Journal Article On Variable Majority Rule and Kramer's Dynamic Competitive Process Get access Douglas H. Blair Douglas H. Blair University of Pennsylvania Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 46, Issue 4, October 1979, Pages 667–673, https://doi.org/10.2307/2297034 Published: 01 October 1979 Article history Received: 01 December 1975 Accepted: 01 November 1978 Published: 01 October 1979

We consider a model oflabor union behavior in which workers make decisions about wages and employment by simple majority rule. We show that under general conditions such a union has a well-behaved objective function, different from those previously postulated in the literature. We then show that the union's majority preferences generally lack a von Neumann-Morgenstern utility representation and thus cannot be inserted into traditional bargaining models. We then develop and characterize the solutions to a new bargaining model that is consistent with the structure of union preferences. Several comparative-statics results are presented.

This paper establishes a natural and satisfying characterization of the class of collective choice rules which are acyclic and satisfy the Arrow axioms (unrestricted domain, independence of irrelevant alternatives, and the weak Pareto principle). We show that, when the number of alternatives is larger than the number of individuals, there must exist an individual who can at least some critical number of pairwise decisions. This critical number of veto pairs depends on the number of alternatives and individuals, and, as the number of alternatives increases without limit, the fraction of all pairs which some individual can veto approaches unity. We also present a global veto theorem and an axiomatic characterization of the Pareto extension rule which utilizes acyclicity rather than quasi-transitivity. ARROW [1] SHOWED that the only collective choice rules that yield weak order social preference relations and satisfy unrestricted domain, independence of irrelevant alternatives, and the weak Pareto principle are dictatorial. Gibbard [9] demonstrated that by relaxing the rationality requirement from transitivity to quasi-transitivity (i.e., transitivity of the strict preference relation) we can evade the letter though not the spirit of the Arrow dictatorship result: oligarchy, a weaker form of dictatorship, still obtains when the other three axioms are imposed. In this paper we prove a theorem parallel to those of Arrow and Gibbard for the weaker rationality requirement of acyclicity (i.e., the absence of cycles of strict preference). Since acyclicity is a necessary and sufficient condition for the existence of a nonempty set of maximal elements in every finite feasible set, there are powerful reasons for imposing it. Moreover, as we argue in Blair and Pollak [2], it is difficult to justify any stronger rationality property such as quasi-transitivity without at the same time justifying some even stronger rationality condition which implies dictatorship. Our principal result shows that, when the number of alternatives is larger than the number of individuals, there must exist an individual who can at least some critical number of pairwise decisions. (We say that individual i has a veto over the ordered pair (y, x) if he is weakly decisive for x against y-that is, if his strict preference for x over y implies weak social preference for x over y, regardless of the preferences of other individuals.) This critical number of veto pairs depends on the number of alternatives and the number of individuals. As the number of alternatives increases without limit, the fraction of all pairs that some individual can veto approaches unity. There may be more than one individual who can veto at least the critical number of pairs; indeed, it is possible for every individual to have a veto over every ordered pair of alternatives.

We analyze a model of a hostile takeover attempt in which shareholders are free to sell common-share voting rights as well as the shares themselves. Without taxation, only welfare-improving take-overs succeed. Allowing vote sales has no effect on the success of attempted takeovers or the profits of incumbent management or raiders. When taxes are levied, however, an inefficiently small number of value-increasing takeovers succeed if vote sales are prohibited. Allowing vote sales facilitates such takeovers and raises welfare. With taxation, incumbents would never prefer to defend against take-overs by purchasing votes, but raiders might well prefer this method.