Constructive Vs Toxic Argumentation In Debates

Two debaters address an audience by sequentially choosing their information strategies. We compare the setting where the second mover reveals additional information (constructive argumentation) with the setting where the second mover obfuscates the first mover's information (toxic argumentation). We reframe both settings as constrained optimization of the first mover. We show that when the preferences are zero-sum or risk-neutral, constructive debates reveal the state, while toxic debates are completely uninformative. Moreover, constructive debates reveal the state under the assumption on preferences that capture autocratic regimes, whereas toxic debates are completely uninformative under the assumption on preferences that capture democratic regimes.