We suggest a generalization of Karchmer-Wigderson communication games to the multiparty setting. Our generalization turns out to be tightly connected to circuits consisting of threshold gates. This allows us to obtain new explicit constructions of such circuits for several functions. In particular, we provide an explicit (polynomial-time computable) log-depth monotone ... more >>>

We show that the ''majority is least stable'' conjecture is true for $n=1$ and $3$ and false for all odd $n\geq 5$.

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