IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v88y2020i2p799-844.html
   My bibliography  Save this article

Arrovian Aggregation of Convex Preferences

Author

Listed:
  • Florian Brandl
  • Felix Brandt

Abstract

We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.

Suggested Citation

  • Florian Brandl & Felix Brandt, 2020. "Arrovian Aggregation of Convex Preferences," Econometrica, Econometric Society, vol. 88(2), pages 799-844, March.
    • Handle: RePEc:wly:emetrp:v:88:y:2020:i:2:p:799-844
    DOI: 10.3982/ECTA15749
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA15749
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA15749?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jean-FranÚois Laslier, 2000. "Aggregation of preferences with a variable set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 269-282.
    2. Marc Fleurbaey & Maurice Salles & John A. Weymark, 2008. "Justice, Political Liberalism, and Utilitarism : Themes from Harsanyi and Rawls," Post-Print halshs-00337593, HAL.
    3. repec:cup:judgdm:v:13:y:2018:i:3:p:217-236 is not listed on IDEAS
    4. Rubinstein, Ariel & Segal, Uzi, 2012. "On the likelihood of cyclic comparisons," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2483-2491.
    5. B. Douglas Bernheim, 2009. "Behavioral Welfare Economics," Journal of the European Economic Association, MIT Press, vol. 7(2-3), pages 267-319, 04-05.
    6. Fishburn, Peter C, 1989. "Retrospective on the Utility Theory of von Neumann and Morgenstern," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 127-157, June.
    7. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    8. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(2), pages 185-192.
    9. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804, January.
    10. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    11. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    12. Schwartz, Thomas, 1976. "Choice functions, "rationality" conditions, and variations on the weak axiom of revealed preference," Journal of Economic Theory, Elsevier, vol. 13(3), pages 414-427, December.
    13. 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..
    14. Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2017. "A Comprehensive Approach to Revealed Preference Theory," American Economic Review, American Economic Association, vol. 107(4), pages 1239-1263, April.
    15. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
    16. B. Douglas Bernheim & Antonio Rangel, 2009. "Beyond Revealed Preference: Choice-Theoretic Foundations for Behavioral Welfare Economics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(1), pages 51-104.
    17. Fishburn, Peter C. & Gehrlein, William V., 1987. "Aggregation theory for SSB utility functionals," Journal of Economic Theory, Elsevier, vol. 42(2), pages 352-369, August.
    18. Fishburn, Peter C, 1991. "Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-134, April.
    19. 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.
    20. Bordes, Georges & Breton, Michel Le, 1989. "Arrovian theorems with private alternatives domains and selfish individuals," Journal of Economic Theory, Elsevier, vol. 47(2), pages 257-281, April.
    21. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    22. 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.
    23. Young, H. P., 1988. "Condorcet's Theory of Voting," American Political Science Review, Cambridge University Press, vol. 82(4), pages 1231-1244, December.
    24. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    25. Richard Zeckhauser, 1969. "Majority Rule with Lotteries on Alternatives," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 83(4), pages 696-703.
    26. Llinares, Juan-Vicente, 1998. "Unified treatment of the problem of existence of maximal elements in binary relations: a characterization," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 285-302, April.
    27. Border, Kim C., 1983. "Social welfare functions for economic environments with and without the pareto principle," Journal of Economic Theory, Elsevier, vol. 29(2), pages 205-216, April.
    28. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
    29. Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-879, May.
    30. Pavlo Blavatskyy, 2006. "Axiomatization of a Preference for Most Probable Winner," Theory and Decision, Springer, vol. 60(1), pages 17-33, February.
    31. 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.
    32. Fleurbaey,Marc & Salles,Maurice & Weymark,John A. (ed.), 2008. "Justice, Political Liberalism, and Utilitarianism," Cambridge Books, Cambridge University Press, number 9780521640930, January.
    33. Elizabeth Maggie Penn, 2019. "Introduction to a special issue in honor of Kenneth Arrow," Public Choice, Springer, vol. 179(1), pages 1-6, April.
    34. 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.
    35. Pavlo R. Blavatskyy, "undated". "Axiomatization of a Preference for Most Probable Winner," IEW - Working Papers 230, Institute for Empirical Research in Economics - University of Zurich.
    36. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    37. Ehud Kalai & Eitan Muller & Mark Satterthwaite, 1979. "Social welfare functions when preferences are convex, strictly monotonic, and continuous," Public Choice, Springer, vol. 34(1), pages 87-97, March.
    38. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
    39. 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.
    40. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 521-542.
    41. Nishimura, Hiroki, 2018. "The transitive core: inference of welfare from nontransitive preference relations," Theoretical Economics, Econometric Society, vol. 13(2), May.
    42. Schoemaker, Paul J H, 1982. "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations," Journal of Economic Literature, American Economic Association, vol. 20(2), pages 529-563, June.
    43. Douglas H. Blair & Robert A. Pollak, 1983. "Polychromatic Acyclic Tours in Colored Multigraphs," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 471-476, August.
    44. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94, Elsevier.
    45. Fishburn, P.C., 1984. "SSB Utility theory: an economic perspective," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 63-94, August.
    46. Marc Fleurbaey & Maurice Salles & John A. Weymark, 2008. "Justice, Political Liberalism and Utilitarianism," Post-Print hal-00246415, HAL.
    47. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401, January.
    48. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    49. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    50. Loomes, Graham & Sugden, Robert, 1987. "Some implications of a more general form of regret theory," Journal of Economic Theory, Elsevier, vol. 41(2), pages 270-287, April.
    51. 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.
    52. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
    53. Hylland, Aanund, 1980. "Aggregation Procedure for Cardinal Preferences: A Comment," Econometrica, Econometric Society, vol. 48(2), pages 539-542, March.
    54. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    55. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Forrest Jeffrey Yi-Lin & Tiglioglu Tufan & Liu Yong & Mong Donald & Cardin Marta, 2023. "Various Convexities and Some Relevant Properties of Consumer Preference Relations," Studia Universitatis „Vasile Goldis” Arad – Economics Series, Sciendo, vol. 33(4), pages 145-168, December.
    2. 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.
    3. Florian Brandl & Felix Brandt, 2021. "A Natural Adaptive Process for Collective Decision-Making," Papers 2103.14351, arXiv.org, revised Mar 2024.
    4. 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.
    5. Brandl, Florian & Brandt, Felix, 2024. "A natural adaptive process for collective decision-making," Theoretical Economics, Econometric Society, vol. 19(2), May.
    6. Eden, Maya, 2020. "Aggregating Welfare Gains," CEPR Discussion Papers 14783, C.E.P.R. Discussion Papers.

    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. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    2. 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.
    3. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    4. Lederer, Patrick, 2024. "Bivariate scoring rules: Unifying the characterizations of positional scoring rules and Kemeny's rule," Journal of Economic Theory, Elsevier, vol. 218(C).
    5. 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.
    6. Aki Lehtinen, 2011. "A welfarist critique of social choice theory," Journal of Theoretical Politics, , vol. 23(3), pages 359-381, July.
    7. Kotaro Suzumura, 2002. "Introduction to social choice and welfare," Temi di discussione (Economic working papers) 442, Bank of Italy, Economic Research and International Relations Area.
    8. 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.
    9. Buturak, Gökhan & Evren, Özgür, 2017. "Choice overload and asymmetric regret," Theoretical Economics, Econometric Society, vol. 12(3), September.
    10. Kontek, Krzysztof, 2015. "Fanning-Out or Fanning-In? Continuous or Discontinuous? Estimating Indifference Curves Inside the Marschak-Machina Triangle using Certainty Equivalents," MPRA Paper 63965, University Library of Munich, Germany.
    11. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    12. Michael Birnbaum & Ulrich Schmidt, 2008. "An experimental investigation of violations of transitivity in choice under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 37(1), pages 77-91, August.
    13. Simone Cerreia-Vioglio & Efe A. Ok, 2018. "The Rational Core of Preference Relations," Working Papers 632, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    14. Le Breton, Michel & Weymark, John A., 2002. "Arrovian Social Choice Theory on Economic Domains," IDEI Working Papers 143, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2003.
    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. Marc Willinger, 1990. "La rénovation des fondements de l'utilité et du risque," Revue Économique, Programme National Persée, vol. 41(1), pages 5-48.
    17. Kant, Shashi & Lee, Susan, 2004. "A social choice approach to sustainable forest management: an analysis of multiple forest values in Northwestern Ontario," Forest Policy and Economics, Elsevier, vol. 6(3-4), pages 215-227, June.
    18. Georgios Gerasimou, 2016. "Partially dominant choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 127-145, January.
    19. Denis Bouyssou & Marc Pirlot, 2008. "On some ordinal models for decision making under uncertainty," Annals of Operations Research, Springer, vol. 163(1), pages 19-48, October.
    20. Sudeep Bhatia & Graham Loomes & Daniel Read, 2021. "Establishing the laws of preferential choice behavior," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1324-1369, November.
    21. Michael Birnbaum & Ulrich Schmidt, 2010. "Testing transitivity in choice under risk," Theory and Decision, Springer, vol. 69(4), pages 599-614, October.

    More about this item

    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:wly:emetrp:v:88:y:2020:i:2:p:799-844. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.