ECONOMY

arry r. weingast & donald a. wittman 15
positions but not about their relative quality. Again, the voters are rational and the
pressure group has private information (in this case, about the relative quality of
the candidates). A number of recent papers consider this case but employ differing
subsidiary assumptions: advertising has content (see Coate 2004; Wittman forthcoming);
advertising has no content, but expenditures on advertising signal information
(Prat 2002, this volume); pressure groups make the offers (Coate, Prat),
candidates make the offers; there is one pressure group, there are multiple pressure
groups; the candidates are only interested in winning, and the candidates have policy
goals. These various modeling efforts do not all come to the same positive conclusion
as the previous paragraph. In general, the results depend on whether the value of
the revealed information is outweighed by the loss from inferior candidate positions
when the candidates compete for pressure group funds. In turn, this balance depends
to a great degree on the number of pressure groups and whether it is the candidates or
the pressure groups that make the offer. All these various modeling efforts take into
account that information valuable to uniformed voters is revealed by the pressure
group’s donation or endorsement and all of them assume rationality of the voters.
This is the key methodological advance—how voters can incorporate information
that others might want to distort or hide (see Prat, this volume).
We have shown how uninformed voters can make inferences from behavior and
thereby become more informed. Because all of this is embedded in a game, all
other players take this behavior and information into account when they make their
decisions; and of course the uninformed take the other players’ strategies into account
when they make their own inferences. 15
The final example for this section considers aggregation of information in the
context of voting. Suppose a set of voters face a decision about how much money
to spend. To gain intuition, we begin with an exceedingly simple example. Suppose
that there are five voters with identical preferences: three have unbiased estimates of
the correct action to take, while two are fully informed. The voters know whether they
are informed or not. The uninformed know that there are informed voters, but not
how many. Suppose further that the correct action is to spend $7 million and that,
with equal probability, the uninformed players receive a signal that it should be 5, 7,
or 9 million dollars. Assuming that the voters cannot communicate with each other,
howlikelyisitthatthemajorityruledecisionisnot7? The answer is zero if the voters
are rational: all the uninformed voters will rationally abstain. By doing so, they know
that only informed voters will participate and that these informed voters will make
the correct decision.
This example illustrates two important but related issues. First, the more informed
people will choose to vote (here, at least, the argument does not go against conventional
wisdom). Second, the potential voter asks: given that he will be pivotal, should
¹⁵ There are other ways in which voters can be informed despite an apparent lack of information.
Parties create brand names so that party labels are in fact informative about a candidate’s position (Cox
and McCubbins 1993, 2005). Relying on biased information can be rational for voters who have strong
priors in favor of one of the parties (Calvert 1985). And, uninformed voters can learn from polls of
informed voters (McKelvey and Ordeshook 1986).