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Piercing numbers in approval voting

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  • Su, Francis Edward
  • Zerbib, Shira

Abstract

We survey a host of results from discrete geometry that have bearing on the analysis of geometric models of approval voting. Such models view the political spectrum as a geometric space, with geometric constraints on voter preferences. Results on piercing numbers then have a natural interpretation in voting theory, and we survey their implications for various classes of geometric constraints on voter approval sets.

Suggested Citation

  • Su, Francis Edward & Zerbib, Shira, 2019. "Piercing numbers in approval voting," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 65-71.
    • Handle: RePEc:eee:matsoc:v:101:y:2019:i:c:p:65-71
    DOI: 10.1016/j.mathsocsci.2019.06.007
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    References listed on IDEAS

    as
    1. Myerson, Roger B. & Weber, Robert J., 1993. "A Theory of Voting Equilibria," American Political Science Review, Cambridge University Press, vol. 87(1), pages 102-114, March.
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    3. Jean-François Laslier, 2009. "The Leader rule: a model of strategic approval voting in a large electorate," Post-Print hal-00363218, HAL.
    4. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.
    5. Núñez, Matías & Xefteris, Dimitrios, 2017. "Implementation via approval mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 169-181.
    6. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    7. Jean-François Laslier & M. Remzi Sanver, 2010. "The Basic Approval Voting Game," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 153-163, Springer.
    8. Laslier, Jean-François & Núñez, Matías & Pimienta, Carlos, 2017. "Reaching consensus through approval bargaining," Games and Economic Behavior, Elsevier, vol. 104(C), pages 241-251.
    9. repec:ulb:ulbeco:2013/162238 is not listed on IDEAS
    10. Jean-François Laslier, 2009. "The Leader Rule," Journal of Theoretical Politics, , vol. 21(1), pages 113-136, January.
    11. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
    12. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
    Full references (including those not matched with items on IDEAS)

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