Supermajority voting, social indifference and status quo constraints

We develop several results related to equilibrium in sophisticated voting under an amendment agenda procedure and supermajoritarian voting rules. Contrary to the simple majority case, we demonstrate that attainable equilibria are a function of the location of the status quo ex ante as well as the tie-breaking rule in place. Most importantly, we demonstrate that the Banks set (the set of sophisticated voting outcomes) does not reduce to the core under certain conditions. Moreover, in generalizing and extending the results in Colomer (1999), we define three analytically distinct regions, defined by the location of the status quo alternative, which determine the extent of the intersection between the Banks set and the core.