Majority and plurality problems

Abstract

Given a set of n balls each colored with a color, a ball is said to be a majority, k-majority, or plurality ball if its color class has size larger than half of the number of balls, has size at least k, or has size larger than any other color class, respectively. We address the problem of finding the minimum number of queries (comparisons of a pair of balls as regards whether they have the same color or not) needed to decide whether a majority, k-majority or plurality ball exists and, if it does, then to show one such ball. We consider both adaptive and non-adaptive strategies and, for certain cases, we also address weighted versions of the problems. © 2012 Elsevier B.V. All rights reserved.