Abstract

This chapter discusses the effects of four different revisions of the domain for a collective choice rule. In the first revision, the set N of individuals is no longer constrained to be finite. This revision permits construction of collective choice rules that satisfy all Arrow's conditions. However, an impossibility result by Kirman and Sondermann can be shown to hold for the infinite N case. The second revision considers populations of different sizes. Each profile has only finitely many orderings but not all profiles have the same number of orderings. The third revision has collective choice operating on cardinal utilities rather than preference preorderings.

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