In search of optimum ?relative unanimity?: A comment

Abstract

In a recent issue of this journal Richard Cebula and Milton Kafoglis (1983) (hereafter called C&K), present a model which is designed to determine the optimal voting rule. Their analysis builds on the work of Fishkin (1979) and Rae (1975) who had offered criticisms of Buchanan and Tullock's (B&T) determination of the optimal voting rule. The purpose of this note is to indicate that C&K have left some misleading trails in their search and to rectify these false leads. The central concern of C&K's paper is to analyse the distinct possibility that some collective outcomes may be sacrificed '... because "negative minorities" may be able to block efficient decisions' (C&K, 1983: 196). To this end they '...formulate a simple framework for the selection of a decision rule which recognizes these costs of surrendered outcomes' (C&K, 1983: 196). Figure 1, which is reproduced here from C&K's discussion, represents in part the most reasonable depiction 1 of the costs and benefits to the collectivity of all the voting rules from simple majority to unanimity. The benefit curve is assumed to rise as the voting rule becomes more inclusive. It is alleged that the 'free rider' problem and the related inefficiency diminishes as the voting rule approaches unanimity. 2 In substance this curve does not differ markedly from that found in B&T's model. 3 The discussion by C&K of this concept is, however, confusing. Cebula and Kafoglis consistently refer to the GB curve as representing the group's gross benefits but fail to clearly indicate what gross refers to. They note, for example, in their final paragraph that B&T's framework uses net benefits whereas their analysis refers to gross benefits. And to be sure, B&T did at one stage 4 propose to use net benefits, measured as the difference between the benefits and costs of provision (B&T, 1962: 44). Presumably C&K therefore take gross benefits to reflect the value of collective provision without any regard whatsoever to what has to be given up. But if this is so, then it is not at all clear why the benefit curve is of much analytical interest. Ninety years ago Wicksell admonished economists for their failure to take