Public Choice

, Volume 172, Issue 1–2, pp 75–107 | Cite as

The robustness of quadratic voting

Article

Abstract

Lalley and Weyl (Quadratic voting, 2016) propose a mechanism for binary collective decisions, Quadratic Voting (QV), and prove its approximate efficiency in large populations in a stylized environment. They motivate their proposal substantially based on its greater robustness when compared with pre-existing efficient collective decision mechanisms. However, these suggestions are based purely on discussion of structural properties of the mechanism. In this paper, I study these robustness properties quantitatively in an equilibrium model. Given the mathematical challenges with establishing results on QV fully formally, my analysis relies on a number of structural conjectures that have been proven in analogous settings in the literature, but in the models I consider here. While most of the factors I study reduce the efficiency of QV to some extent, it is reasonably robust to all of them and quite robustly outperforms one-person-one-vote. Collusion and fraud, except on a very large scale, are deterred either by unilateral deviation incentives or by the reactions of non-participants to the possibility of their occurring. I am able to study aggregate uncertainty only for particular parametric distributions, but using the most canonical structures in the literature I find that such uncertainty reduces limiting efficiency, but never by a large magnitude. Voter mistakes or non-instrumental motivations for voting, so long as they are uncorrelated with values, may either enhance or harm efficiency depending on the setting. These findings contrast with existing (approximately) efficient mechanisms, all of which are highly sensitive to at least one of these factors.

Keywords

Robust mechanism design Quadratic voting Collusion Paradox of voting 

JEL Classification

D47 D61 D71 C72 D82 H41 P16 

References

  1. Adler, A. (2006). Exact laws for sums of ratios of order statistics from the pareto distribution. Central European Journal of Mathematics, 4(1), 1–4.CrossRefGoogle Scholar
  2. Arrow, K. J. (1979). The property rights doctrine and demand revelation under incomplete information. In M. Boskin (Ed.), Economics and human welfare (pp. 23–39). New York: Academic Press.CrossRefGoogle Scholar
  3. Ausubel, L. M., & Milgrom, P. (2005). The lovely but lonely Vickrey auction. In P. Cramton, R. Steinberg, & Y. Shoham (Eds.), Combinatorial auctions (pp. 17–40). Cambridge, MA: MIT Press.CrossRefGoogle Scholar
  4. Blais, A. (2000). To vote or not to vote: The merits and limits of rational choice theory. Pittsburgh, PA: University of Pittsburgh Press.Google Scholar
  5. Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. K. (1987). Occam’s razor. Information Processing Letters, 24(6), 377–380.CrossRefGoogle Scholar
  6. Cárdenas, J. C., Mantilla, C., & Zárate, R. D. (2014). Purchasing votes without cash: Implementing quadratic voting outside the lab. http://www.aeaweb.org/aea/2015conference/program/retrieve.php?pdfid=719.
  7. Chamberlain, G., & Rothschild, M. (1981). A note on the probability of casting a decisive vote. Journal of Economic Theory, 25(1), 152–162.CrossRefGoogle Scholar
  8. Chandar, B., & Weyl, E. G. (2016). The efficiency of quadratic voting in finite populations. http://ssrn.com/abstract=2571026.
  9. Clarke, E. H. (1971). Multipart pricing of public goods. Public Choice, 11(1), 17–33.CrossRefGoogle Scholar
  10. d’Aspremont, C., & Gérard-Varet, L. A. (1979). Incentives and incomplete information. Journal of Public Economics, 11(1), 25–45.CrossRefGoogle Scholar
  11. DellaVigna, S., List, J. A., Malmendier, U., & Rao, G. (2017). Voting to tell others. Review of Economic Studies, 84(1), 143–181.CrossRefGoogle Scholar
  12. Downs, A. (1957). An economic theory of democracy. New York: Harper.Google Scholar
  13. Fiorina, M. P. (1976). The voting decision: Instrumental and expressive aspects. Journal of Politics, 38(2), 390–413.CrossRefGoogle Scholar
  14. Gelman, A., Silver, N., & Edlin, A. (2010). What is the probability your vote will make a difference? Economic Inquiry, 50(2), 321–326.CrossRefGoogle Scholar
  15. Goeree, J. K., & Zhang, J. (Forthcoming). One man, one bid. Games and Economic Behavior.Google Scholar
  16. Good, I. J., & Mayer, L. S. (1975). Estimating the efficacy of a vote. Behavioral Science, 20(1), 25–33.CrossRefGoogle Scholar
  17. Groves, T. (1973). Incentives in teams. Econometrica, 41(4), 617–631.CrossRefGoogle Scholar
  18. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–292.CrossRefGoogle Scholar
  19. Kawai, K., & Watanabe, Y. (2013). Inferring strategic voting. American Economic Review, 103(2), 624–662.CrossRefGoogle Scholar
  20. Klüppelberg, C., & Mikosch, T. (1997). Large deviations of heavy-tailed random sums with applications in insurance and finance. Journal of Applied Probability, 34(2), 293–308.CrossRefGoogle Scholar
  21. Krishna, V., & Morgan, J. (2001). Asymmetric information and legislative rules: Some ammendments. American Political Science Review, 95(2), 435–452.CrossRefGoogle Scholar
  22. Krishna, V., & Morgan, J. (2012). Majority rule and utilitarian welfare. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2083248.
  23. Krishna, V., & Morgan, J. (2015). Majority rule and utilitarian welfare. American Economic Journal: Microeconomics, 7(4), 339–375.Google Scholar
  24. Laffont, J. J., & Martimort, D. (1997). Collusion under asymmetric information. Econometrica, 65(4), 875–911.CrossRefGoogle Scholar
  25. Laffont, J. J., & Martimort, D. (2000). Mechanism design with collusion and correlation. Econometrica, 68(2), 309–342.CrossRefGoogle Scholar
  26. Laine, C. R. (1977). Strategy in point voting: A note. Quarterly Journal of Economics, 91(3), 505–507.CrossRefGoogle Scholar
  27. Lalley, S. P., & Weyl, E. G. (2016). Quadratic voting. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2003531.
  28. Ledyard, J. (1984). The pure theory of large two-candidate elections. Public Choice, 44(1), 7–41.CrossRefGoogle Scholar
  29. Ledyard, J. O., & Palfrey, T. R. (1994). Voting and lottery drafts as efficient public goods mechanisms. Review of Economic Studies, 61(2), 327–355.CrossRefGoogle Scholar
  30. Ledyard, J. O., & Palfrey, T. R. (2002). The approximation of efficient public good mechanisms by simple voting schemes. Journal of Public Economics, 83(2), 153–171.CrossRefGoogle Scholar
  31. McLean, R. P., & Postelwaite, A. (2015). Implementation with interdependent values. Theoretical Economics, 10(3), 923–952.CrossRefGoogle Scholar
  32. Milgrom, P. R. (1981). Good news and bad news: Representation theorems and applications. Bell Journal of Economics, 12(2), 380–391.CrossRefGoogle Scholar
  33. Milgrom, P. R., & Weber, R. J. (1982). A theory of auctions and competitive bidding. Econometrica, 50(5), 1089–1122.CrossRefGoogle Scholar
  34. Mueller, D. C. (1973). Constitutional democracy and social welfare. Quarterly Journal of Economics, 87(1), 60–80.CrossRefGoogle Scholar
  35. Mueller, D. C. (1977). Strategy in point voting: Comment. Quarterly Journal of Economics, 91(3), 509.CrossRefGoogle Scholar
  36. Myerson, R. B. (2000). Large poisson games. Journal of Economic Theory, 94(1), 7–45.CrossRefGoogle Scholar
  37. Stigler, G. J. (1964). A theory of oligopoly. Journal of Political Economy, 72(1), 44–61.CrossRefGoogle Scholar
  38. Thompson, E. A. (1966). A pareto-efficient group decision process. Public Choice, 1(1), 133–140.CrossRefGoogle Scholar
  39. Tideman, N. N., & Tullock, G. (1976). A new and superior process for making social choices. Journal of Political Economy, 84(6), 1145–1159.CrossRefGoogle Scholar
  40. Vickrey, W. (1961). Counterspeculation, auctions and competitive sealed tenders. Journal of Finance, 16(1), 8–37.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.New York CityUSA

Personalised recommendations