Mathematical structure of voting paradoxes

Donald G. Saari ()
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Donald G. Saari: Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA

Economic Theory, 2000, vol. 15, issue 1, 53 pages

Abstract: A theory is developed to identify, characterize, and explain all possible positional and pairwise voting outcomes that can occur for any number of alternatives and any profile. This paper describes pairwise voting where new results include explanations for all paradoxes, cycles, conflict between Borda and Condorcet rankings, differences among procedures using pairwise votes (such as the Borda Count, Kemeny's method, and the Arrow-Raynaud rule), and discrepancies among the societal rankings as candidates are dropped or added. Other new results include new relationships among the Borda and Condorcet "winners" and "losers." The theory also shows how to construct all supporting profiles. The following companion paper does the same for positional methods.

Keywords: Positional voting; Voting paradoxes; Social choice. (search for similar items in EconPapers)
Date: 1999-11-22
Note: Received: June 22, 1998; revised version: February 14, 1999
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