Abstract
This paper considers the notion of cycle avoiding trajectories in majority voting tournaments and shows that they underlie and guide several apparently disparate voting processes. The set of alternatives that are maximal with respect to such trajectories constitutes a new solution set of considerable significance. It may be dubbed the Banks set, in recognition of the important paper by Banks (1985) that first made use of this set. The purpose of this paper is to informally demonstrate that the Banks set is a solution set of broad relevance for understanding group decision making in both cooperative and non-cooperative settings and under both sincere and sophisticated voting. In addition, we show how sincere and sophisticated voting processes can be viewed as mirror images of one another — embodying respectively, “dmemory” and “foresight.” We also show how to develop the idea of a “sophisticated agenda,” one in which the choice of what alternatives to propose is itself a matter of strategic calculation.
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This research was supported by NSF Political Science Program Grant SES 85-09680 (to Miller) and NSF Decision and Management Sciences SES 85-06376 (to Grofman). Earlier versions of this paper were given at the 1986 Annual Meeting at the Public Choice Society and the Weingart Conference on Formal Models of Voting, California Institute of Technology, Pasadena, California, 22–23 March 1985. In particular, we thank participants at both meetings for helpful comments. Thomas Schwartz called our attention to the relationship between our work and that of Riker's work in heresthetics; and we had several useful discussions with Jeffrey Banks, to whom we also owe a more general intellectual debt. Final manuscript typing was done by the staff in the Word Processing Center, UCI. We are indebted to Dorothy Gormick for bibliographic assistance.
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Miller, N.R., Grofman, B. & Feld, S.L. Cycle avoiding trajectories, strategic agendas, and the duality of memory and foresight: An informal exposition. Public Choice 64, 265–277 (1990). https://doi.org/10.1007/BF00124371
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DOI: https://doi.org/10.1007/BF00124371