Topology and Social Choice

In this chapter we apply earlier results to the study of social choice and modelling elections. In Chap. 3 we showed the Nakamura Theorem. that a social choice could be guaranteed as long as the dimension of the space did not exceed k(σ)=2. We now consider what can happen in dimension above k(σ)=1. We then go on to consider “probabilistic” social choice, where there is some uncertainty over voters’ preferences, by constructing an empirical model of the 2008 U.S. presidential election.

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