Quadratic Election Law

Eric Posner and Nicholas Stephanopoulos

One of the major problems with the American political system, and indeed all political systems, is the difficulty of aggregating the values and interests of diverse populations. Many democratic countries employ a version of majority rule based on the principle of one-person-one-vote. But majority rule of this sort leads to tyranny of the majority: a majority that prefers one candidate only slightly to another candidate, or that prefers one choice in a referendum only slightly to another, can outvote a minority that cares intensely about the outcome. If people take turns being in the majority, the result is that over time the political system will generate policies that do not advance the public good. This may explain why the general public is often so unsatisfied with the political choices made by democracies. And if people don’t take turns being in the majority, the result is typically the systemic domination of a minority group, which must employ civil disobedience to protect its interests. The civil rights movement, of course, is the major example.

Our political system has struggled with these problems since the founding. The most important approach to them has been judicial enforcement of constitutional rights. Courts now routinely strike down majority-supported laws that harm certain “discrete and insular minorities,” like African Americans. However, judicial review is extremely controversial. Many people object to its undemocratic character, which allows judges to strike down laws that they disagree with for ideological reasons. Many other Band-Aids have been applied to our political system—from racial gerrymandering to executive discretion—but the public seems as unhappy as ever.

It’s a good time to rethink some of the premises of this system. The underlying problem—the difficulty of aggregating preferences for the purpose of making collective decisions—has preoccupied economists for decades. A recent proposal by the economist Glen Weyl offers an interesting solution called “quadratic voting.” Weyl points out that if the problem with one-person-one-vote is that it does not allow people to express the intensities of their political preferences, the remedy is a system that allows people to cast more votes for political outcomes they care about, while forcing them to cast fewer votes for political outcomes when they are indifferent.

In the version of quadratic voting that we explore, every citizen is given an equal budget of an artificial currency, which he uses to “buy” votes in different elections and referenda. The citizen pays the square of the number of votes he buys—for example, 4 units for 2 votes, 16 units for 4 votes. He could, for example, spend 4 units to cast 2 votes for one of the candidates in the mayoral election; 9 units to cast 3 votes for a presidential candidate; 0 units to cast 0 votes in a referendum; and so on. The ability to cast multiple votes in a particular contest allows the voter to express varying preference intensities, while the quadratic pricing mechanism and the budget constraint prevent him from exaggerating his support in contests that matter the most to him.

Exponential costs

Could quadratic voting be used in place of the current system for state and federal elections, and for state referenda? Within broad constraints set by constitutional law and American political norms, it could. And if so, it could have a number of beneficial effects for recurrent controversies across the electoral domain.

With respect to the lawfulness of quadratic voting, there are three relevant lines of Supreme Court precedent, of which two are favorable and one is more ambiguous. First, in a series of 1960s cases, the Court prohibited electoral rules from distinguishing between rich and poor voters. Quadratic voting makes no such distinction, since every voter, regardless of his wealth, is allotted the same number of votes. Second, the Court subjects electoral rules to what is known as “sliding-scale scrutiny,” under which the intensity of judicial review varies based on the severity of a rule’s burden on the right to vote. Quadratic voting imposes no more of a burden than any other nondiscriminatory voting system. Whatever burden it levies is also justified by the compelling ends it serves: avoiding the tyranny of the majority and increasing voter welfare.

And third, the Court’s one-person-one-vote principle requires not just equally sized districts but also voter equality more generally. At a high level, quadratic voting is consistent with voter equality, since each voter receives the same budget of the artificial currency. In particular elections, though, quadratic voting implies (in fact, requires) that voters will cast different numbers of ballots. Given that courts have upheld the voting systems most similar to quadratic voting (cumulative and preferential voting), we are cautiously optimistic that it would be sustained despite its election-specific inequality. But we must concede that its constitutionality is not entirely assured.

If quadratic voting were implemented, its most dramatic consequences might be in the area of redistricting. At present, partisan gerrymandering is widespread throughout America. Gerrymandering relies on the mapmaker’s ability to predict with reasonable accuracy how a district will perform in the future. A district that is drawn to favor the gerrymandering party by 55 percent to 45 percent, for example, can usually be expected to elect that party’s candidate for the rest of the decade.

Quadratic voting throws a wrench into these calculations. Take the 55 percent–45 percent district whose performance is fairly certain under the status quo. Under quadratic voting, it is quite unclear who would win this district. The members of the minority might have more intense preferences than the individuals in the majority, in which case it would take only a few additional votes per minority member to flip the district’s outcome. Or the majority might feel more strongly than the minority, in which case a race that was forecast to be close would turn into a blowout. The general point is that quadratic voting undermines the prognostications on which gerrymandering depends. It thus makes it more difficult to gerrymander effectively.

In this conference presentation, Nicholas Stephanopoulos identifies the legal barriers to the adoption of quadratic voting, discusses modified versions that could pass muster, and shows how even a modified version would address many of the pathologies of the existing system.

Another advantage of quadratic voting is that it could avert the need to hold separate primary and general elections. The basic rationale for primaries is that they allow the major parties to winnow their candidates to a single nominee. That way the parties do not risk losing winnable races due to the fragmentation of their general election vote. But under quadratic voting, voters may vote for and against multiple candidates, and to different degrees. They are not forced to choose one candidate for whom to cast their one ballot. Fields featuring several candidates, even several candidates from the same party, therefore become much less problematic. By properly calibrating and ordering their choices, voters may prevent so-called “wrong-winner outcomes” from arising.

In the campaign finance context too, quadratic voting could helpfully change how candidates deploy their resources. Currently, candidates focus their efforts (and their spending) on the small proportion of moderate or independent voters who could plausibly support either candidate. The far larger masses of voters whose views are set are mostly ignored. But under quadratic voting, all equally sized changes in voter intensity are equally valuable, whether they occur among mushy centrists or rigid ideologues. More votes are more votes, no matter who casts them. Candidates would thus have an incentive to spend money advertising to all voters (or at least all voters whose intensity could shift significantly). Our campaigns would no longer be dominated by targeted appeals to a narrow minority of the electorate.

Campaign finance also prompts our final point about quadratic voting, which is that its logic can be extended beyond the ballot itself. Instead of purchasing votes quadratically, for instance, citizens could buy contributions to candidates. Four dollars would result in a 2-dollar donation, 16 dollars in a 4-dollar donation, and so on, with the extra funds either going to the Treasury or subsidizing smaller contributions. Similarly, voters could be provided with publicly financed vouchers, which they would then convert quadratically into donations.

Of course, votes and dollars are not identical for decision-making purposes. Crucially, votes directly determine electoral outcomes, while dollars only indirectly influence them. Nevertheless, dollars do at least play a role in how races are won and how policy is then enacted. This role means that if they too were subjected to quadratic dynamics, societal welfare would again increase.



Eric Posner is Kirkland & Ellis Distinguished Service Professor of Law and Arthur and Esther Kane Research Chair. Nicholas Stephanopoulos is an Assistant Professor of Law.

Professors Posner and Stephanopoulos’s paper on quadratic election law is available on SSRN. The paper, along with other papers from the Becker-Friedman Institute’s conference on “Quadratic Voting and the Public Good,” will be published in a special issue of Public Choice in 2017.