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.
Highlights
Our results show that the rational ignorance hypothesis is generally satisfied in the committee decision with information acquisition, but a larger committee serves the society better than what the rational ignorance hypothesis indicates at first glance
Even if the committee members can only report 0 and 1, Propositions 10 and 11 show that the limit of the probability of the appropriate decision goes to 1 if and only if the marginal cost at zero information acquisition is zero and the limit is strictly less than 1 if and only if the marginal cost at zero information acquisition is positive, the rational ignorance hypothesis still holds irrespective of the information cost function. This conclusion differs from Martinelli [8]: in a strategic voting model with binary signals, he shows that the limit of the appropriate decision goes to 1 if and only if both the marginal cost and the second-order derivative at zero information acquisition are zero; the reason is that the information is coarser than ours so that there needs to be stricter conditions for the Condorcet Jury Theorem (CJT) to hold
In a model where there is no interest conflict among individuals but the information is costly, we show that committee members have less incentive to acquire information in a larger committee if the committee size is large enough and each member tends to acquire zero information when the committee size goes to infinity
Summary
Even if the committee members can only report 0 and 1, Propositions 10 and 11 show that the limit of the probability of the appropriate decision goes to 1 if and only if the marginal cost at zero information acquisition is zero and the limit is strictly less than 1 if and only if the marginal cost at zero information acquisition is positive, the rational ignorance hypothesis still holds irrespective of the information cost function This conclusion differs from Martinelli [8]: in a strategic voting model with binary signals, he shows that the limit of the appropriate decision goes to 1 if and only if both the marginal cost and the second-order derivative at zero information acquisition are zero; the reason is that the information is coarser than ours so that there needs to be stricter conditions for the CJT to hold.
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