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Beyond neutrality: Extended difference of votes rules

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  • King, Sarah Schulz
  • Powers, Robert C.

Abstract

In a voting situation where there are two alternatives, simple majority rule outputs the alternative with the most votes or outputs a tie if both alternatives receive the same number of votes. For any nonnegative integer k, the difference of votes rule Mk outputs the alternative that beats the competing alternative by more than k votes. If the two alternatives are not necessarily treated equally, then we get the class of Mk,l rules where the integers k and l are the thresholds for when one alternative beats the other. Llamazares (2006) characterized the class of Mk rules with the conditions of anonymity, neutrality, monotonicity, weak Pareto and cancellation. We extend Llamazares’ Theorem by proving that the Mk,l rules are the only voting rules satisfying anonymity, monotonicity, and cancellation. In addition, we describe the class of voting rules that satisfy only monotonicity and cancellation.

Suggested Citation

  • King, Sarah Schulz & Powers, Robert C., 2018. "Beyond neutrality: Extended difference of votes rules," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 146-152.
    • Handle: RePEc:eee:matsoc:v:93:y:2018:i:c:p:146-152
    DOI: 10.1016/j.mathsocsci.2018.03.006
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    References listed on IDEAS

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    1. Garcia-Lapresta, Jose Luis & Llamazares, Bonifacio, 2001. "Majority decisions based on difference of votes," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 463-481, June.
    2. Houy, Nicolas, 2007. "Some further characterizations for the forgotten voting rules," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 111-121, January.
    3. Bonifacio Llamazares, 2013. "On the structure of voting systems between two alternatives," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 239-248, September.
    4. José Luis Garcí a-Lapresta & Bonifacio Llamazares, 2010. "Preference Intensities and Majority Decisions Based on Difference of Support Between Alternatives," Group Decision and Negotiation, Springer, vol. 19(6), pages 527-542, November.
    5. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    6. Perry, Jonathan & Powers, Robert C., 2010. "Anonymity, monotonicity, and quota pair systems," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 57-60, July.
    7. Perry, Jonathan & Powers, Robert C., 2008. "Aggregation rules that satisfy anonymity and neutrality," Economics Letters, Elsevier, vol. 100(1), pages 108-110, July.
    8. Llamazares, Bonifacio, 2006. "The forgotten decision rules: Majority rules based on difference of votes," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 311-326, May.
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    Cited by:

    1. Ali I. Ozkes & M. Remzi Sanver, 2021. "Anonymous, neutral, and resolute social choice revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 97-113, July.

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