Marquis de Condorcet and the Two-dimensional Jury Model

The two-dimensional jury model, which is the core of this paper, demonstrates the two, partly conflicting, dimensions in Condorcet’s work and life. There is the dimension of enlightenment, reflected in Condorcet’s jury theorem, i.e., the belief that there is some truth can be approximated in collective decision-making. On the other hand, there is creed that individual preferences are the building blocks of the society with the consequence of inevitable conflicts in aggregating them. This paper combines the idea of winning a maximum of votes in a voting game with utility maximization that derives from the winning proposition. The model assumes a first mover, the plaintiff, and a second mover, the counsel of the defendant. Typically, these agents represent parties that have conflicting interests. Here they face an arbitration court in the form of jury that consists of three voters such that no single voter has a majority of votes. The agents are interested in both gaining the support of a majority of jury members and seeing their preferred alternative selected as outcome. It will be demonstrated that equilibrium decision-making can be derived for this model.