477. A Unifying Impossibility Theorem for Compact Metricsocial Alternatives Space

Priscilla Man and Shino Takayama, School of Economics Discussion Paper No. 477 May 2013, School of Economics, The University of Queensland. Australia.

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Abstract

In Man and Takayama (2013) (henceforth MT) we show that many classical impossibility theorems follow from three simple and intuitive axioms on the social choice correspondence when the set of social alternatives is finite. This note extends the main theorem (Theorem 1) in MT to the case where the set of social alternatives is a compact metric space. We also qualify how versions of Arrow's Impossibility Theorem and the Muller-Satterthwaite Theorem (Muller and Satterthwaite, 1977) can be obtained as corollaries of the extended main theorem. A generalized statement of the Muller-Satterthwaite Theorem for social choice correspondences with weak preferences on a compact metric social alternatives domain under a modified definition of Monotonicity is given. To the best of our knowledge, this is the first paper to document this version of the Muller-Satterthwaite Theorem. This note is mainly technical. Readers interested in the motivations and discussions of our axioms and main theorem should consult MT.