IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/627.html
   My bibliography  Save this paper

Approximate implementation of Relative Utilitarianism via Groves-Clarke pivotal voting with virtual money

Author

Listed:
  • Pivato, Marcus

Abstract

`Relative Utilitarianism' (RU) is a version of classical utilitarianism, where each person's utility function is rescaled to range from zero to one. As a voting system, RU is vulnerable to preference exaggeration by strategic voters. The Groves-Clarke Pivotal Mechanism elicits truthful revelation of preferences by requiring each voter to `bid' a sum of real money to cast a pivotal vote. However, this neglects wealth effects and gives disproportionate power to rich voters. We propose a variant of the Pivotal Mechanism using fixed allotments of notional `voting money'; this `Voting Money Pivotal Mechanism' (VMPM) is politically egalitarian and immune to wealth effects. In the large-population limit, the only admissible (i.e. weakly undominated) voting strategies in the VMPM are approximately truthful revelations of preferences; thus the VMPM yields an arbitrarily close approximation of RU.

Suggested Citation

  • Pivato, Marcus, 2006. "Approximate implementation of Relative Utilitarianism via Groves-Clarke pivotal voting with virtual money," MPRA Paper 627, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:627
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/627/1/MPRA_paper_627.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Riker, William H. & Brams, Steven J., 1973. "The Paradox of Vote Trading," American Political Science Review, Cambridge University Press, vol. 67(4), pages 1235-1247, December.
    2. Shmuel Nitzan & Jacob Paroush & Shlomo Lampert, 1980. "Preference expression and misrepresentation in points voting schemes," Public Choice, Springer, vol. 35(4), pages 421-436, January.
    3. Edi Karni, 1998. "Impartiality: Definition and Representation," Econometrica, Econometric Society, vol. 66(6), pages 1405-1416, November.
    4. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    5. Mueller,Dennis C., 2003. "Public Choice III," Cambridge Books, Cambridge University Press, number 9780521894753.
    6. Sjostrom, Tomas, 1991. "A new characterization of the Groves- Clarke mechanism," Economics Letters, Elsevier, vol. 36(3), pages 263-267, July.
    7. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    8. Gordon Tullock, 1959. "Problems of Majority Voting," Journal of Political Economy, University of Chicago Press, vol. 67, pages 571-571.
    9. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    10. Dennis Mueller & Geoffrey Philpotts & Jaroslav Vanek, 1972. "The social gains from exchanging votes: A simulation approach," Public Choice, Springer, vol. 13(1), pages 55-79, September.
    11. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
    12. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    13. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61, pages 434-434.
    14. Yew-Kwang Ng, 1975. "Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 545-569.
    15. Mueller,Dennis C. (ed.), 1997. "Perspectives on Public Choice," Cambridge Books, Cambridge University Press, number 9780521553773.
    16. 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.
    17. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309-309.
    18. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    19. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
    20. I. Good, 1977. "Justice in voting by demand revelation," Public Choice, Springer, vol. 29(2), pages 65-70, March.
    21. Shmuel Nitzan, 1975. "Social preference ordering in a probabilistic voting model," Public Choice, Springer, vol. 24(1), pages 93-100, December.
    22. Coleman, James S., 1970. "Political Money," American Political Science Review, Cambridge University Press, vol. 64(4), pages 1074-1087, December.
    23. Eric Maskin, 1978. "A Theorem on Utilitarianism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 93-96.
    24. 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.
    25. Moulin, H., 1986. "Characterizations of the pivotal mechanism," Journal of Public Economics, Elsevier, vol. 31(1), pages 53-78, October.
    26. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    27. Donald John Roberts & Andrew Postlewaite, 1973. "The Incentives for Price-Taking Behavior In Large Economies," Discussion Papers 44, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. Pivato, Marcus, 2007. "A non-monetary form of Clarke pivotal voting," MPRA Paper 3964, University Library of Munich, Germany.
    2. Marcus Pivato, 2009. "Twofold optimality of the relative utilitarian bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 79-92, January.
    3. Dennis Mueller, 2012. "Gordon Tullock and Public Choice," Public Choice, Springer, vol. 152(1), pages 47-60, July.
    4. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    5. Emmanuelle Auriol & Robert Gary-Bobo, 2012. "On the optimal number of representatives," Public Choice, Springer, vol. 153(3), pages 419-445, December.
    6. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," 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 10, pages 459-541, Elsevier.
    7. Segal, Uzi & Sobel, Joel, 2002. "Min, Max, and Sum," Journal of Economic Theory, Elsevier, vol. 106(1), pages 126-150, September.
    8. Miralles, Antonio, 2012. "Cardinal Bayesian allocation mechanisms without transfers," Journal of Economic Theory, Elsevier, vol. 147(1), pages 179-206.
    9. Tilman Börgers & Yan-Min Choo, 2017. "Revealed Relative Utilitarianism," CESifo Working Paper Series 6613, CESifo.
    10. Laffont, Jean-Jacques, 1996. "William Vickrey: A Pioneer in the Economics of Incentives," Nobel Prize in Economics documents 1996-2, Nobel Prize Committee.
    11. Mizukami, Hideki & Saijo, Tatsuyoshi & Wakayama, Takuma, 2003. "Strategy-Proof Sharing," Working Papers 1170, California Institute of Technology, Division of the Humanities and Social Sciences.
    12. Toyotaka Sakai, 2017. "Considering Collective Choice: The Route 328 Problem in Kodaira City," The Japanese Economic Review, Japanese Economic Association, vol. 68(3), pages 323-332, September.
    13. Claude Hillinger, 2005. "The Case for Utilitarian Voting," Homo Oeconomicus, Institute of SocioEconomics, vol. 23, pages 295-321.
    14. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," 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 5, pages 237-288 Elsevier.
    15. Philippe Jehiel & Laurent Lamy, 2018. "A Mechanism Design Approach to the Tiebout Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 735-760.
    16. Debasis Mishra & Abdul Quadir, 2012. "Deterministic single object auctions with private values," Discussion Papers 12-06, Indian Statistical Institute, Delhi.
    17. Tomoya Kazumura & Shigehiro Serizawa, 2016. "Efficiency and strategy-proofness in object assignment problems with multi-demand preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 633-663, October.
    18. Claude d'Aspremont & Jacques Crémer & Louis-André Gérard-Varet, 2003. "Correlation, independence, and Bayesian incentives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 281-310, October.
    19. Tommy Andersson & Lars Ehlers & Lars-Gunnar Svensson & Ryan Tierney, 2022. "Gale’s Fixed Tax for Exchanging Houses," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 3110-3128, November.
    20. Miljkovic, Dragan, 2009. "International organizations and arrangements: Pivotal countries and manipulations," Economic Modelling, Elsevier, vol. 26(6), pages 1398-1402, November.

    More about this item

    Keywords

    Relative Utilitarianism; Groves-Clarke; pivotal mechanism; demand-revealing mechanism; voting dollars; point voting;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    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:pra:mprapa:627. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.