RUI:Equity-Efficiency Trade-Offs

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A social welfare function is a formula for aggregating conflicting individual preferences into a social preference scheme to be used for collective decision making. The formula should satisfy basic demographic values or axioms. K.J.Arrow received the Noble prize in part for his proof of the Impossibility Theorem, i.e., that it is impossible to construct a social welfare function consistent with basic assumptions of equity and economics. The Impossibility Theorem has survived many attempts to restore consistency by weakening these axioms. Unlike other treatments of the Impossibility Theorem which simply seek to extend standard theorems in welfare economics, the investigator has developed methods for exploiting the algebraic and topological structure of the standard allocation models to obtain very general insights into public choice. For example, the investigator proved recently that the social welfare function is either completely unresponsive to individual preference or there is some individual who is denied any share in the economy's private goods at every turn. The project continues to investigate social choice in economic environments under weaker transitivity assumptions, in models with public and private goods, under less demanding and more realistic preference revelation desiderata, and in intergenerational social choice models. The contribution of this project comes from developing a new way of looking at the question of providing an axiomatic foundation for public decision making. The investigator has already succeeded in proving new theorems about the trade-offs between equity and efficiency in the types of economic settings found in real-world public policy problems. Further development of this promising approach is warranted because the new methods will provide useful tools for analyzing collective choice and substantial new insights into many economic problems.