IDEAS home Printed from https://ideas.repec.org/a/the/publsh/5589.html
   My bibliography  Save this article

Randomized collective choices based on a fractional tournament

Author

Listed:
  • Sprumont, Yves

    (Department of Economics, Deakin University)

Abstract

An extension rule assigns to each fractional tournament x (specifying, for every pair of social alternatives a and b, the proportion x_{ab} of voters who prefer a to b) a random choice function y (specifying a collective choice probability distribution for each subset of alternatives) which chooses a from {a,b} with probability x_{ab}. There exist multiple neutral and stochastically rationalizable extension rules. Both Linearity (requiring that y be an affine function of x) and Independence of Irrelevant Comparisons (asking that the probability distribution on a subset of alternatives depend only on the restriction of the fractional tournament to that subset) are incompatible with very weak properties implied by Stochastic Rationalizability. We identify a class of maximal domains, which we call sequentially binary, guaranteeing that every fractional tournament arising from a population of voters with preferences in such a domain has a unique admissible stochastically rationalizable extension.

Suggested Citation

  • Sprumont, Yves, 0. "Randomized collective choices based on a fractional tournament," Theoretical Economics, Econometric Society.
    • Handle: RePEc:the:publsh:5589
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5589/39854/1
    File Function: Working paper version. Paper will be copyedited and typeset before publication.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    2. Barbera, Salvador & Sonnenschein, Hugo, 1978. "Preference aggregation with randomized social orderings," Journal of Economic Theory, Elsevier, vol. 18(2), pages 244-254, August.
    3. Puppe, Clemens & Slinko, Arkadii, 2022. "Maximal Condorcet domains: A further progress report," Working Paper Series in Economics 159, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    4. Jose Apesteguia & Miguel A. Ballester & Jay Lu, 2017. "Single‐Crossing Random Utility Models," Econometrica, Econometric Society, vol. 85, pages 661-674, March.
    5. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).
    6. Morgan McClellon, 2015. "Unique Random Utility Representations," Working Paper 262661, Harvard University OpenScholar.
    7. Pattanaik, Prasanta K & Peleg, Bezalel, 1986. "Distribution of Power under Stochastic Social Choice Rules," Econometrica, Econometric Society, vol. 54(4), pages 909-921, July.
    8. Florian Brandl & Felix Brandt & Hans Georg Seedig, 2016. "Consistent Probabilistic Social Choice," Econometrica, Econometric Society, vol. 84, pages 1839-1880, September.
    9. 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.
    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. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).
    2. Daniele Caliari & Henrik Petri, 2024. "Irrational Random Utility Models," Papers 2403.10208, arXiv.org.
    3. Jean-Paul Doignon & Kota Saito, 2022. "Adjacencies on random ordering polytopes and flow polytopes," Papers 2207.06925, arXiv.org.
    4. Yaron Azrieli & John Rehbeck, 2022. "Marginal stochastic choice," Papers 2208.08492, arXiv.org.
    5. McClellon, Morgan, 2016. "Confidence models of incomplete preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 30-34.
    6. Regenwetter, Michel & Marley, A. A. J. & Grofman, Bernard, 2002. "A general concept of majority rule," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 405-428, July.
    7. Chambers, Christopher P., 2009. "An axiomatic theory of political representation," Journal of Economic Theory, Elsevier, vol. 144(1), pages 375-389, January.
    8. Angelo Petralia, 2024. "Harmful choices," Papers 2408.01317, arXiv.org, revised Dec 2024.
    9. Furtado, Bruno A. & Nascimento, Leandro & Riella, Gil, 2023. "Rational choice with full-comparability domains," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 124-135.
    10. Tom Demeulemeester & Dries Goossens & Ben Hermans & Roel Leus, 2023. "Fair integer programming under dichotomous and cardinal preferences," Papers 2306.13383, arXiv.org, revised Apr 2024.
    11. Florian Brandl & Felix Brandt, 2021. "A Natural Adaptive Process for Collective Decision-Making," Papers 2103.14351, arXiv.org, revised Mar 2024.
    12. Martin Lackner & Piotr Skowron, 2017. "Consistent Approval-Based Multi-Winner Rules," Papers 1704.02453, arXiv.org, revised Oct 2019.
    13. Manzini, Paola & Mariotti, Marco, 2018. "Dual random utility maximisation," Journal of Economic Theory, Elsevier, vol. 177(C), pages 162-182.
    14. 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.
    15. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2020. "On the Structure of Stable Tournament Solutions," Papers 2004.01651, arXiv.org.
    16. Nandeibam, Shasikanta, 2000. "Distribution of coalitional power under probabilistic voting procedures," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 63-84, July.
    17. 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.
    18. Carlos Alós-Ferrer & Ernst Fehr & Nick Netzer, 2021. "Time Will Tell: Recovering Preferences When Choices Are Noisy," Journal of Political Economy, University of Chicago Press, vol. 129(6), pages 1828-1877.
    19. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2018. "On the structure of stable tournament solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 483-507, March.
    20. Apesteguia, Jose & Ballester, Miguel A., 2023. "Random utility models with ordered types and domains," Journal of Economic Theory, Elsevier, vol. 211(C).

    More about this item

    Keywords

    Fractional tournament; voting; random choice; stochastic rationalizability;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    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:the:publsh:5589. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.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.