Abstract : Given a set of $n$ elements, each of which is colored one of $c$ colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We prove that $(c-1)(n-c)/2$ color comparisons are necessary in the worst case to determine the plurality color and give an algorithm requiring $(0.775 c + 5.9)n + O(c^2)$ color comparisons for $c \geq 9$.
Laurent Alonso, Edward M. Reingold. Determining Plurality. ACM Transactions on Algorithms, Association for Computing Machinery, 2008, 4 (3), pp.26:1,26:19. ⟨10.1145/1367064.1367066⟩. ⟨inria-00169184⟩