The consensus functional equation in Agreement Theory

Abstract We introduce the concept of the consensus functional equation, for a bi-variate map defined on an abstract choice set. This equation is motivated by mis-cellaneous examples coming from different contexts. In particular, it appears in the analysis of sufficiently robust agreements arising in Social Choice. We study the solutions of this equation, relating them to the notion of a rationalizable agreement rule. Specific functional forms of the solutions of the consensus functional equation are also considered when the choice sets have particular common features. Some extension of the consensus equation to a multivariate context are also explored