Independence of Irrelevant Alternatives and Revealed Group Preferences
证明，在二维欧氏空间正象限的紧凸子集上，帕累托最优且连续的单值选择函数最大化某个实值函数当且仅当满足无关选择独立性条件；在更高维时则需满足显示偏好强公理。结果可应用于非线性预算集的消费者需求理论和推广纳什谈判解。
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.