Variants of the majority problem Original Research Article

Suppose we are given n balls colored with two colors. How many color-comparisons are needed to produce a ball of the majority color? The answer (first given by Saks and Werman) is M(n)=n−B(n), where B(n) is the number of 1ʹs in the binary representation of n. We consider in this paper several generalizations and variants of the majority problem such as producing a k-majority ball, determining the color status of all balls, non-adaptive versions and the closely related liar problem.