Abstract The general problem in location theory deals with functions that find sites on a graph (discrete case) or network (continuous case) in such a way as to minimize some cost (or maximize some benefit) to a given set of clients represented by vertices on the graph or points on the network. The axiomatic approach seeks to uniquely distinguish, by using a list of intuitively pleasing axioms,...

In this paper we introduce a median operator between two sets of interpretations (worlds) in a finite propositional language. Our definition is based on morphological operations and Hausdorff distance. It provides a result which lies “halfway” between both sets and accounts for the “extension” or “shape” of the sets. We prove several interesting properties of this operator and compare it with f...

We use a Ramsey-theoretic argument to obtain the first lower bounds for approximations over Zm by nonlinear polynomials: A degree-2 polynomial over Zm (m odd) must differ from the parity function on at least a 1=2 1=2(logn) (1) fraction of all points in the Boolean n-cube. A degree-O(1) polynomial over Zm (m odd) must differ from the parity function on at least a 1=2 o(1) fraction of all points...

Deene the MOD m-degree of a boolean function F to be the smallest degree of any polynomial P, over the ring of integers modulo m, such that for all 0-1 assignments ~ x, F(~ x) = 0 ii P(~ x) = 0. By exploring the periodic property of the binomial coeecients modulo m, two new lower bounds on the MOD m-degree of the MOD l and :MOD m functions are proved, where m is any composite integer and l has ...

British troops surrendering at Yorktown, Virginia in October of 1781 reportedly marched to the 17th century English song “The World Turned Upside Down.”2 Government embodied in the United States and built on the tradition of English Common Law changed the world over subsequent generations. The deceptively simple Enlightenment notion of the “consent of the governed” required majority rule, but t...

A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the remoteness value, that is, the sum of the distances to the elements in the profile. The median (or 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 (or obnoxious) facility in a network. The median fu...

As noted by Anscombe (1976), the disposition of a set of proposals by majority rule does not preclude the existence of a majority of voters, each of whom disagrees with the outcomes in a majority of cases. It is intuitively clear, however, that when proposals are adopted or rejected, on average, by a sufficiently strong consensus, such a state of affairs cannot materialize. Indeed, we show for ...

Although much evidence indicates that RT increases as a function of computational load in many cognitive tasks, quantification of changes in neural activity related to increasing demand of cognitive control has rarely been attempted. In this fMRI study, we used a majority function task to quantify the effect of computational load on brain activation, reflecting the mental processes instantiated...

The IETF has had a long tradition of doing its technical work through a consensus process, taking into account the different views among IETF participants and coming to (at least rough) consensus on technical matters. In particular, the IETF is supposed not to be run by a "majority rule" philosophy. This is why we engage in rituals like "humming" instead of voting. However, more and more of our...

We introduce a general setting for information elicitation in multi-agent systems, where agents may be approached both sequentially and simultaneously in order to compute a function that depends on their private secrets. We consider oblivious mechanisms for sequential-simultaneous information elicitation. In such mechanisms the ordering of agents to be approached is fixed in advance. Surprising...