Stable constitutions

We consider a constitution as a pair of voting rules (f,F) in which the given rule f is for the decision on the final outcome, and the base rule F is for the decision on the change of a voting rule. Which constitutions would stably survive? We define the concepts of interim/ex-post stability, whereby agents' preferences over the outcomes are privately/publicly known when they change a voting rule. We fully characterize the set of interim stable constitutions, which consist of anonymous voting rules. Furthermore, we show that it is equivalent to the set of ex-post stable constitutions. We compare the characteristics of three sets of stable constitutions—ex-ante, interim, and ex-post stable constitutions—and discuss the relationship of inclusions. We also discuss the environmental independence of the concepts of stability, the alternative definition of stability, and the stability of higher-level constitutions composed of more than two voting rules.