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Assent-maximizing social choice

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  • Katherine Baldiga

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  • Jerry Green

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Abstract

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population’s preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population’s preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality. Copyright Springer-Verlag 2013

Suggested Citation

  • Katherine Baldiga & Jerry Green, 2013. "Assent-maximizing social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 439-460, February.
  • Handle: RePEc:spr:sochwe:v:40:y:2013:i:2:p:439-460
    DOI: 10.1007/s00355-011-0614-6
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    File URL: http://hdl.handle.net/10.1007/s00355-011-0614-6
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    References listed on IDEAS

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    1. Craven, John, 1996. "Best Fit Social Choices: An Alternative to Arrow," Economic Journal, Royal Economic Society, vol. 106(438), pages 1161-1174, September.
    2. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    3. David S. Ahn & Santiago Oliveros, 2012. "Combinatorial Voting," Econometrica, Econometric Society, vol. 80(1), pages 89-141, January.
    4. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    5. Christian Klamler, 2008. "A distance measure for choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 419-425, April.
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    Citations

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    Cited by:

    1. Burak Can & Ali Ozkes & Ton Storcken, 2017. "Generalized Measures of Polarization in Preferences," Working Papers halshs-01597720, HAL.
    2. Jorge Alcalde-Unzu & Marc Vorsatz, 2016. "Do we agree? Measuring the cohesiveness of preferences," Theory and Decision, Springer, vol. 80(2), pages 313-339, February.
    3. Can, Burak & Ozkes, Ali Ihsan & Storcken, Ton, 2015. "Measuring polarization in preferences," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 76-79.
    4. Athanasoglou, Stergios, 2016. "Strategyproof and efficient preference aggregation with Kemeny-based criteria," Games and Economic Behavior, Elsevier, vol. 95(C), pages 156-167.
    5. Katherine Baldiga Coffman, 2016. "Representative democracy and the implementation of majority-preferred alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 477-494, March.

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