The activities of very large coalitions of producers are, in theory and in legislation, generally considered to be inimical to social welfare. By contrast, the formation of large coalitions -political parties and interest groups -is usually encouraged within the political realm. This paper treats a class of collective decision mechanisms within which the formation of large coalitions is both possible and legal.
If every coalition has the potential for coalescing the appropriate equilibrium notion is strong Nash equilibrium; a configuration of strategies is in strong Nash equilibrium if there exists no coalition which can improve upon the outcome to the satisfaction of each of its members without the cooperation of nonmembers. But political decision making has two properties, no veto power and unrestricted domain, which ensure that no strong Nash equilibrium exists for many configurations of voter preference orderings ([5] and [10]). No veto power is satisfied if any individual is denied his most-preferred alternative whenever all other voters unite in declaring some other alternative as most-preferred for them. Unrestricted domain asserts the plausibility of any profile of voter preference orderings.
Although no equilibrium exists in some cases it is not beyond man's ingenuity to develop an alternative method of characterizing the set of alternatives which are sustainable in the long run. When no equilibrium exists various coalitions will form and break up and reform and the outcome will change frequently over time. Some outcomes, or alternatives, will be recurrent -the system keeps returning to them -and we ask if the recurrent alternatives belong to the set of optimal states defined by a social choice functionJ If so, the social choice function is called weakly implementable.
The plurality method of voting, considered as a choice function, is not weakly implementable. It is often pointed out (e.g., [6], ) that plurality voting illustrates very well the phenomenon of voter manipulation. But plurality voting considered as a game form is not so easy to fault. It has the
Theory and Decision 13 (