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Quadratic election law


The standard form of electoral system in the United States—plurality voting with one person, one vote—suffers from countless defects, many of which stem from its failure to enable people to register the intensity of their preferences for political outcomes when they vote. Quadratic voting, an elegant alternative system proposed by Glen Weyl, provides a theoretically attractive solution to this problem but is an awkward fit with America’s legal and political traditions. We identify the legal barriers to the adoption of quadratic voting, discuss modified versions that could pass muster, and show how even a modified version would address many of the pathologies of the existing system.

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  1. The exact number of credits would depend on the number of elections.

  2. This might be understood in monetary terms, albeit with the understanding that wealth differences could skew outcomes.

  3. The problem is that it also can give the majority excessive power, and may tax the attention of voters.

  4. When we refer to “modified QV,” we mean QV with equal budgets. We generally refer to the representative version, but most of what we say would apply to the referendum version as well.

  5. It may be possible to distinguish these precedents on the ground that they addressed voting systems whose purpose and effect were to block certain categories of people—the poor and urban residents, respectively—from influencing electoral outcomes. By contrast, pure QV gives everyone—poor or rich, urban or rural—the ability to convert their dollars into votes. Moreover, by redistributing the funds collected from vote purchases, pure QV effectively gives the poor an entitlement they lacked under the systems struck down by the Court. However, these distinctions probably do not blunt the precedents’ force. They do mean that pure QV is quite different from a poll tax or a malapportioned district plan. But the Court’s decisions are written broadly enough to encompass not just these policies, but also others that share the crucial defect of differentiating among voters.

  6. Like cumulative or preferential voting, QV also serves the “legitimate interest[] in providing voters an opportunity to express nuanced voting preferences” (Dudum v. Arntz 2011, at 1116).

  7. The problem for the line-drawer is that as the gerrymander becomes more extreme, the minority in the district will have a stronger incentive to expend credits for its favored candidate. This adds to the cost of gerrymandering under QV.

  8. This discussion focuses on a district plan in its entirety—the level at which gerrymandering takes place. But modified QV would also have beneficial consequences in individual districts. It would reduce the likelihood of election of candidates whose views differ radically from those of the electorate, since voters could cast more votes to prevent such candidates from prevailing.

  9. However, even if minorities are unable to elect their most preferred candidate in a given district, modified QV may enable them to prevent their least preferred candidate from being elected. Minorities could credibly threaten to cast many more votes to oppose, say, a racist candidate. And this point is generalizable: Because extreme candidates may be expected to provoke more intense opposition, modified QV should benefit more moderate candidates, even if they do not belong to certain voters’ race or party of choice.

  10. This, of course, is not the only goal of money in politics. It may also be used, for example, to spur turnout or to pave the way for particular policies to be enacted.

  11. A related justification is that campaign speech can be seen as a public good (at least in some of its forms), and QV is an efficient mechanism for providing public goods.

  12. The cutoff between public financing and taxing would be located at the square of the multiplier. With a multiplier of 10, for example, a $100 donation would result in $100 going to the campaign (($100^.5) × 10).

  13. As noted above, a secondary interest advanced by QV-based campaign finance is incentivizing small donations and expenditures, which are augmented by the multiplier.

  14. Presumably, the same currency would be used in primaries as in general elections; voters would be able to make tradeoffs among primary and general election races as they saw fit.

  15. For example, assume that Donald Trump wins 40% of the vote in a primary, Ted Cruz wins 35%, and Marco Rubio wins 25%, but that Rubio would beat either Trump or Cruz in a head-to-head matchup. Then Trump prevails even though a majority of voters prefer Rubio.


  • Ackerman, B., & Ayres, I. (2002). Voting with dollars: A new paradigm for campaign finance. London: Yale University Press.

    Google Scholar 

  • Barber, M. (2014). Representing the preferences of voters, partisans, and donors in the U.S. Senate. Unpub. m.s.

  • Brennan Center for Justice. (2016). States with new voting restrictions since the 2010 election.

  • Cox, A. B., & Holden, R. T. (2011). Reconsidering racial and partisan gerrymandering. University of Chicago Law Review, 78, 553.

    Google Scholar 

  • FairVote for a More Perfect Union. (2016). Primaries.

  • Gilens, M. (2012). Affluence and influence: Economic inequality and political power in America. Princeton: Princeton University Press.

    Google Scholar 

  • Grofman, B., & Brunell, T. L. (2005). The art of the dummymander: The impact of recent redistrictings on the partisan makeup of southern house seats. In P. Galderisi (Ed.), Redistricting in the new millennium. Lanham: Lexington Books.

    Google Scholar 

  • Hasen, R. L. (1996). Clipping coupons for democracy: An egalitarian/public choice defense of campaign finance vouchers. California Law Review, 84, 1.

    Article  Google Scholar 

  • Klarner, C. E., & Evans, H. (2015). Retrospectives on the state legislative and gubernatorial elections of 2014. Unpub. m.s.

  • Lalley, S. P., & Weyl, E. G. (2016). Quadratic voting. Unpub. m.s.

  • Laurence, B., & Sher, I. (2016). Ethical considerations on quadratic voting. Public Choice.

  • Ober, J. (2016). Equality, legitimacy, interests, and preferences: Historical notes on quadratic voting in a political context. Public Choice.

  • Pew Research Center. (2015). A deep dive into partisan affiliation.

  • Posner, E. A., & Weyl, E. G. (2015). Voting squared: Quadratic voting in democratic politics. Vanderbilt Law Review, 68, 441.

    Google Scholar 

  • Stephanopoulos, N. O. (2013). Our electoral exceptionalism. University of Chicago Law Review, 80, 769.

    Google Scholar 

  • Stephanopoulos, N. O. (2014). Elections and alignment. Columbia Law Review, 114, 283.

    Google Scholar 

  • Stephanopoulos, N. O. (2015). Aligning campaign finance law. Virginia Law Review, 101, 1425.

    Google Scholar 

  • Stephanopoulos, N. O. (2016). Race, place, and power. Stanford Law Review (forthcoming).

  • Stephanopoulos, N. O., & McGhee, E. M. (2015). Partisan gerrymandering and the efficiency gap. University of Chicago Law Review, 82, 831.

    Google Scholar 

  • Weyl, E. G. (2012). Quadratic vote buying. Unpub. m.s.


  • Ariz. Free Enter. Club’s Freedom Club PAC v. Bennett, 131 S. Ct. 2806 (2011).

  • Buckley v. Valeo, 424 U.S. 1 (1976).

  • Burdick v. Takushi, 504 U.S. 428 (1992).

  • Cal. Dem. Party v. Jones, 530 U.S. 567 (2000).

  • Crawford v. Marion Cty. Elec. Bd., 553 U.S. 181 (2008).

  • Dudum v. Arntz, 640 F.3d 1098 (9th Cir. 2011).

  • Gray v. Sanders, 372 U.S. 368 (1963).

  • Harper v. Va. St. Bd. of Elec., 383 U.S. 663 (1966).

  • McCoy v. Chicago Hghts., 6 F. Supp. 2d 973 (N.D. Ill. 1998).

  • McCutcheon v. FEC, 134 S. Ct. 1434 (2014).

  • Minn. Voters Alliance v. City of Minneapolis, 766 N.W.2d 683 (Minn. 2009).

  • Nixon v. Shrink Mo. Gov’t PAC, 528 U.S. 377 (2000).

  • Reynolds v. Sims, 377 U.S. 533 (1964).

  • United Jewish Orgs. v. Carey, 430 U.S. 144 (1977).

  • Wash. State Grange v. Wash. State Rep. Party, 552 U.S. 442 (2008).

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Thanks to Glen Weyl and participants at the conference on quadratic voting, as well as at a conference at the Washburn University School of Law, for helpful comments. Posner thanks the Russell Baker Scholars Fund for financial support.

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Correspondence to Eric A. Posner.

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Posner, E.A., Stephanopoulos, N.O. Quadratic election law. Public Choice 172, 265–282 (2017).

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  • Electoral systems
  • Election law
  • Collective decision-making