The plurality problem with three colors and more

For c=2, the problem is equivalent to the well-known majority problem which has already been solved (Combinatorica 11 (1991) 383-387). In this paper we show that 3⌊n/2⌋-2⩽L3(n)⩽⌊5n/3⌋-2. Moreover, for any c⩽n, we show that surprisingly the naive algorithm for the plurality problem is asymptotically optimal.