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...

Amedian of a sequence π = x1, x2, . . . , xk of elements of a finite metric space (X, d) is an element x for which ∑k i=1 d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(π) = {x : x is a median of π} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(π)...

We elaborate on the convexity properties of (not necessarily finite) weakly median graphs and their prime constituents in order to establish a number of equations in terms of the weakly median operation. Then the weakly median graphs can be identified with the discrete members of an equational class of ternary algebras satisfying five independent axioms on two to four points. This demonstrates ...

The concept and technics of real space renormalization group are applied to study majority rule voting in hierarchical structures. It is found that democratic voting can lead to totalitarianism by keeping in power a small minority. Conditions of this paradox are analyzed and singled out. Indeed majority rule produces critical thresholds to absolute power. Values of these thresholds can vary fro...