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Incentives in social decision schemes with pairwise comparison preferences

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  • Brandt, Felix
  • Lederer, Patrick
  • Suksompong, Warut

Abstract

Social decision schemes (SDSs) map the ordinal preferences of voters over multiple alternatives to a probability distribution over the alternatives. To study the axiomatic properties of SDSs, we lift preferences over alternatives to preferences over lotteries using the natural—but little understood—pairwise comparison (PC) preference extension. This extension postulates that one lottery is preferred to another if the former is more likely to return a preferred outcome. We settle three open questions raised by Brandt (2017) and show that (i) no Condorcet-consistent SDS satisfies PC-strategyproofness; (ii) no anonymous and neutral SDS satisfies both PC-efficiency and PC-strategyproofness; and (iii) no anonymous and neutral SDS satisfies both PC-efficiency and strict PC-participation. We furthermore settle an open problem raised by Aziz et al. (2015) by showing that no path of PC-improvements originating from an inefficient lottery may lead to a PC-efficient lottery.

Suggested Citation

  • Brandt, Felix & Lederer, Patrick & Suksompong, Warut, 2023. "Incentives in social decision schemes with pairwise comparison preferences," Games and Economic Behavior, Elsevier, vol. 142(C), pages 266-291.
    • Handle: RePEc:eee:gamebe:v:142:y:2023:i:c:p:266-291
    DOI: 10.1016/j.geb.2023.08.009
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    References listed on IDEAS

    as
    1. Felix Brandt & Patrick Lederer, 2021. "Characterizing the Top Cycle via Strategyproofness," Papers 2108.04622, arXiv.org, revised Jun 2023.
    2. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    3. Florian Brandl & Felix Brandt, 2020. "Arrovian Aggregation of Convex Preferences," Econometrica, Econometric Society, vol. 88(2), pages 799-844, March.
    4. Brandt, Felix & Geist, Christian & Peters, Dominik, 2017. "Optimal bounds for the no-show paradox via SAT solving," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 18-27.
    5. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
    6. P. C. Fishburn, 1984. "Probabilistic Social Choice Based on Simple Voting Comparisons," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 683-692.
    7. Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    8. Salvador Barbera, 1979. "Majority and Positional Voting in a Probabilistic Framework," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 379-389.
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    14. Felix Brandt & Martin Bullinger & Patrick Lederer, 2021. "On the Indecisiveness of Kelly-Strategyproof Social Choice Functions," Papers 2102.00499, arXiv.org, revised Mar 2022.
    15. Aziz, Haris & Brandl, Florian & Brandt, Felix, 2015. "Universal Pareto dominance and welfare for plausible utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 123-133.
    16. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
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    18. Florian Brandl & Felix Brandt & Christian Stricker, 2022. "An analytical and experimental comparison of maximal lottery schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 5-38, January.
    19. Felix Brandt & Patrick Lederer & Ren'e Romen, 2022. "Relaxed Notions of Condorcet-Consistency and Efficiency for Strategyproof Social Decision Schemes," Papers 2201.10418, arXiv.org.
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    More about this item

    Keywords

    Randomized social choice; Pairwise comparison preferences; Strategyproofness; Participation;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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