The Ambiguity of Determining the Optimal Majority

James Buchanan and Gordon Tullock’s (1999) Calculus of Consent model, published in 1962, is usually considered an analytical defense of majority rule in a constitutional democracy. Their model offers a method of determining the optimal majority in a voting system as the solution to the minimization problem of the total social costs. Nevertheless, the existence and uniqueness of an interior solution rests upon an implicit assumption of the convexity of the total social costs curve. This article points out the possibilities for noninterior solutions and briefly touches upon the case for multiple optimal majorities. As such, the article highlights possible cases in which either private choice or unanimity is socially optimal and the ambiguity that arises when a multiplicity of optimalities exists.