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Integer Programming and Arrovian Social Welfare Functions

Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Department of Decision Sciences, National University of Singapore, Singapore 119260
Department of Managerial Economics and Decision Sciences, Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208
jay{at}ace.ieor.columbia.edu
bizteocp{at}nus.edu.sg
r-vohra{at}kellogg.northwestern.edu

We characterize the class of Arrovian Social Welfare Functions (ASWFs) as integer solutions to a collection of linear inequalities. Many of the classical possibility, impossibility, and characterization results can be derived in a simple and unified way from this integer program. Among the new results we derive is a characterization of preference domains that admit a nondictatorial, neutral ASWF. We also give a polyhedral characterization of all ASWFs on single-peaked domains.

Key Words: Social welfare function; impossibility theorem; single-peaked domain; linear programming
History: Received: November 10, 2001; revision received: November 6, 2002;