science

The Democratic caucus of the Colorado State House of Representatives had a problem—but it was the good kind. The 2016 election put Democrats in charge of the House, the State Senate, and the governorship. Now it was time to decide, out of somewhere between 60 and 100 appropriations bills, which policies to fund first. But … well, you know how Democrats are, right? The only thing they really agree on is that the most efficient shape for a firing squad is a circle.

The state reps could have just voted, of course, but each of those 41 Democrats in the House was probably the sponsor of at least one of those bills. So they’d vote out of self-interest. No help there. What the Dems needed was a way to capture desire, to know which bills were everyone’s priority. “We have a limited pot of money to spend on new legislation every year,” says Chris Hansen, a state representative from Denver and chair of the House Appropriations Committee. “So we needed to devise a method for accurately capturing the preference of those caucus members.” Hansen isn’t just a pol. He’s a PhD energy economist with an interest in game theory. He’s open to weird science, is the point. So a pal of his, hearing about his plight, told him about a new idea: quadratic voting.

The result of some concept work by a Microsoft Research economist named Glen Weyl, quadratic voting is designed to force people to express their honest opinions about their choices by attaching a cost. One vote costs one unit of value—in its purest form, you would literally buy that vote with your own hard-earned American dollars. But not so fast, because the cost of a vote increases—by the number of votes times itself, to be precise. (That's the "quadratic" part.)¹ So two votes cost four dollars; three votes cost nine. Ten votes? One hundred dollars. The point is, you can yell as loudly as you want, but louder yelling costs more—so you have to be really incentivized to do it.

“Fundamentally, quadratic voting addresses the problem of the tyranny of the majority, a standard criticism of democracy,” Weyl says. “Standard rules are based on the notion that everybody is exactly the same and cares the same amount. If you doubt that’s a problem, think about the plight of African Americans in the United States, or the drug war, which dramatically affects certain groups of people.” But with quadratic voting, you can vote harder on what’s closer to home. And when the vote is over, all the money in the pot gets distributed to each voter equally, which is supposed to sort of re-grade the playing field for next time.

Like a lot of other similarly intricate ideas, quadratic voting sets out to solve a fundamental problem in the field of “social choice,” which is to say, how groups of people choose what they want. It may seem like the purest solution is one-person-one-vote, sometimes delightfully abbreviated as “1p1v.” But it doesn’t work as well as it should. Like, a “plurality election” is where the candidate with the most votes wins, but when you have multiple candidates, it’s possible for someone to get a small number of votes but still win if his or her total was higher than the next candidate down. (That happens in a crowded presidential primary.) The American Electoral College system allocates points on a state-by-state, winner take all basis, which means someone can lose the 1p1v “popular” vote by quite a lot and still win. (Hello, Mr. President.) And in the US, slightly more than half of voters, or half of congress, can enforce their will over the other less-than-half—even if the numbers are really close or the will is really disproportionate.

Plenty of other options exist. In a “Borda Count,” named after the French scientist Jean-Charles de Borda, people put candidates in order of preference. There’s an approach called “antiplurality,” where everyone chooses their least favorite candidate, and whoever gets the fewest votes wins. And what you’d like in any multi-choice election is for the “Condorcet winner” to also be the actual winner—which is to say, the thing that would beat all other things in head-to-head races should also win the overall race. So for example, all other concerns aside, in the 2016 election, Hillary Clinton beat Bernie Sanders and Donald Trump beat a lot of other people. Then Donald Trump beat Hillary Clinton. But would Clinton have lost to Jeb Bush? Would Bernie Sanders have lost to Trump?

What? Too soon?

In any case, this is all hard to fix in practice. Maybe even—as the 1950s economist Kenneth Arrow proposed—impossible. In fact, he won a Nobel Prize for his perhaps-too-on-the-nosedly named Arrow’s Impossibility Theorem, which says … eh, you can probably guess. Arrow came up with a bunch of criteria for an election that let everyone express their personal truth but didn’t let weird counting methods screw a choice unfairly, and showed with math that no method would allow it to happen. Democracy! So bad, right?

So people have suggested approaches to make democracy less impossible. Cities in the California Bay Area frequently use approval voting. It can lead to its own kind of confusion while counts get redone as candidates get knocked out of the running, as happened last year in San Francisco. But it fulfills Arrow’s criteria and isn’t impossible, so a lot of professional societies use it to elect their leadership.

Hansen and the Colorado Democrats had tried to solve these kinds of problems before. Last year they arbitrarily assigned everyone 15 tokens to put on their 15 favorite bills. This might work for priorities at a company retreat, but for budgeting, it “didn’t give us as good a signal,” Hansen says. So after talking to Weyl and working with software developers he knew, the caucus put together a computer interface to serve a modified version of quadratic voting. No dollars here. The members weren’t using their own money—each of them got 100 virtual tokens to buy votes. And unlike Weyl’s original version, the tokens didn’t get redistributed to all the voters at the end.

So in mid-April, the representatives voted. Sure, each one could have put ten tokens on their pet project. But consider the or: Nine votes on one (cost: 81 tokens) but then three votes on another (cost: nine tokens). Or five votes each (25 tokens) on four different bills!

In Colorado at least, it worked, kind of. “There was a pretty clear signal on which items, which bills, were the most important for the caucus to fund,” Hansen says. The winner was Senate Bill 85, the Equal Pay for Equal Work Act, with 60 votes. “And then there’s kind of a long tail,” Hansen says. “The difference was much more clear with quadratic voting.” This use case is somewhat unusual, of course. The bills still have to get past the Senate and get signed by the Governor—not impossible, with all Democrats in charge.

As a test case, the appropriations vote at least advances the hypothesis that quadratic voting (or some other equally tricksy system) could improve the American Experiment. Maybe the nation’s seemingly intractable political divisions aren’t a product of Russians, racism, and algorithms but a system that doesn’t let everyone speak with an authentic voice. “Many of these methods have advantages, and most of the experts agree that those other methods are preferable,” says Dan Ullman, a mathematician who teaches a mathematics and policy class at George Washington University and, to be clear, thinks the Electoral College is pretty dumb. Quadratic voting, though? “I’m not so persuaded,” Ullman says. “It’s very different from one person, one vote, and cost-free voting is very American, in my opinion. It seems like people value the right to vote as something that is intrinsic, that it doesn’t cost anything and you’re allowed to express yourself as loudly as you want.”

To be even clearer, in reality you probably don’t want people to be able to buy influence. Quadratic voting would potentially be a real friend to, for example, the not-in-my-backyard side of density fights, where a minority that cares deeply about a vacant lot might be actively jeopardizing the welfare of the majority. And these problems get even worse in a system corrupted by pricey lobbyists and dark-money campaign contributions. Some people already pay for a louder voice. Weyl acknowledges this; he says the first approximate uses of quadratic votes should probably use an artificial currency like the Colorado tokens—at least until all of us are on the same level of Universal Basic Income and have the same starting-point bank account. (This might be why some blockchain advocates have embraced the idea.) “The truth is, no one actually lives in ‘one person, one vote.’ It’s like an imaginary thing,” Weyl says. Things like municipalities, electoral colleges, and bicameral legislatures are really just improvisatory compromises. “So we think, oh, the problem is we don’t have enough democracy. But if you can actually solve it with a general-purpose solution, you don’t need all these kludgy things that solve it really poorly.” Fixing democracy sounds difficult—but not impossible.

¹ Updated 4/16/19 10:30 AM PDT Fixed the explanation of the math.

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