What is quadratic voting (QV)? Essentially, voters would make a one-time purchase of votes from a clearinghouse at a price equal to the square of the number of votes purchased. It is a proposed approach towards limiting the power of the majority or wealthy interests.
According to this research paper:
If individuals take the chance of a marginal vote being pivotal as given, like a market price, QV is the unique pricing rule that is always efficient. In an independent private values environment, any type-symmetric Bayes-Nash equilibrium converges towards this efficient limiting outcome as the population grows large, with inefficiency decaying as 1/N.
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.
My reservation about this and other voting schemes (such as demand revelation mechanisms) is that our notions of formal efficiency are too narrow to make good judgments about political processes through social choice theory. The actual goal is not to take current preferences and translate them into the the right outcomes in some Coasean or Arrovian sense. Rather the goal is to encourage better and more reasonable preferences and also to shape a durable consensus for future belief in the polity.
I would gladly have gay marriage legal throughout the United States. But overall, like David Hume, I am more fearful of the intense preferences of minorities than not. I do not wish to encourage such preferences, all things considered. If minority groups know they have the possibility of buying up votes as a path to power, paying the quadratic price along the way, we are sending intense preference groups a message that they have a new way forward. In the longer run I fear that will fray democracy by strengthening the hand of such groups, and boosting their recruiting and fundraising. Was there any chance the authors would use the anti-abortion movement as their opening example?
By elevating persuasion over trading in politics (at some margins, at least), we encourage centrist and majoritarian groups. We encourage groups which think they can persuade others to accept their points of view. This may not work well in every society but it does seem to work well in many. It may require some sense of persuadibility, rather than all voting being based on ethnic politics, as it would have been in say a democratic Singapore in the early years of that country.
I had never heard of quadratic voting. It's a fascinating idea, essentially putting some sort of effective cap on the strategy of buying votes, perhaps forcing wealthy minority interests to adopt other strategies, like persuasion. Most approaches to combating the seeming inevitability of democratic sclerosis rely on combatting money with money, but quadratic voting just looks to place a ceiling on the value of the money.
Seems like this model would work best in a society without such sharply drawn lines between two parties. It does get me wondering whether some social network could be designed to try to optimize for more centrism. Are flame wars that just entrench both sides the inevitable outcome of all comment threads on controversial topics? Maybe it's built into the prevalent designs of online discussion threads.