Independence of Irrelevant Alternatives and Revealed Group Preferences

It is shown that a Pareto optimal and continuous single-valued choice function defined on the compact convex subsets of the positive orthant of the n-dimensional Euclidean space maximizes a real-valued function if and only if it satisfies the independence of irrelevant alternatives condition if n=2, and the strong axiom of revealed preference otherwise. The results can be applied to consumer demand theory to deal with nonlinear budget sets, and to bargaining game theory to generalize the Nash bargaining solution.

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