The Good Way to Buy Votes

Did New Yorkers really want bike sharing? The city should have tried Quadratic Vote Buying to figure that out.

This is a local copy of an article by Eric Posner in Slate 5 June 2013. We do not endorse it.

New York City's Bike Share program launched last week to enthusiasm but also complaints, epitomized by Dorothy Rabinowitz's infamous video rant at the Wall Street Journal against the "totalitarians" who run the city and are "begriming" its neighborhoods with "blazing blue Citibank bikes." While Rabinowitz has been met with ridicule, her objections raise a serious question: How should a city decide when to implement a public project that people are clamoring both for and against?

New Yorkers live in a democracy, and one possible response is that they elected their mayor and must live with his decisions. But mayors make mistakes, and New Yorkers have no practical way to punish Mayor Michael Bloomberg if they do not like his decisions because he is a lame duck who cannot run for re-election. And even if Bloomberg sought to act in the public good, how would he know how to weight the views of NYC Bike Share fans and foes? Polling might help, but polls don't aggregate the strength of people's preferences. They give equal weight to a passionate opponent like Rabinowitz and a person who doesn't really care.

Many states let the voters decide big questions, like same-sex marriage, through ballot referendums. But this kind of direct democracy is controversial. The problem is that an indifferent majority can outvote a passionate minority. In 2008, when California's gay marriage ban was on the ballot, many people probably voted for it simply because gay marriage seemed strange, without a strong stake in the outcome. By contrast, the issue is of considerable significance to a minority—the gay couples it affects. If they care a lot, and the majority cares a little, it seems reasonable that minority interests should prevail. But the ordinary one-person, one-vote rule dictates otherwise.

Economists have given a lot of thought to this problem. In writing about what's called "mechanism design," they have invented an array of ingenious procedures for aggregating people's preferences, taking into account their intensity. The U.S. government has used their proposals to auction off rights to the electromagnetic spectrum for communications, including television broadcasts. Other mechanisms that take into account intensity of preference have been used for matching residents and hospitals, and kidney donors and recipients. Economists like William Vickrey, Alvin Roth, and Lloyd Shapley have received Nobel Prizes in recognition for their work in this field.

The effort to develop a mechanism that would aggregate preferences for public goods like NYC Bike Share has been less successful. The most famous attempt, known as the Vickrey-Clarke-Groves mechanism (named after its inventors, including William Vickrey) resembles an auction in which the winners submit bids (for or against a project like Bike Share), and the project is approved if the total in favor exceeds the total against, while any winner whose vote is pivotal to the outcome must make a partial payment to the losers. But the VCG mechanism has never been used because it can be gamed pretty easily (for example, people can avoid being pivotal voters by getting together), wastes money, and is probably too complicated.

Recently, however, an economist at the University of Chicago named Glen Weyl has developed an ingenious new mechanism that is simpler and more robust, and could help a city decide whether to introduce bike sharing. He calls it Quadratic Vote Buying and it works like this.

Consider a group of New Yorkers, Anne, Bruce, and Carla. The city is trying to decide whether to implement a bike sharing program. Under QVB, each person has the right to buy as many votes as he wants at a price equal to the square of the number of votes that he buys:

Number of Votes        Price
1                                   $1
2                                   $4
3                                   $9
10                                 $100

The outcome is determined by majority rule, based on this method of vote calculation. If Anne buys eight votes in favor of the program, Bruce buys four votes against, and Carla buys two votes against, then the program is approved by a vote of eight to six. By contrast, with ordinary voting the project would be rejected two to one. Voters vote and pay through a mobile app or website.

And then their payments are distributed—to each other, in equal shares. Anne paid $64, Bruce paid $16, and Carla paid $4, for a total of $84, and now each person receives a third of that total, $28. Anne's net loss is $36, but she benefits from the bike-sharing program, while Bruce nets $12 and Carla nets $24, buffering their relative levels of disappointment. The redistribution of the money reduces the impact of a loss, in contrast to a winner-take-all system like ordinary voting.

Not everyone is made better off by the program even with redistribution. (Bruce is a little worse off because he received a bit less than he would have paid to block the program.) But over time, as additional votes are held on additional city projects, it is highly likely that everyone gains more than he or she loses. This is again in contrast with ordinary voting, where a minority can be repeatedly outvoted.

Why does QVB work? It forces voters to pay for the impact of their votes on other people, in the same way that a tax forces factories to take into account the effects of pollution on others. In economic terms, the voter chooses a number of votes that equalizes the marginal benefit for her, in terms of her influence on policy, and the marginal cost for those who vote the other way. People who are dying for bike sharing exert more influence than those who are kind of anti—but squaring the cost of voting ensures that they don't go too far.

The major objection to QVB is that people must pay to vote, and thus wealthy people will influence outcomes more than poor people do. There are several responses.

First, because the price of voting is the square of the number of votes cast, the price goes up extremely quickly. If Donald Trump wants to spend $1 million to oppose the bike-sharing program, he will be able to cast only 1,000 votes—a drop in the bucket relative to the number of New York voters who would be willing to pay a dollar or so to be heard. And although there may be troublesome cases in which rich people align themselves against the poor, the bike-sharing program is not one of them. Mayor Bloomberg could easily outvote the Donald.

Second, keep in mind that the collected funds are returned to New Yorkers. If Trump spends $1 million to outvote cyclers, he's going to get little of his money back, while all the people who buy only a handful of votes will rake in his money. This will happen whether or not Trump wins. And, for the poorest New Yorkers, the money will be a lot more valuable than whatever modest advantage they would obtain from renting bikes.

Third, the QVB system can be modified to weaken the influence of wealth. A city could cap the number of votes that people may cast, or use chits or coupons rather than votes. Imagine, for example, that New York raises taxes by $100 per person, and then gives people $100 in votes that they can cast in different referendums. People who don't spend any of their coupons could instead trade them back for cash. Under this system, the advantage of wealth would be minimal.

There are other contexts in which QVB could be valuable. Glen Weyl and I have argued that it could be used for corporate governance—for example, as a way for shareholders to approve or reject a proposed merger. In this context, worries about buying votes should play no role because that already happens, when people buy additional shares. Employers could also use QVB to evaluate demand among employees for amenities like gyms.

New York's Bike Share program uses 21st-century technology to make it easy for customers to rent bikes. But it is using the primordial method of the mayoral election to determine its citizens preferences. To be truly forward-thinking, the city should switch to QVB. Along with bikes, it's the future.


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