods because he considers other election
methods to be quite unacceptable. The fact that Arrow's favorite
election method (the so-called "Arrow-Raynaud method"; Kenneth
Joseph Arrow, Herve Raynaud, "Social Choice and Multicriterion
Decision-Making", MIT Press, 1986) is a paretian non-dictatorial
rank method supports this interpretation.

Markus Schulze