Choosing How to Choose: Self Stable Majority Rules

We consider the endogenous choice of a voting rule, characterized by the majority size needed to elect change over the status quo, by a society who will use the rule to make future decisions. Under simple assumptions on the uncertainty concerning the future alternatives that will be voted upon, voters' have induced preferences over voting rules that are single-peaked and intermediate. We explore the existence of self-stable voting rules, i.e., voting rules such that there is no alternative rule that would beat the given voting rule if the given voting rule is used to choose between the rules. There are situations where self-stable voting rules do not exist. We explore conditions that guarantee existence, as well as issues relating to efficiency and constitutional design.