Is a continuous rational social aggregation impossible on continuum spaces?
Resource
Soc Choice Welf 32:635–686
Journal
Social Choice and Welfare
Pages
635-686
Date Issued
2009
Date
2009
Author(s)
Huang, Wu-Hsiung
Abstract
This paper provides a global topological setting for the social choice theory on continuum spaces of alternatives, in contrast to the local differentiable setting of Chichilnisky. Chichilnisky proved that a rational continuous social choice must be discontinuous in her setting. Our paper revisits her theorem to trace the source of this discontinuity. We find that the discontinuity is irrelevant to social aggregation, per se. The main theorem states that there exist a number of continuous social utility maps which are anonymous and satisfy the Pareto condition. As a corollary, we show that there exist corresponding continuous social welfare functions, if singularity is not separated from regular preferences in social preference topology. This extends the possibility result of Jonnes-Zhang-Simpson on linear preferences, to the general ones. The notion of singularity of preferences, relative to the given mathematical structure of an alternative space, is carefully studied. © 2008 Springer-Verlag.
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Type
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