Distributional analysis is widely used to study social choice in Euclidean models ([35], [36], [1], [5], [11], [19], [7] and [4], e.g). This method assumes a continuum of voters distributed according to a probability measure. Since infinite populations do not exist, the goal of distributional...

The yolk, defined by McKelvey as the smallest ball intersecting all median hyperplanes, is a key concept in the Euclidean spatial model of voting. Koehler conjectured that the yolk radius of a random sample from a uniform distribution on a square tends to zero. The following sharper and more...

Democratic simple majority voting is perhaps the most widely used method of group decision making in our time. Standard theory, based on "instability" theorems, predicts that a group employing this method will almost always fail to reach a stable conclusion. But empirical observations do not...

If n points are sampled independently from an absolutely continuous distribution with support a convex subset of [real]2, then the center and radius of the ball determined by the bounding median lines (the LP yolk) converge with probability one to the center and radius of the yolk. The linear...

The minimum spillage sequencing problem, which arises in real-time satellite signal data processing, requires a set of numbers to be arranged so as to minimize the "overflow" of the partial sums above an upper bound. We subject several heuristics to worst-case analysis, average-case analysis,...

Given a set V of voter ideal points in the plane, a point x is in the epsilon core if for any other point y, x is within epsilon of being as close as y is to at least half the voters in V. The idea is that under majority rule x cannot be dislodged by any other point y if x is given an advantage...