1 Advantages of using the GSS include a) its measurement of Protestants has not changed over the years, b) its high quality (e.g. its high overall response rate and low item non-response on religion), and c) its large sample size (over 43,000 respondents in 1972-2002).

We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a M...

We define the class of two-player zero-sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For games in this class we establish sufficient conditions for existence of a value of the game and minimax or Nash equilibrium strategies for the players. We prove first that if all discontinuities favor one player then a value exists and t...

The paper presents a general setting for studying majority-based collective decision procedures where the electorate is divided into constituencies according to an equal-representation principle. It generalizes the well-known Referendum Paradox to the non-dichotomous choice case, and shows that all Condorcet choice rules are sensitive to the design of the apportionment of the electorate, in the...

We analyze an overlapping generations model of voting on “reform projects”. These resemble investments in that they first require some investment expenditure and later pay off. Since the time during which old people get the benefit is shorter, or because older people are more wealthy and hence pay more taxes, they are more conservative (against reforms) than young people. We show that if people...

We prove that every digraph has a vertex 4-colouring such that for each vertex v, at most half the out-neighbours of v receive the same colour as v. We then obtain several results related to the conjecture obtained by replacing 4 by 3.

Given a set of n balls each colored with a color, a ball is said to be majority, kmajority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class; respectively. We address the problem of finding the minimum number of queries (a comparison of a pair of balls if they have the same color or not) that is needed...