Endogenous agenda formation processes with the one-deviation property

We study collective choice via an endogenous agenda setting process. At each stage, a status quo is implemented unless it is replaced by a majority (winning coalition) with a new status quo outcome. The process continues until the prevailing status quo is no longer challenged. We impose a one-time deviation restriction on the feasible policy processes, reflecting farsightedness of voters. The key feature of the solution is history dependence. The existence of the solution is proven by iterating a version of the uncovered set. We show that the resulting fixed point is the largest set of outcomes that can be implemented via any policy process that meets the one-deviation restriction. Finally, we relate our solution to a concrete noncooperative model, and show that it can be interpreted as a refinement of the solution of Bernheim and Slavov (2009) in the context of repeated voting, and of the solution of Konishi and Ray (2003) and Vartiainen (2011) in the context of coalition formation.