Sharp Thresholds for Monotone Non Boolean Functions and Social Choice Theory

Gil Kalai, Elchanan Mossel

A key fact in the theory of Boolean functions $f:\{0,1{\}}^n\to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f:\{0,1{\}}^n\to \{0,1\}$ is m…