In the context of spatial majority voting games, considerable experimental support exists for the core as a solution hypothesis when it is not empty (Berl et al., 1976; Fiorina and Plott, 1978; Isaacs and Plott, 1978). Specifically, these experiments show that if a simple majority voting game possesses a Core point-a point that cannot be defeated by a majority vote-subjects choose outcomes at o...

A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the sum of the distances to the elements in the profile. The median (antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (obnoxious) facility in a network. The median function is well studied. For instance ...

The synchronized bit communication model, defined recently by Impagliazzo and Williams in [1], is a communication model which allows the participants to share a common clock. The main open problem posed in this paper was the following: does the synchronized bit model allow a logarithmic speed-up for all functions over the standard deterministic model of communication? We resolve this question i...

New proofs are given for Monjardet’s theorem that all strong simple games (i.e., ipsodual elements of the free distributive lattice) can be generated by the median operation. Tighter limits are placed on the number of iterations necessary. Comparison is drawn with the χ function which also generates all strong simple games.

We extend Valiant's construction of monotone formulae for the majority function to obtain an eecient probabilistic construction of small monotone formulae for arbitrary positive linear threshold functions. We show that any positive linear threshold function on n boolean variables which has weight complexity q(n) can be computed by a monotone boolean formula of size O(q(n) 3:3 n 2): Our techniqu...

The fair way to decide an election between two candidates a and b is majority rule; if more than half the electorate prefer a to b, then a is elected; otherwise b is elected. Arrow’s theorem asserts that no fair election procedure exists for choosing from among three or more candidates. This note gives an exposition of Arrow’s theorem. It also describes the relation of election procedures betwe...

In this paper we consider multilateral stochastic bargaining models with general agreement rules. For n-player games where in each period a player is randomly selected to allocate a stochastic level of surplus and q n players have to agree on a proposal to induce its acceptance, we characterize the set of stationary subgame perfect equilibrium payoffs and establish their existence. We show that...

Our model of multi-party negotiations is a many parties, many issues model. The whole multi-party negotiation consists of a set of mutually influencing bilateral negotiations that are focused on different bilateral issues. We propose to use majority rule to help parties reach group agreements. When a party is not satisfied with another party’s negotiation progress, he can send a primitive oppos...

In previous work, two axiomatic characterizations were given for the median function on median graphs: one involving the three simple and natural axioms anonymity, betweenness and consistency; the other involving faithfulness, consistency and 12 -Condorcet. To date, the independence of these axioms has not been a serious point of study. The aim of this paper is to provide the missing answers. T...