Abstract:

The well-known Condorcet’s Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study an asymmetric setup, where supporters of both candidates may have different participation costs, and share a (possibly heuristic) estimation of the chance that a single voter is pivotal.

We identify a single property of the pivotality estimation function, called tie-sensitivity, which determines the equilibria of this game: tie-insensitive estimation functions (which include the `standard’ Calculus of Voting and its variations from the literature), lead to a unique trivial equilibrium, in which only 0-cost voters vote. In contrast, tie-sensitive estimation functions give rise to an additional stable equilibria where candidates are nearly-tied.

Finally, for a parametric version of the model, we characterize exactly which equilibria admit a `Jury theorem’, where majority opinion is selected with a probability that approaches 1; or, in contrast, both candidates can win with a least a constant probability that does not depend on the size of the population, neither on the distribution of participation costs.

Joint work with Ganesh Ghalme.