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A characterization result for approval voting with a variable set of alternatives

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  • Norihisa Sato

Abstract

In this paper, we present a new result for axiomatic characterization of approval voting. Having defined a model in which the actual set of alternatives becomes known only after a vote has been taken, we characterize approval voting as the only voting procedure (to be precise, “family of ballot aggregation functions”) that satisfies faithfulness ( F), consistency ( C), stability on selected alternatives ( SSA), and independence of dropped alternatives ( IDA). SSA, which is a version of the property introduced by Arrow (Economica 16:121–127, 1959 ), states that if the actual set of alternatives is smaller than the original set, we should select those alternatives, if any, that would have been selected on the first vote and that are still feasible. On the other hand, IDA suggests that we should select alternatives based on the outcome of the second vote. Therefore, given F and C, approval voting is the only voting procedure that selects the same set of alternatives irrespective of which vote counts, that is, the first or second vote. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Norihisa Sato, 2014. "A characterization result for approval voting with a variable set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 809-825, December.
    • Handle: RePEc:spr:sochwe:v:43:y:2014:i:4:p:809-825
    DOI: 10.1007/s00355-014-0811-1
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    1. Jordi Massó & Marc Vorsatz, 2008. "Weighted approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 129-146, July.
    2. Sertel, Murat R., 1988. "Characterizing approval voting," Journal of Economic Theory, Elsevier, vol. 45(1), pages 207-211, June.
    3. 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.
    4. Marc Vorsatz, 2007. "Approval Voting on Dichotomous Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 127-141, January.
    5. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    6. Baigent, Nick & Xu, Yongsheng, 1991. "Independent necessary and sufficient conditions for approval voting," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 21-29, February.
    7. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    8. 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.
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    Cited by:

    1. François Maniquet & Philippe Mongin, 2015. "Approval voting and Arrow’s impossibility theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 519-532, March.
    2. Sato, Norihisa, 2019. "Approval voting and fixed electorate with dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 51-60.
    3. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2019. "Strongly sincere best responses under approval voting and arbitrary preferences," Games and Economic Behavior, Elsevier, vol. 117(C), pages 388-401.
    4. 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.
    5. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).

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