IDEAS home Printed from https://ideas.repec.org/p/aed/wpaper/0012.html
   My bibliography  Save this paper

Is the preference of the majority representative ?

Author

Listed:
  • Nicolas Gravel
  • Mihir Bhattacharya

Abstract

Given a profile of preferences on a set of alternatives, a majority relation is a complete binary relation that agrees with the strict preference of a strict majority of these preferences whenever such strict majority is observed. We show that a majority binary relation is, among all conceivable binary relations, the most representative of the profile of preferences from which it emanates. We define “the most representative” to mean “the closest in the aggregate”. This requires a definition of what it means for a pair of preferences to be closer to each other then another. We assume that this definition takes the form of a distance function defined over the set of all conceivable preferences. We identify a necessary and sufficient condition for such a distance to be minimized by the preference of the majority. This condition requires the distance to be additive with respect to a plausible notion of compromise between preferences. The well-known Kemeny distance between preference does satisfy this property. We also provide a characterization of the class of distances satisfying this property as numerical representations of a primitive qualitative proximity relation between preferences.

Suggested Citation

  • Nicolas Gravel & Mihir Bhattacharya, 2019. "Is the preference of the majority representative ?," CSH-IFP Working Papers 0012, Centre de Sciences Humaines, New Delhi, revised Aug 2019.
    • Handle: RePEc:aed:wpaper:0012
    as

    Download full text from publisher

    File URL: https://www.csh-delhi.com/wp-content/uploads/2019/09/Preference-of-the-Majority_WP12-1.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. repec:hal:pseose:halshs-00670854 is not listed on IDEAS
    2. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    3. Walter Bossert & Burak Can & Conchita D’Ambrosio, 2016. "Measuring rank mobility with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 917-931, April.
    4. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    5. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 95-109, March.
    6. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
    7. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    8. Benjamin Hadjibeyli & Mark C. Wilson, 2019. "Distance rationalization of anonymous and homogeneous voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 559-583, March.
    9. Sean Horan & Martin J. Osborne & M. Remzi Sanver, 2019. "Positively Responsive Collective Choice Rules And Majority Rule: A Generalization Of May'S Theorem To Many Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(4), pages 1489-1504, November.
    10. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2012. "Rationalizations of Condorcet-consistent rules via distances of hamming type," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 891-905, October.
    11. Suzumura, Kotaro, 2001. "Pareto principles from Inch to Ell," Economics Letters, Elsevier, vol. 70(1), pages 95-98, January.
    12. Lerer, Ehud & Nitzan, Shmuel, 1985. "Some general results on the metric rationalization for social decision rules," Journal of Economic Theory, Elsevier, vol. 37(1), pages 191-201, October.
    13. Can, B. & Storcken, A.J.A., 2015. "Comparing orders, rankings, queues, tournaments and lists," Research Memorandum 020, Maastricht University, Graduate School of Business and Economics (GSBE).
    14. 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.
    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. Hiroki Nishimura & Efe A. Ok, 2023. "Best Complete Approximations of Preference Relations," Papers 2311.06641, arXiv.org.

    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. Mihir Bhattacharya & Nicolas Gravel, 2019. "Is the Preference of the Majority Representative?," Working Papers 1028, Ashoka University, Department of Economics.
    2. Stergios Athanasoglou & Somouaoga Bonkoungou & Lars Ehlers, 2023. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Working Papers 519, University of Milano-Bicocca, Department of Economics.
    3. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2015. "Distance rationalization of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 345-377, September.
    4. Slinko, Arkadii, 2019. "Condorcet domains satisfying Arrow’s single-peakedness," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 166-175.
    5. Gilbert Laffond & Jean Lainé & M. Remzi Sanver, 2020. "Metrizable preferences over preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 177-191, June.
    6. Burak Can & Péter Csóka & Emre Ergin, 2021. "How to choose a fair delegation?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1339-1373, November.
    7. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.
    8. Burak Can & Peter Csoka & Emre Ergin, 2017. "How to choose a non-manipulable delegation?," CERS-IE WORKING PAPERS 1713, Institute of Economics, Centre for Economic and Regional Studies.
    9. Walter Bossert & Burak Can & Conchita D'Ambrosio, 2018. "A Head‐count Measure of Rank Mobility and its Directional Decomposition," Economica, London School of Economics and Political Science, vol. 85(340), pages 793-807, October.
    10. Walter Bossert & Burak Can & Conchita D’Ambrosio, 2016. "Measuring rank mobility with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 917-931, April.
    11. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2015. "Level $$r$$ r consensus and stable social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 805-817, December.
    12. Gabrielle Demange, 2017. "The stability of group formation," Revue d'économie politique, Dalloz, vol. 127(4), pages 495-516.
    13. Shmuel Nitzan, 2010. "Demystifying the ‘metric approach to social compromise with the unanimity criterion’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 25-28, June.
    14. Dinko Dimitrov & Emiliya A. Lazarova & Shao-Chin Sung, 2016. "Inducing stability in hedonic games," University of East Anglia School of Economics Working Paper Series 2016-09, School of Economics, University of East Anglia, Norwich, UK..
    15. Andjiga, Nicolas G. & Mekuko, Aurelien Y. & Moyouwou, Issofa, 2014. "Metric rationalization of social welfare functions," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 14-23.
    16. Eyal Baharad & Shmuel Nitzan, 2016. "Is majority consistency possible?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 287-299, February.
    17. Dotti, Valerio, 2014. "Generalized Comparative Statics for Political Economy Models," MPRA Paper 60711, University Library of Munich, Germany.
    18. Josep Freixas & Montserrat Pons, 2021. "An extension and an alternative characterization of May’s theorem," Annals of Operations Research, Springer, vol. 302(1), pages 137-150, July.
    19. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.
    20. Pongou, Roland & Tchantcho, Bertrand, 2021. "Round-robin political tournaments: Abstention, truthful equilibria, and effective power," Games and Economic Behavior, Elsevier, vol. 130(C), pages 331-351.

    More about this item

    Keywords

    preferences; majority; dissimilarity; distance; aggregation;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:aed:wpaper:0012. 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: CSH (email available below). General contact details of provider: https://edirc.repec.org/data/cshndin.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.