The central influencer theorem: spatial voting contests with endogenous coalition formation

We introduce a spatial voting contest without the ‘one person, one vote’ restriction. Players exert costly effort to influence the policy and the outcome is obtained through an adjustment function. Players are heterogeneous in terms of the position in the policy line, disutility function, and the effort cost. In equilibrium, two groups endogenously emerge: players in one group try to implement more leftist policy, while those in the other group try more rightist one. Since the larger group suffers a more severe free-riding problem, the equilibrium policy converges to the center only when the larger group has a cost advantage. We demonstrate how the location of the center (i.e., the steady-state point) can be either median, or a mean of all points, or a mean of the extreme points, depending on the convexities of the utility and cost functions. This reflects some well-known results as special cases. We extend the model to an infinite horizon setting and show that the median outcome can be reached only under certain conditions.