Democracy and Quadratic Voting

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 ranked choice voting, which 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. Approval voting fulfills Arrow’s criteria and isn’t impossible, so a lot of professional societies use it to elect their leadership.2

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.