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Collective approval

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  • Duddy, Conal
  • Piggins, Ashley

Abstract

We consider the problem of aggregating individual approval ballots into one collective approval ballot. An approval ballot is simply a subset of a given set of alternatives. An individual may approve of as many alternatives as he or she wishes. Each approval is counted as a vote. We show that if an aggregation rule is neutral, consistent and discerning, then an alternative is collectively approved of if it receives a number of votes greater than the mean number of votes received by the alternatives and is not approved of if it receives a number of votes less than the mean.

Suggested Citation

  • Duddy, Conal & Piggins, Ashley, 2013. "Collective approval," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 190-194.
    • Handle: RePEc:eee:matsoc:v:65:y:2013:i:3:p:190-194
    DOI: 10.1016/j.mathsocsci.2012.12.004
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    References listed on IDEAS

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    1. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 621-625, December.
    2. B. Fine & K. Fine, 1974. "Social Choice and Individual Rankings II," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(4), pages 459-475.
    3. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    4. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    5. Sertel, Murat R., 1988. "Characterizing approval voting," Journal of Economic Theory, Elsevier, vol. 45(1), pages 207-211, June.
    6. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    7. B. Fine & K. Fine, 1974. "Social Choice and Individual Ranking I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(3), pages 303-322.
    8. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
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    Cited by:

    1. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    2. McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.
    3. Trevor Leach & Robert C. Powers, 2020. "Majority rule on j-rich ballot spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 639-655, April.

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