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A characterization of pairwise dictatorial approbatory social welfare functions

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  • Santos-García, Gustavo
  • Alcantud, José Carlos R.

Abstract

This paper defines approbatory social welfare functions. They are the natural counterpart of Arrovian social welfare functions when the expression of preferences is accompanied by a common choice of “approved” alternatives in a consistent manner. First, we count the number of consistent preference-approval profiles (the domain of approbatory social welfare functions). Then we show that pairwise dictatorial behaviors are characterized by unanimity and independence of irrelevant alternatives, a replication of Arrow’s characterization of dictatorships for this restricted version of the preference-approval model defined by Brams and Sanver in 2009.

Suggested Citation

  • Santos-García, Gustavo & Alcantud, José Carlos R., 2025. "A characterization of pairwise dictatorial approbatory social welfare functions," Economics Letters, Elsevier, vol. 248(C).
    • Handle: RePEc:eee:ecolet:v:248:y:2025:i:c:s0165176525000540
    DOI: 10.1016/j.econlet.2025.112217
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    References listed on IDEAS

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    1. Alexander Karpov, 2019. "On the Number of Group-Separable Preference Profiles," Group Decision and Negotiation, Springer, vol. 28(3), pages 501-517, June.
    2. Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 535-555, October.
    3. José Alcantud & Annick Laruelle, 2014. "Dis&approval voting: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 1-10, June.
    4. Eric Kamwa, 2023. "On Two Voting systems that combine approval and preferences: Fallback Voting and Preference Approval Voting," Working Papers hal-03614585, HAL.
    5. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
    6. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    7. Guy Barokas & Yves Sprumont, 2022. "The broken Borda rule and other refinements of approval ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 187-199, January.
    8. Barokas, Guy, 2023. "A non-lexicographic rule in the preference-approval setting," Economics Letters, Elsevier, vol. 227(C).
    9. Alcantud, José Carlos R. & Cantone, Domenico & Giarlotta, Alfio & Watson, Stephen, 2023. "Rationalization of indecisive choice behavior by pluralist ballots," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    10. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Ranking; Approval; Social welfare function; Voting; Dictatorship;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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