Glen Weyl has uploaded a new version of his paper, Quadratic Voting (written with Steven Lalley), to SSRN, which now includes the completed proofs. Quadratic voting is the most important idea for law and public policy that has emerged from economics in (at least) the last ten years.

Quadratic voting is a procedure that a group of people can use to jointly choose a collective good for themselves. Each person can buy votes for or against a proposal by paying into a fund the square of the number of votes that he or she buys. The money is then returned to voters on a per capita basis. Weyl and Lalley prove that the collective decision rapidly approximates efficiency as the number of voters increases. By contrast, no extant voting procedure is efficient. Majority rule based on one-person-one-vote notoriously results in tyranny of the majority–a large number of people who care only a little about an outcome prevail over a minority that cares passionately, resulting in a reduction of aggregate welfare.

The applications to law and public policy are too numerous to count. In many areas of the law, we rely on highly imperfect voting systems (corporate governance, bankruptcy) that are inferior to quadratic voting. In other areas of the law, we require judges or bureaucrats to make valuations while knowing they are not in any position to do so (environmental regulation, eminent domain). Quadratic voting can be used to supply better valuations that aggregate private information of dispersed multitudes. But the most important setting is democracy itself. An incredibly complicated system of institutional self-checking (separation of powers, federalism) and judicially enforced constitutional rights try to correct for the defects of one-person-one-vote, but do so very badly. Can quadratic voting do better? Glen and I argue that it can.