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The Sum of the Parts Can Violate the Whole

Published online by Cambridge University Press:  13 April 2005

Donald G. Saari
Donald G. Saari
Affiliation:
Donald G. Saari is Professor of Economics and Mathematics, University of California, Irvine, CA 92697-5100 ([email protected]). Katri K. Sieberg is Assistant Professor of Economics, College of William and Mary, Williamsburg, VA 23187-8795 ([email protected]),,
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Abstract

We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives and to offer new interpretations for pairwise voting. The source of the problems—an unanticipated loss of available information—also explains a variety of other phenomena, such as Simpson’s paradox (a statistical paradox in which the behavior of the “parts” disagrees with that of the “whole”) and Arrow’s theorem from social choice.

Type
Research Article
Information
American Political Science Review , Volume 95 , Issue 2 , June 2001 , pp. 415 - 433
Copyright
2001 by the American Political Science Association

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