Social Choice, Coase Theorem, Contracts, and Logrolling

The problems connected with logrolling (Bernholz, 1974) and vote-trading (Kramer, 1973; McKelvey, 1976; Plott, 1967) are special cases of much wider phenomena (Bernholz, 1981; Schwartz, 1981, 1986). These phenomena are, in fact, the only reasons for the inconsistencies of nondictatorial societies described by Arrow’s General Impossibility Theorem (Arrow, 1963/51; see Sen, 1987, for a review of Social Choice Theory) “if more than one issues are implied, if individuals have separable preference orderings and if such inconsistencies are not present concerning the alternatives of single issues”. Moreover, the respective “paradoxes” of voting and logrolling, usually distinguished in the literature, are identical (Bernholz, 2000). Also, the implied social inconsistencies can occur even if participating individuals have identical preferences but face different restrictions (Breyer, 1980). Finally, the problems put into the center of attention by Arrow would not exist without the presence of negative externalities (in its broad sense, that is, including also political externalities) (Bernholz, 1982). But then, as suggested by the Coase Theorem, generalized below, stable Pareto-optimal outcomes do result in the absence of transaction costs in spite of the validity of Arrow’s Theorem, provided that binding contracts are possible. Consequently, the following statement by Sen (1987, p. 383) is true only if contracts are not binding: “… it would appear that there is no way of arriving at a social choice procedure specifying what is to be chosen…, satisfying the appropriately interpreted (i.e., in terms of choice) conditions specified by Arrow…”.