The condorcet jury theorem with information acquisition

Abstract

We analyze a committee decision in which individuals with common preferences are uncertain which of two alternatives is better for them. Members can acquire costly information. Private signals and information choice are both continuous. As is consistent with Down’s rational ignorance hypothesis, each member acquires less information in a larger committee and tends to acquire zero information when the committee size goes to infinity. However, with more members, a larger committee can gather more aggregate information in equilibrium. The aggregate information is infinite with the size going to infinity if and only if marginal cost at “zero information acquisition” is zero. When the marginal cost at “zero information acquisition” is positive, the probability of making an appropriate decision tends to be less than one.