Cowen believes that QV would encourage extreme preferences:
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?
There are two possible interpretations of this argument.
First, QV would encourage people with extreme preferences to engage in activities that are disruptive of democracy. But the opposite is more likely the case. The problem with one-person-one-vote-majority-rule is that minorities are shut out unless they can organize. This is why minority groups so often resort to civil disobedience, protest marches, strikes, and boycotts. They can vindicate their preferences in the political arena only by making life miserable for the majority. By contrast, QV allows them to vindicate their intense preferences, and in such a way that partly compensates the majority.
Maybe a more attractive version of this argument is that people with intense preferences would lose the incentive to try to persuade the majority to agree with them. Under QV, they pay them off instead. But the difference between the two systems is marginal along this dimension. The cost of buying votes becomes expensive very quickly; so if persuasion can be effective, then minorities will adopt that strategy instead or (more likely) in conjunction with voting.
Second, Cowen might believe that QV would actually change people’s preferences, causing moderate people to become extreme. There are no good theories about how preferences change, so it is hard to evaluate this claim. Perhaps his idea is that under ordinary voting systems people with extreme preferences who are always outvoted somehow become persuaded that their preferences are wrong and drop them. Maybe. But it is just as likely that they give up on a political system that disregards their deepest commitments and search for extra-legal or disruptive means to vindicate them.
We can’t wish away people with intense preferences, and shouldn’t want to. Indeed, nearly everyone has intense preferences along different dimensions; that is why there is a sense in which our rights-based system, which provides judicial protection to minorities with intense preferences under certain conditions, is supported by the majority. But QV provides a better way to incorporate intense preferences into the social welfare function.