Group Wisdom at a Price: Jury Theorems with Costly Information

We study epistemic voting on binary issues where voters are characterized by their competence, i.e., the probability of voting for the correct alternative, and can choose between two actions: voting or abstaining. In our setting voting involves the expenditure of some effort, which is required to achieve the appropriate level of competence, whereas abstention carries no effort. We model this scenario as a game and characterize its equilibria under several variations. Our results show that when agents are aware of everyone's incentives, then the addition of effort may lead to Nash equilibria where wisdom of the crowds is lost. We further show that if agents' awareness of each other is constrained by a social network, the topology of the network may actually mitigate this effect.