Plurality is Stablest Conjecture

Let $n$ be large, let $k\geq 3$ be the number of candidates, and let voters cast independent uniformly random votes. A voting method is balanced when each candidate has equal probability of winning, and each voter is assumed to have small influence on the outcome. Votes are independently corrupted by leaving each vote unchanged with probability $1-\rho$ and replacing it by a uniformly random candidate otherwise, for the corresponding noise parameter. Plurality is Stablest Conjecture. Among all balanced voting methods, the plurality function maximizes the probability that the election outcome is preserved under independent vote corruption. This is an open generalization of the two-candidate Majority is Stablest theorem; some cases are known, but the full conjecture for at least three candidates remains open.