Journal Article On the Possibility of Consistent Voting Procedures Get access Bhaskar Dutta Bhaskar Dutta University of Delhi Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 3, April 1980, Pages 603–616, https://doi.org/10.2307/2297311 Published: 01 April 1980 Article history Received: 01 June 1976 Accepted: 01 May 1979 Published: 01 April 1980

A game form is acceptable if for every preference profile, a Nash equilibrium exists and the outcomes corresponding to Nash equilibria are Pareto efficient. A game form is strongly consistent if the set of strong Nash equilibria is always nonempty. The paper shows that no game form can be both acceptable and strongly consistent. The set of game forms which are both acceptable and dominance-solvable is also characterized in terms of the effectivity functions of game forms.

A concept of an egalitarian solution is developed within the framework of cooperative game theory. The solution is designed to capture the interplay between social values (in this case, egalitarianism) and individual behavior. Both the final outcomes possible coalitional deviations are constrained by these social norms. The authors' main result: despite using a partial order (the Lorenz criterion) to compare allocations, their solution concept yields at most one allocation for each game. The concept is illustrated by a detailed study of convex games, and by a number of examples and applications.

The main result of this paper is to characterize the class of two-person social choice correspondences which are Nash-implementable. The characterization result is used to formulate domain restrictions which allow the construction of non-dictatorial and Pareto-efficient social choice correspondences which are Nash-implementable.

The paper discusses certain problems raised recently by B. Peleg, about the existence of equilibria and 'nice' equilibria for various classes of voting games. First it is shown that under practically every non-dictatorial voting procedure, and for every sincere preference profile, one can find a Nash equilibrium with nice properties. Secondly, a Paretian and anonymous decision procedure is constructed, under which one can always find equilibria with certain attractive properties. Lastly, it is shown that if the number of alternatives is large enough, then for some sincere preference profile, no equilibrium may exist under many decision procedures.

We explore a sequential offers model of n-person coalitional bargaining with transferable utility and with time discounting. Our focus is on the efficiency properties of stationary equilibria of strictly superadditive games, when the discount factor δ is sufficiently large; we do, however, consider examples of other games where subgame perfectness alone is employed. It is shown that delay and the formation of inefficient subcoalitions can occur in equilibrium, the latter for some or all orders of proposer. However, efficient stationary equilibrium payoffs converge to a point in the core, as δ → 1. Strict convexity is a sufficient condition for there to exist an efficient stationary equilibrium payoff vector for sufficiently high δ. This vector converges as δ → 1 to the egalitarian allocation of Dutta and Ray (1989).

We study the incentives of candidates to strategically affect the outcome of a voting procedure. We show that the outcomes of every nondictatorial voting procedure that satisfies unanimity will be affected by the incentives of noncontending candidates (i.e., who cannot win the election) to influence the outcome by entering or exiting the election.