On the Geometry of Unanimity Rule

Abstract

A spatial analysis of decision-making by unanimity rule shows that outcomes largely depend on the initial state or the status quo. The closer the status quo is to the ideal points of the actors, the more restricted, more biased and likely less socially efficient the set of decisions by unanimity tends to be. Calculations show that any point inside the Pareto-optimum set of alternatives bounded by the actors' ideal points only can be reached from a status quo placed outside an area which is at least eight times larger than the area of the Pareto-optimum set. The social-utility optimum point which minimizes the sum of the squared distances from the actors' ideal points only can be reached from a status quo placed outside an area which is at least three times larger than the Pareto-optimum set. From very unsatisfactory initial states, very satisfactory and stable outcomes are feasible; from more satisfactory initial states, mediocrity tends to endure.