A Conversational War of Attrition

We explore costly dynamic deliberation by two differentially informed and biased jurors, a hawk Lones and a dove Moritz, who must agree to convict or acquit a defendant of a crime. In a deferential equilibrium, debate ends by some drop-dead date. But our analysis focuses on a communicative equilibrium, for which debate is potentially unbounded. For if jurors are not too biased, the communicative equilibrium is Pareto-dominant and the unique stable equilibrium.We find that patient and not too biased debaters play devil's advocate, exploiting the option value of debate to vote against to their posterior beliefs. Central to our paper is a taxonomy of debate styles: When jurors are sufficiently patient or biased, debate is close in spirit to a war of attrition. Jurors are intransigent, and Lones, say, wishes to win a conviction against all types of Moritz about to concede. But when jurors are impatient or not too biased, they are ambivalent, and debate is more win-win: Lones wishes that the strongest conceding types of Moritz would push back for acquittal.We show that the game tips from strategic substitutes to strategic complements as intransigence tips into ambivalence, reversing some predictions. For instance, as Lones grows more hawkish, he argues more forcefully for convictions, reducing wrongful acquittals. With intransigence, this tougher posture begets a weaker stance by the dove Moritz, leading to more wrongful convictions. But if debate is ambivalent, Moritz pushes back and this ultimately reduces both wrongful acquittals and convictions.