Glen Weyl and I have posted a revised draft of Voting Squared on SSRN. We argue that quadratic voting can and should play a role in democratic decisionmaking.

Quadratic voting is a voting procedure where people are allowed to buy votes for or against a proposal (or candidate) by paying the square of the number of votes they cast (e.g., 3 votes cost $9). The votes are totaled up and the majority prevails. Quadratic voting enables people with strong interests in an outcome to exert influence in proportion to the strength of their interest, so a passionate numerical minority of voters may be able to outvote an indifferent majority. Weyl shows  in another paper that with a sufficiently large population (say, a few dozen), a proposal will win a quadratic vote if and only if the aggregate gains to the winners exceed the aggregate losses to the losers in willingness-to-pay terms.

The main point of our joint paper is that conventional voting rules (for example, one-person-one-vote with majority rule) do a very bad job because they provide people with no way to exert influence on outcomes in proportion to the intensity of the effect of those outcomes on their well-being. This leads to the familiar tyranny-of-the-majority problem. We then discuss all the ways that have been developed to address this problem–judicial review, cost-benefit analysis, supermajority rule, and so on–and show that they do worse than quadratic voting would if it were implemented.

Finally, we address the objections to quadratic voting for democratic politics, including:

• It would favor the rich.
• It would violate a taboo against vote-buying.
• It would lead to political instability.

We show that these objections are mistaken.