An influential argument makes the following claim: A well-functioning democracy requires that voters actually know what policies would be in their interests so that they can vote for politicians who implement such policies. However, the argument continues, in a democratic system there is a “public goods problem” with respect to information leading to systematically bad vote decisions and, thus, policy choices in democracies.

(a) Explain what externality this argument is pointing to in claiming there is a public goods problem.

(b) Consider the following model. There are three voters a, b, and c and two candidates advocating two different policies 1 and 2. None of the voters know which policy would be better for her. Moreover, the voters believe it is equally likely that they each prefer either policy.

Each voter, individually, can either invest in becoming an informed voter (at cost C) or not (at cost 0). If a voter invests, she learns the policy she prefers, but she does not have the opportunity to communicate it to the other voters. Moreover, let’s assume (for simplicity) that, were they all informed, all the voters would prefer the same policy (i.e., there is a correct policy). The payoff of having the correct policy chosen is B > C. The payoff of having the wrong policy chosen is 0. Assume all voters vote and that if a voter is uninformed she flips a coin to choose between 1 and 2.

i. Suppose a voter expects the other two voters not to become informed. What has to be true about the relationship between B and C for her to become informed?

ii. Suppose a voter expects one of the other voters to become informed and one of the other voters not to become informed. Under what conditions on B and C will she become informed?

iii. Suppose a voter expects both other voters to become informed. Under what conditions on B and C will she become informed?

iv. Given the answers above, there are two things that can happen in equilibrium. What happens in equilibrium if C < B/4? What happens in equilibrium if C > B/4?

(c) Compare this to a model with one voter who simply chooses the policy. Under what conditions does this single voter become informed?

(d) How does the comparison of the results from parts (b) and (c) illustrate the public goods problem in democracy?

(e) Suggest a policy one could implement to increase the number of voters who become informed.

(f) What do you think would happen as we increased the number of voters in part (b)? Why?