Recently, Adrian Vermeule had a review of the new book by Melissa Schwartzberg on supermajority rules – Counting the Many: The Origins and Limits of Supermajority Rules. I haven’t read Schwartzberg’s book yet, but Vermeule does discuss a number of arguments against supermajority rules.
One such argument is based on May’s Theorem. According to the Theorem, only majority rule satisfies four conditions on group decisionmaking. Two of the key ones are anonymity (the group decision treats each voter identically) and the neutrality (the group decision treats both outcomes the same, in that reversing the preferences reverses the group decision).
Supermajority rules satisfy the anonymity condition. Under ordinary supermajority rules, each voter receives one vote. But supermajority rules violates the neutrality conditions. Under a 3/5 supermajority rule for passing new spending, if a majority is opposed to the new spending, it gets it way and the spending does not pass, but if a majority is in favor of the new spending, it doesn’t get its way and again the spending does not pass. Clearly, this 3/5 supermajority rule privileges in a sense the decision against new spending.
Is this a problem? Advocates of May’s Theorem certainly treat it as one. But all that the violation of the neutrality condition shows is that there is a privileging of a decision (as compared to majority rule) and that this privileging needs a justification.