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Frequency based analysis of collective aggregation rules

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  • Chatterjee, Swarnendu
  • Storcken, Ton

Abstract

A new property for collective aggregation rules called positive discrimination is introduced. This property is satisfied by many anonymous and neutral collective aggregation rules. We discuss unimodal profiles (or distributions) for which this property on its own determines the outcome as the mode of a unimodal distribution. We investigate relaxations of this unimodal distribution condition and show that the Condorcet consistent rules as well as the Borda rule and the plurality rule have the mode as the outcome at such profiles. Further, we show, by an example, how the addition of unimodal profiles and the property of positive discrimination can help to determine an outcome in the case of a large number of voters.

Suggested Citation

  • Chatterjee, Swarnendu & Storcken, Ton, 2020. "Frequency based analysis of collective aggregation rules," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 56-66.
    • Handle: RePEc:eee:mateco:v:87:y:2020:i:c:p:56-66
    DOI: 10.1016/j.jmateco.2020.01.003
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    References listed on IDEAS

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    1. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    2. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    3. Raúl Pérez-Fernández & Bernard De Baets, 2018. "The supercovering relation, the pairwise winner, and more missing links between Borda and Condorcet," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 329-352, February.
    4. Grandmont, Jean-Michel & Laroque, Guy & Younes, Yves, 1978. "Equilibrium with quantity rationing and recontracting," Journal of Economic Theory, Elsevier, vol. 19(1), pages 84-102, October.
    5. Ilia Tsetlin & Michel Regenwetter & Bernard Grofman, 2003. "The impartial culture maximizes the probability of majority cycles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 387-398, December.
    6. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
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