This introduction to the Public Choice special issue on “quadratic voting (QV) and the public good” provides an opinionated narrative summary of the contents and surveys the broader literature related to QV. QV is a voting rule, proposed by one of us Weyl (Quadratic vote buying. http://goo.gl/8YEO73, 2012), Lalley and Weyl (Quadratic voting. https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=2003531, 2016) building off earlier work by Groves and Ledyard (Econometrica 45(4):783–810 1977a), Hylland and Zeckhauser (A mechanism for selecting public goods when preferences must be elicited, Kennedy School of Government Discussion Paper D, 70, 1980), where individuals buy as many votes as they wish by paying the square of the votes they buy using some currency. An appreciation of the history of research in the field suggests that QV is uniquely practically relevant compared to the other approximately Pareto-efficient mechanisms economists have proposed for collective decisions on public goods. However, it faces a number of sociological and ethical concerns regarding how a political system organized around QV would achieve the efficiency aims stated in abstract theory and whether the pure aggregate income-maximizing definition of efficiency QV optimizes in its simplest form is desirable. The papers in this volume flesh out and formalize these concerns, but also provide important responses in two ways: by suggesting domains where they are unlikely to be applicable (primarily related to survey research of various kinds) and versions of QV (using an artificial currency) that maintain many of QV’s benefits while diffusing the most important critiques. Together this work suggests both a practical path for applying QV in the near-term and a series of research questions that would have to be addressed to broaden its application.
This is a preview of subscription content,to check access.
Access this article
Benjamin et al. also consider whether the NGA can be adapted to the goals of the basic form of QV: to make a binary decision allowing trade between real money and influence on that decision. Their motivation, beyond relating the mechanisms to each other theoretically, is to derive a version of QV in which individuals may report their preferences directly rather than having to buy votes in proportion to those preferences. This may be useful because it avoids individuals having to estimate their chances of their being pivotal. The only existing form of QV that is “direct” in this sense was proposed by Goeree and Zhang (Forthcoming) and applies only to the non-generic case when an election ends in an exact tie. Benjamin et al. use NGA to derive a version that works in the generic case when one alternative clearly is superior to the other. Like the Goeree and Zhang mechanism, however, this requires the designer to have very fine knowledge of the value distribution in order to choose the parameters appropriately. By contrast, QV requires no such details, even if it does demand from (very rational) participants speculation about their chances of being pivotal. However, as Weyl shows in his contribution, even if participants do not all share common views about this, are not very rational in forming their beliefs about it or are not even motivated by their chances of being pivotal, QV can perform quite well. These more direct mechanisms, by contrast, are simply ill-defined in such cases and thus cannot be applied. This is why we share the assessment of Benjamin et al. that this is “is not an implementation of NGA that we would actually recommend”.
However, as Posner and Stephanopoulos highlight, the party and primary systems might change significantly under mQV. The current two-party US system is to some extent an outgrowth of the necessity of forming viable coalitions created by the current first-past-the-post plurality voting system (Duverger 1959). In a system like mQV that would be less sensitive to various paradoxes of 1p1v’s rules, parties might be less necessary or at least more fluid and primaries thus might play a less central role.
Other budgeted methods, based on linear budgets, have been shown to give rise to extreme behavior similar to Likert, though in many cases even worse as respondents simply place none of their budget on issues other than those of most interest to them (Haley and Case 1979).
Arrow, K. (1951). Social choice and individual values. New York: Wiley.
Attiyeh, G., Franciosi, R., & Isaac, R. M. (2000). Experiments with the pivot process for providing public goods. Public Choice, 102(1–2), 95–114.
Bowen, H. R. (1943). The interpretation of voting in the allocation of economic resources. The Quarterly Journal of Economics, 58(1), 27–48.
Budish, E. (2011). The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. Journal of Political Economy, 119(6), 1061–1103.
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.
Clarke, E. H. (1971). Multipart pricing of public goods. Public Choice, 11(1), 17–33.
Duverger, M. (1959). Political parties: Their organization and activity in the modern state trans B. and R. North. London: Methuen.
Feddersen, T., & Pesendorfer, W. (1996). The swing voter’s curse. The American Economic Review, 86(3), 408–424.
Feddersen, T., & Pesendorfer, W. (1997). Voting behavior and information aggregation in elections with private information. Econometrica, 65(5), 1029–1058.
Feddersen, T., & Pesendorfer, W. (1998). Convicting the innocent: The inferiority of unanimous jury verdicts under strategic voting. American Political Science Review, 92(1), 23–35.
Goeree, J. K., & Zhang, J. (Forthcoming). One man, one bid. Games and Economic Behavior. doi:10.1016/j.geb.2016.10.003.
Groves, T. (1973). Incentives in teams. Econometrica, 41(4), 617–631.
Groves, T., & Ledyard, J. (1977a). Optimal allocation of public goods: A solution to the free rider problem. Econometrica, 45(4), 783–810.
Groves, T., & Ledyard, J. (1977b). Some limitations of demand-revealing processes. Public Choice, 29(2S), 107–124.
Haley, R. I., & Case, P. B. (1979). Testing thirteen attitude scales for agreement and brand discrimination. Journal of Marekting, 43(4), 20–32.
Hamilton, D. L. (1968). Personality attributes associated with extreme response style. Psychological Bulletin, 69(3), 192–203.
Hausman, J. (2012). Contingent valuation: From dubious to hopeless. The Journal of Economic Perspectives, 26(4), 43–56.
Hirschman, A. O. (1982). Shifting involvements: Private interests and public action. Oxford: Martin Robertson.
Hylland, A., & Zeckhauser, R. (1980). A mechanism for selecting public goods when preferences must be elicited, Kennedy School of Government Discussion Paper D, 70.
Laine, C. R. (1977). Strategy in point voting: A note. The Quarterly Journal of Economics, 91(3), 505–507.
Lalley, Steven P., & Weyl, E. Glen (2016). Quadratic voting. Available at: https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=2003531.
Mailath, G. J., & Postlewaite, A. (1990). Asymmetric information bargaining problems with many agents. Review of Economic Studies, 57(3), 351–367.
McLennan, A. (1998). Consequences of the Condorcet Jury Theorem for beneficial information aggregation by rational agents. American Political Science Review, 92(2), 413–418.
Mouffe, C. (1999). Deliberative democracy or agonistic pluralism? Social Research, 66(3), 745–758.
Mueller, D. C. (1973). Constitutional democracy and social welfare. The Quarterly Journal of Economics, 87(1), 60–80.
Mueller, D. C. (1977). Strategy in point voting: Comment. The Quarterly Journal of Economics, 91(3), 509.
Ober, J. (2013). Democracy’s wisdom: An Aristotelian middle way for collective judgment. American Political Science Review, 107(1), 104–122.
Petit, P. (2012). Analytical philosophy. In R. Goodin, P. Pettit, & T. Pogge (Eds.), A companion to contemporary political philosophy (pp. 5–35). Oxford: Blackwell.
Posner, E., & Weyl, E. G. (2014). Quadratic voting as efficient corporate governance. University of Chicago Law Review, 81(1), 251–272.
Posner, E., & Weyl, E. G. (2015). Voting squared: Quadratic voting in democratic politics. Vanderbilt Law Review, 68(2), 441–499.
Roberts, D. J. & Postelwaite, A. (1976). The incentives for price-taking behavior in large exchange economies. Econometrica, 44(1):115–127
Roth, A. E. (2008). What have we learned from market design? Economic Journal, 118(527), 285–310.
Samuelson, P. A. (1954). The pure theory of public expenditure. Review of Economics and Statistics, 36(4), 387–389.
Tideman, T. N., & Tullock, G. (1976). A new and superior process for making social choices. Journal of Political Economy, 84(6), 1145–1159.
Tuck, R. (2012). History. In R. Goodin, P. Pettit, & T. Pogge (Eds.), A companion to contemporary political philosophy (pp. 69–87). Oxford: Blackwell.
Vickrey, W. (1961). Counterspeculation, auctions, and competitive sealed tenders. The Journal of Finance, 16(1), 8–37.
Weyl, E. G. (2012). Quadratic vote buying. http://goo.gl/8YEO73.
Willig, R. (1976). Consumer’s surplus without apology. American Economic Review, 66(4), 589–597.
About this article
Cite this article
Posner, E.A., Weyl, E.G. Quadratic voting and the public good: introduction. Public Choice 172, 1–22 (2017). https://doi.org/10.1007/s11127-017-0404-5