Social Choice Theory

In this paper, we consider relationships between the collective preference and the non-cooperative game-theoretic approaches to positive political theory. In particular, we show that an apparently decisive difference between the two approaches - that in sufficiently complex environments (e.g. high dimensional choice spaces) direct preference aggregation models are incapable of generating any prediction at all, whereas non-cooperative game-theoretic models almost always generate predictions - is indeed only an apparent difference. More generally, we argue that there is a fundamental tension when modeling collective decisions between insuring existence of well-defined predictions, a criterion of minimal democracy and general applicability to complex environments: while any two of the three are compatible under either approach, neither collective preference nor non-cooperative game theory can support models that simultaneously satisfy all three desiderata.