The silence that precedes hypocrisy: a formal model of the spiral of silence theory

This paper exposes a formal model of the spiral of silence theory. It is based on game theoy. The game consists on three players: players 1 and two have two strategies, to speak (s) or not (~s); the third player is Nature, which decides whether players 1 and 2 agree in their opinion or not. If players 1, 2 speak and agree, they receive a payoff b. If they speak and disagree, they receive a payoff -c, for b, c > 0. The Nash equilibrium is in mixed strategies and each player chooses the profile $(s, c(b + c)^{-1}; ~s, 1-c(b + c)^{-1}$. To analyse what happens when there are many players and interactions, I have run some simulations where players can update their beliefs about the opinion climate. The time when the spiral of silence process begins decays exponentially with the initial beliefs.