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Choosing subsets: a size-independent probabilistic model and the quest for a social welfare ordering

Author

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  • Bernard Grofman

    (Department of Politics and Society, University of California at Irvine, Irvine, CA 92697-5100, USA)

  • Michel Regenwetter

    (Decision Sciences Department, The Fugua School of Business, Duke University, Durham, NC 27708-0120, USA)

Abstract

"Subset voting" denotes a choice situation where one fixed set of choice alternatives (candidates, products) is offered to a group of decision makers, each of whom is requested to pick a subset containing any number of alternatives. In the context of subset voting we merge three choice paradigms, "approval voting" from political science, the "weak utility model" from mathematical psychology, and "social welfare orderings" from social choice theory. We use a probabilistic choice model proposed by Falmagne and Regenwetter (1996) built upon the notion that each voter has a personal ranking of the alternatives and chooses a subset at the top of the ranking. Using an extension of Sen's (1966) theorem about value restriction, we provide necessary and sufficient conditions for this empirically testable choice model to yield a social welfare ordering. Furthermore, we develop a method to compute Borda scores and Condorcet winners from subset choice probabilities. The technique is illustrated on an election of the Mathematical Association of America (Brams, 1988).

Suggested Citation

  • Bernard Grofman & Michel Regenwetter, 1998. "Choosing subsets: a size-independent probabilistic model and the quest for a social welfare ordering," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 423-443.
    • Handle: RePEc:spr:sochwe:v:15:y:1998:i:3:p:423-443
    Note: Received: 18 August 1995 / Accepted: 13 February 1997
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    Citations

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    Cited by:

    1. Regenwetter, Michel & Grofman, Bernard & Marley, A. A. J., 2002. "On the model dependence of majority preference relations reconstructed from ballot or survey data," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 451-466, July.
    2. Mostapha Diss & Eric Kamwa, 2020. "Simulations in Models of Preference Aggregation," Post-Print hal-02424936, HAL.
    3. Joe, Harry, 2002. "Stochastic orderings in random utility models," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 391-404, July.
    4. Isaac Lara & Sergio Rajsbaum & Armajac Ravent'os-Pujol, 2024. "A Generalization of Arrow's Impossibility Theorem Through Combinatorial Topology," Papers 2402.06024, arXiv.org, revised Jul 2024.
    5. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    6. Regenwetter, Michel & Marley, A. A. J. & Grofman, Bernard, 2002. "A general concept of majority rule," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 405-428, July.
    7. Michel Regenwetter & James Adams & Bernard Grofman, 2002. "On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity," Theory and Decision, Springer, vol. 53(2), pages 153-186, September.

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