IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2204.12436.html
   My bibliography  Save this paper

Incentives in Social Decision Schemes with Pairwise Comparison Preferences

Author

Listed:
  • Felix Brandt
  • Patrick Lederer
  • Warut Suksompong

Abstract

Social decision schemes (SDSs) map the ordinal preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order 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): (i) there is no Condorcet-consistent SDS that satisfies PC-strategyproofness; (ii) there is no anonymous and neutral SDS that satisfies PC-efficiency and PC-strategyproofness; and (iii) there is no anonymous and neutral SDS that satisfies PC-efficiency and strict PC-participation. All three impossibilities require $m\geq 4$ alternatives and turn into possibilities when $m\leq 3$. We furthermore settle an open problem raised by Aziz et al. (2015) by showing that no path of PC-improvements originating from an in

Suggested Citation

  • Felix Brandt & Patrick Lederer & Warut Suksompong, 2022. "Incentives in Social Decision Schemes with Pairwise Comparison Preferences," Papers 2204.12436, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2204.12436
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2204.12436
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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..
    2. Fishburn, P. C., 1984. "Dominance in SSB utility theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 130-148, October.
    3. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    4. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    5. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    6. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    7. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    8. Pavlo Blavatskyy, 2006. "Axiomatization of a Preference for Most Probable Winner," Theory and Decision, Springer, vol. 60(1), pages 17-33, February.
    9. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    2. Florian Brandl & Felix Brandt, 2020. "Arrovian Aggregation of Convex Preferences," Econometrica, Econometric Society, vol. 88(2), pages 799-844, March.
    3. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).
    4. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    5. Liu, Peng, 2020. "Local vs. global strategy-proofness: A new equivalence result for ordinal mechanisms," Economics Letters, Elsevier, vol. 189(C).
    6. 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.
    7. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    8. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    9. Brandl, Florian & Brandt, Felix & Suksompong, Warut, 2016. "The impossibility of extending random dictatorship to weak preferences," Economics Letters, Elsevier, vol. 141(C), pages 44-47.
    10. Lê Nguyên Hoang, 2017. "Strategy-proofness of the randomized Condorcet voting system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 679-701, March.
    11. Sulagna Dasgupta & Debasis Mishra, 2022. "Ordinal Bayesian incentive compatibility in random assignment model," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 651-664, December.
    12. Harless, Patrick & Phan, William, 2022. "Efficient mixtures of priority rules for assigning objects," Games and Economic Behavior, Elsevier, vol. 132(C), pages 73-89.
    13. 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.
    14. Dorian Jullien, 2016. "Under Uncertainty, Over Time and Regarding Other People: Rationality in 3D," GREDEG Working Papers 2016-20, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    15. Ehlers, Lars & Majumdar, Dipjyoti & Mishra, Debasis & Sen, Arunava, 2020. "Continuity and incentive compatibility in cardinal mechanisms," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 31-41.
    16. Chatterji, Shurojit & Roy, Souvik & Sen, Arunava, 2012. "The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 353-366.
    17. Pištěk, Miroslav, 2018. "Continuous SSB representation of preferences," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 59-65.
    18. Cho, Wonki Jo & Park, Chang Woo, 2018. "Fractional group identification," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 66-75.
    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.
    20. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2204.12436. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.