Majority and Plurality Problems

TL;DR

This paper investigates the minimum number of pairwise comparison queries needed to identify majority, k-majority, or plurality balls in a set, considering adaptive, non-adaptive, and weighted scenarios.

Contribution

It provides bounds and strategies for the query complexity of majority and plurality problems, including weighted cases and different adaptivity models.

Findings

Derived bounds for adaptive and non-adaptive query strategies.

Extended analysis to weighted versions of the problems.

Identified optimal strategies in specific cases.

Abstract

Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, 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 to decide whether a majority, k-majority or plurality ball exists and if so then show one such ball. We consider both adaptive and non-adaptive strategies and in certain cases, we also address weighted versions of the problems.