1932

Abstract

Voters have strong incentives to increase their influence by trading votes, acquiring others’ votes when preferences are strong in exchange for giving votes away when preferences are weak. But is vote trading welfare improving or welfare decreasing? For a practice long believed to be central to collective decisions, the lack of a clear answer is surprising. We review the theoretical literature and, when available, its related experimental tests. We begin with the analysis of logrolling, the exchange of votes for votes. We then focus on vote markets, where votes can be traded against a numeraire. We conclude with procedures allowing voters to shift votes across decisions—that is, allowing one to trade votes with oneself only. We find that vote trading and vote markets are typically inefficient; more encouraging results are obtained by allowing voters to allocate votes across decisions.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-economics-081720-114422
2021-08-05
2024-12-14
Loading full text...

Full text loading...

/deliver/fulltext/economics/13/1/annurev-economics-081720-114422.html?itemId=/content/journals/10.1146/annurev-economics-081720-114422&mimeType=html&fmt=ahah

Literature Cited

  1. Alonso R, Câmara O. 2016.. Persuading voters. . Am. Econ. Rev. 106::3590605
    [Google Scholar]
  2. Arrow KJ. 1951.. Social Choice and Individual Values. New York:: Wiley
    [Google Scholar]
  3. Arrow KJ, Hahn F. 1971.. General Competitive Analysis. San Francisco, CA:: Holder Day
    [Google Scholar]
  4. Aziz H, Brill M, Conitzer V, Elkind E, Freeman R, Walsh T. 2017.. Justified representation in approval-based committee voting. . Soc. Choice Welfare 48::46185
    [Google Scholar]
  5. Bebchuk LA, Kamar E. 2009.. Bundling and entrenchment. . Harvard Law Rev. 123::154995
    [Google Scholar]
  6. Bentley AF. 1908.. The Process of Government: A Study of Social Pressures. Chicago:: Univ. Chicago Press
    [Google Scholar]
  7. Bernholz P. 1973.. Logrolling, Arrow paradox and cyclical majorities. . Public Choice 15::8795
    [Google Scholar]
  8. Bernholz P. 1974.. Logrolling, Arrow paradox and decision rules—a generalization. . Kyklos 27::4962
    [Google Scholar]
  9. Bhagat S, Brickley JA. 1984.. Cumulative voting: the value of minority shareholder voting rights. . J. Law Econ. 27::33965
    [Google Scholar]
  10. Borgers T. 2004.. Costly voting. . Am. Econ. Rev. 94::5766
    [Google Scholar]
  11. Buchanan JM, Tullock G. 1962.. The Calculus of Consent. Ann Arbor:: Univ. Mich. Press
    [Google Scholar]
  12. Câmara O, Eguia JX. 2017.. Slicing and bundling. . J. Politics 79::146064
    [Google Scholar]
  13. Cantú F. 2019.. Groceries for votes: the electoral returns of vote buying. . J. Politics 81::790804
    [Google Scholar]
  14. Carrubba CJ, Volden C. 2000.. Coalitional politics and logrolling in legislative institutions. . Am. J. Political Sci. 44::26177
    [Google Scholar]
  15. Casella A. 2005.. Storable votes. . Games Econ. Behav. 51::391419
    [Google Scholar]
  16. Casella A. 2012.. Storable Votes: Protecting the Minority Voice. Oxford, UK:: Oxford Univ. Press
    [Google Scholar]
  17. Casella A, Gelman A. 2008.. A simple scheme to improve the efficiency of referenda. . J. Public Econ. 92::224061
    [Google Scholar]
  18. Casella A, Laslier JF, Macé A. 2017.. Democracy for polarized committees: the tale of Blotto's lieutenants. . Games Econ. Behav. 106::23959
    [Google Scholar]
  19. Casella A, Llorente-Saguer A, Palfrey TR. 2012.. Competitive equilibrium in markets for votes. . J. Political Econ. 120::593658
    [Google Scholar]
  20. Casella A, Palfrey T. 2018.. Trading votes for votes: a dynamic theory. Soc. Sci. Work. Pap. 1444 , Calif. Inst. Technol., Pasadena:
    [Google Scholar]
  21. Casella A, Palfrey T. 2019.. Trading votes for votes: a dynamic theory. . Econometrica 87::63152
    [Google Scholar]
  22. Casella A, Palfrey T. 2021.. Trading votes for votes: a laboratory study. . Games Econ. Behav. 125::126
    [Google Scholar]
  23. Casella A, Palfrey T, Turban S. 2014.. Vote trading with and without party leaders. . J. Public Econ. 112::11528
    [Google Scholar]
  24. Casella A, Sanchez L. 2021.. Democracy and intensity of preferences: a test of storable votes and quadratic voting on four California propositions. . J. Politics. In press. https://doi.org/10.1086/714782
    [Crossref] [Google Scholar]
  25. Casella A, Turban S. 2014.. Democracy undone: systematic minority advantage in competitive vote markets. . Games Econ. Behav. 88::4770
    [Google Scholar]
  26. Chamberlain G, Rothschild M. 1981.. A note on the probability of casting a decisive vote. . J. Econ. Theory 25::15262
    [Google Scholar]
  27. Chandar B, Weyl EG. 2019.. Quadratic voting in finite populations. Work. Pap., Stanford Grad. Sch. Bus., Stanford, CA:
    [Google Scholar]
  28. Christoffersen SE, Geczy CC, Musto DK, Reed AV. 2007.. Vote trading and information aggregation. . J. Finance 62::2897929
    [Google Scholar]
  29. Chwe MSY. 1994.. Farsighted coalitional stability. . J. Econ. Theory 63::299325
    [Google Scholar]
  30. Cohen L, Malloy CJ. 2014.. Friends in high places. . Am. Econ. J. Econ. Policy 6::6391
    [Google Scholar]
  31. Coleman JS. 1966.. The possibility of a social welfare function. . Am. Econ. Rev. 56::110522
    [Google Scholar]
  32. Coleman JS. 1967.. The possibility of a social welfare function: reply. . Am. Econ. Rev. 57::131117
    [Google Scholar]
  33. Condorcet M de. 1785.. Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. Paris:: Impr. R.
    [Google Scholar]
  34. Cox JD, Ferri F, Honigsberg C, Thomas RS. 2015.. Quieting the shareholders' voice: empirical evidence of pervasive bundling in proxy solicitations. . South. Calif. Law Rev. 89::1179242
    [Google Scholar]
  35. Dal Bo E. 2007.. Bribing voters. . Am. J. Political Sci. 51::789803
    [Google Scholar]
  36. Dekel E, Jackson MO, Wolinsky A. 2008.. Vote buying: general elections. . J. Political Econ. 116::35180
    [Google Scholar]
  37. Dekel E, Jackson MO, Wolinsky A. 2009.. Vote buying: legislatures and lobbying. . Q. J. Political Sci. 4::10328
    [Google Scholar]
  38. Dutta B, Vohra R. 2017.. Rational expectations and farsighted stability. . Theor. Econ. 12::1191227
    [Google Scholar]
  39. Eguia JX, Immorlica N, Ligett K, Weyl G, Xefteris D. 2019.. Quadratic voting with multiple alternatives. Work. Pap. 2019-01 , Dep. Econ, Mich. State Univ., East Lansing:
    [Google Scholar]
  40. Eguia JX, Xefteris D. 2020.. Implementation by vote-buying mechanisms. Work. Pap., Mich. State Univ., East Lansing:
    [Google Scholar]
  41. Esö P, Hansen S, White L. 2014.. A theory of vote-trading and information aggregation. Work. Pap., Univ. Oxford, Oxford, UK:
    [Google Scholar]
  42. Faliszewski P, Rothe J. 2016.. Control and bribery in voting. . In Handbook of Computational Social Choice, ed. F Brandt, V Conitzer, U Endriss, J Lang, AD Procaccia , pp. 14668. Cambridge, UK:: Cambridge Univ. Press
    [Google Scholar]
  43. Ferejohn JA. 1974.. Sour notes on the theory of vote trading. Soc. Sci. Work. Pap. 41 , Calif. Inst. Technol., Pasadena:
    [Google Scholar]
  44. Finan F, Schechter L. 2012.. Vote-buying and reciprocity. . Econometrica 80::86381
    [Google Scholar]
  45. Fischbacher U, Schudy S. 2014.. Reciprocity and resistance to comprehensive reform. . Public Choice 160::41128
    [Google Scholar]
  46. Fischbacher U, Schudy S. 2020.. Agenda control and reciprocity in sequential voting decisions. . Econ. Inq. 58::181329
    [Google Scholar]
  47. Freeman R, Pennock DM, Peters D, Wortman Vaughan J. 2019.. Truthful aggregation of budget proposals. . In Proceedings of the 2019 ACM Conference on Economics and Computation, pp. 75152. New York:: ACM
    [Google Scholar]
  48. Gelman A, Katz JN, Tuerlinckx F. 2002.. The mathematics and statistics of voting power. . Stat. Sci. 17::42035
    [Google Scholar]
  49. Goeree JK, Zhang J. 2017.. One man, one bid. . Games Econ. Behav. 101::15171
    [Google Scholar]
  50. Good IJ, Mayer LS. 1975.. Estimating the efficacy of a vote. . Behav. Sci. 20::2533
    [Google Scholar]
  51. Grandi U, Grossi D, Turrini P. 2019.. Negotiable votes. . J. Artif. Intel. Res. 64::895929
    [Google Scholar]
  52. Groseclose T, Snyder JM Jr. 1996.. Buying supermajorities. . Am. Political Sci. Rev. 90::30315
    [Google Scholar]
  53. Guerrero OA, Matter U. 2016.. Revealing the anatomy of vote trading. Saïd Bus. Sch. Work. Pap. 26 , Univ. Oxford, Oxford, UK:
    [Google Scholar]
  54. Guinier L. 1995.. Tyranny of the Majority: Fundamental Fairness in Representative Democracy. New York:: Free Press
    [Google Scholar]
  55. Haefele ET. 1971.. A utility theory of representative government. . Am. Econ. Rev. 61::35067
    [Google Scholar]
  56. Hortala-Vallve R. 2011.. Generous legislators? A description of vote trading agreements. . Q. J. Political Sci. 6::17996
    [Google Scholar]
  57. Hortala-Vallve R. 2012.. Qualitative voting. . J. Theor. Politics 24::52654
    [Google Scholar]
  58. Hylland A, Zeckhauser R. 1979.. A mechanism for selecting public goods when preferences must be elicited. Work. Pap., Kennedy Sch. Gov., Harvard Univ., Cambridge, MA:
    [Google Scholar]
  59. Iaryczower M, Oliveros S. 2016.. Power brokers: middlemen in legislative bargaining. . J. Econ. Theory 162::20936
    [Google Scholar]
  60. Jackson MO, Sonnenschein HF. 2007.. Overcoming incentive constraints by linking decisions. . Econometrica 75::24157
    [Google Scholar]
  61. Kadane JB. 1972.. On division of the question. . Public Choice 13::4754
    [Google Scholar]
  62. Kaplow L, Kominers SD. 2017.. Who will vote quadratically? Voter turnout and votes cast under quadratic voting. . Public Choice 172::12549
    [Google Scholar]
  63. Koehler DH. 1975.. Vote trading and the voting paradox: a proof of logical equivalence. . Am. Political Sci. Rev. 69::95460
    [Google Scholar]
  64. Koford KJ. 1982.. Centralized vote-trading. . Public Choice 39::24568
    [Google Scholar]
  65. Koriyama Y, Laslier JF, Macé A, Treibich R. 2013.. Optimal apportionment. . J. Political Econ. 121::584608
    [Google Scholar]
  66. Krasa S, Polborn MK. 2009.. Is mandatory voting better than voluntary voting?. Games Econ. Behav. 66::27591
    [Google Scholar]
  67. Krishna V, Morgan J. 2015.. Majority rule and utilitarian welfare. . Am. Econ. J. Microecon. 7::33975
    [Google Scholar]
  68. Kultti K, Salonen H. 2005.. Market for votes. . Homo Oeconomicus 23::32332
    [Google Scholar]
  69. Lackner M. 2020.. Perpetual voting: fairness in long-term decision making. . In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 210310. Palo Alto, CA:: AAAI
    [Google Scholar]
  70. Laine CR. 1977.. Strategy in point voting: a note. . Q. J. Econ. 91::5057
    [Google Scholar]
  71. Lalley SP, Weyl EG. 2018.. Quadratic voting: how mechanism design can radicalize democracy. . AEA Pap. Proc. 108::3337
    [Google Scholar]
  72. Lalley SP, Weyl EG. 2019.. Nash equilibria for quadratic voting. . arXiv:1409.0264v6 [cs.GT]
  73. Lang J, Xia L. 2016.. Voting in combinatorial domains. . In Handbook of Computational Social Choice, ed. F Brandt, V Conitzer, U Endriss, J Lang, AD Procaccia , pp. 197222. Cambridge, UK:: Cambridge Univ. Press
    [Google Scholar]
  74. Laurence B, Sher I. 2017.. Ethical considerations on quadratic voting. . Public Choice 172::195222
    [Google Scholar]
  75. Ledyard JO. 1984.. The pure theory of large two-candidate elections. . Public Choice 44::741
    [Google Scholar]
  76. Levine DK, Palfrey TR. 2007.. The paradox of voter participation? A laboratory study. . Am. Political Sci. Rev. 101::14358
    [Google Scholar]
  77. Margolis H. 1977.. Probability of a tie election. . Public Choice 31::13538
    [Google Scholar]
  78. Mauleon A, Vannetelbosch VJ, Vergote W. 2011.. von Neumann–Morgenstern farsightedly stable sets in two-sided matching. . Theor. Econ. 6::499521
    [Google Scholar]
  79. McAfee RP. 1992.. Amicable divorce: dissolving a partnership with simple mechanisms. . J. Econ. Theory 56::26693
    [Google Scholar]
  80. McKelvey RD, Ordeshook PC. 1980.. Vote trading: an experimental study. . Public Choice 35::15184
    [Google Scholar]
  81. Miller NR. 1977a.. Graph-theoretical approaches to the theory of voting. . Am. J. Political Sci. 21::769803
    [Google Scholar]
  82. Miller NR. 1977b.. Logrolling, vote trading, and the paradox of voting: a game-theoretical overview. . Public Choice 30::5175
    [Google Scholar]
  83. Mueller DC. 1967.. The possibility of a social welfare function: comment. . Am. Econ. Rev. 57::130411
    [Google Scholar]
  84. Mueller DC. 1973.. Constitutional democracy and social welfare. . Q. J. Econ. 87::6080
    [Google Scholar]
  85. Mueller DC, Philpotts GC, Vanek J. 1972.. The social gains from exchanging votes: a simulation approach. . Public Choice 13::5579
    [Google Scholar]
  86. Myerson RB. 1993.. Incentives to cultivate favored minorities under alternative electoral systems. . Am. Political Sci. Rev. 87::85669
    [Google Scholar]
  87. Myerson RB, Satterthwaite MA. 1983.. Efficient mechanisms for bilateral trading. . J. Econ. Theory 29::26581
    [Google Scholar]
  88. Palfrey TR, Rosenthal H. 1983.. A strategic calculus of voting. . Public Choice 41::753
    [Google Scholar]
  89. Palfrey TR, Rosenthal H. 1985.. Voter participation and strategic uncertainty. . Am. Political Sci. Rev. 79::6278
    [Google Scholar]
  90. Park RE. 1967.. The possibility of a social welfare function: comment. . Am. Econ. Rev. 57::13004
    [Google Scholar]
  91. Pesendorfer M. 2000.. A study of collusion in first-price auctions. . Rev. Econ. Stud. 67::381411
    [Google Scholar]
  92. Philipson TJ, Snyder JM. 1996.. Equilibrium and efficiency in an organized vote market. . Public Choice 89::24565
    [Google Scholar]
  93. Piketty T. 1994.. Information aggregation through voting and vote-trading. Unpublished manuscript, Mass. Inst. Technol., Cambridge:. http://www.jourdan.ens.fr/piketty/fichiers/public/Piketty1994c.pdf
    [Google Scholar]
  94. Posner EA, Weyl EG. 2015.. Voting squared: quadratic voting in democratic politics. . Vanderbilt Law Rev. 68::441500
    [Google Scholar]
  95. Ray D, Vohra R. 2015.. The farsighted stable set. . Econometrica 83::9771011
    [Google Scholar]
  96. Riker WH, Brams SJ. 1973.. The paradox of vote trading. . Am. Political Sci. Rev. 67::123547
    [Google Scholar]
  97. Riker WH, Ordeshook PC. 1968.. A theory of the calculus of voting. . Am. Political Sci. Rev. 62::2542
    [Google Scholar]
  98. Sawyer J, MacRae D. 1962.. Game theory and cumulative voting in Illinois: 1902–1954. . Am. Political Sci. Rev. 56::93646
    [Google Scholar]
  99. Schwartz T. 1975.. Vote trading and Pareto efficiency. . Public Choice 24::1019
    [Google Scholar]
  100. Schwartz T. 1977.. Collective choice, separation of issues and vote trading. . Am. Political Sci. Rev. 71::9991010
    [Google Scholar]
  101. Schwartz T. 1981.. The universal-instability theorem. . Public Choice 37::487501
    [Google Scholar]
  102. Shapley L, Shubik M. 1977.. Trade using one commodity as a means of payment. . J. Political Econ. 85::93768
    [Google Scholar]
  103. Shubik M, Van der Heyden L. 1978.. Logrolling and budget allocation games. . Int. J. Game Theory 7::15162
    [Google Scholar]
  104. Taylor CR, Yildirim H. 2010.. A unified analysis of rational voting with private values and group-specific costs. . Games Econ. Behav. 70::45771
    [Google Scholar]
  105. Tideman N, Plassmann F. 2017.. Efficient collective decision-making, marginal cost pricing, and quadratic voting. . Public Choice 172::4573
    [Google Scholar]
  106. Tsakas N, Xefteris D, Ziros N. 2021.. Vote trading in power-sharing systems: a laboratory investigation. . Econ. J. 131::184982
    [Google Scholar]
  107. Tullock G. 1959.. Problems of majority voting. . J. Political Econ. 67::57179
    [Google Scholar]
  108. Tullock G. 1961.. Problems of majority voting: reply to a traditionalist. . J. Political Econ. 69::2003
    [Google Scholar]
  109. Tullock G. 1970.. A simple algebraic logrolling model. . Am. Econ. Rev. 60::41926
    [Google Scholar]
  110. Vicente PC. 2014.. Is vote buying effective? Evidence from a field experiment in West Africa. . Econ. J. 124::F35687
    [Google Scholar]
  111. Walzer M. 1983.. Spheres of Justice: A Defense of Pluralism and Equality. New York:: Basic Books
    [Google Scholar]
  112. Weiss JH. 1988.. Is vote-selling desirable?. Public Choice 59::17794
    [Google Scholar]
  113. Weyl EG. 2017.. The robustness of quadratic voting. . Public Choice 172::75107
    [Google Scholar]
  114. Wilson R. 1969.. An axiomatic model of logrolling. . Am. Econ. Rev. 59::33141
    [Google Scholar]
  115. Xefteris D, Ziros N. 2017.. Strategic vote trading in power sharing systems. . Am. Econ. J. Microecon. 9::7694
    [Google Scholar]
  116. Xefteris D, Ziros N. 2018.. Strategic vote trading under complete information. . J. Math. Econ. 78::5258
    [Google Scholar]
/content/journals/10.1146/annurev-economics-081720-114422
Loading
/content/journals/10.1146/annurev-economics-081720-114422
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error