Who should cast the casting vote? Using sequential voting to amalgamate information

In this study, we are concerned with how agents can best amalgamate their private information about a binary state of Nature. The agents are heterogeneous in their “ability”, the quality of their private information. The agents cannot directly communicate their private information but instead can only vote between the two states (say “Innocent” or “Guilty” on a criminal jury). We first describe possible methods of sequential majority voting, and then we analyze a particular one: the first \(n-1\) jurors vote simultaneously and, in the case of a tie, the remaining juror has the casting vote. We prove that when \(n=3\) (a common situation for a tribunal of three judges), the probability of a correct verdict is maximized when the agent of median ability has the casting vote.     

Spatial Dispersion as a Dynamic Coordination Problem

Following Schelling (1960), coordination problems have mainly been considered in a context where agents can achieve a common goal (e.g., rendezvous) only by taking common actions. Dynamic versions of this problem have been studied by Crawford and Haller (1990), Ponssard (1994), and Kramarz (1996). This paper considers an alternative dynamic formulation in which the common goal (dispersion) can only be achieved by agents taking distinct actions. The goal of spatial dispersion has been studied in static models of habitat selection, location or congestion games, and network analysis. Our results show how this goal can be achieved gradually, by indistinguishable non-communicating agents, in a dynamic setting.