Prof. Bryan Caplan

Econ 410


Week 4: Rational Ignorance and the "Miracle of Aggregation"

I.             The Economics of Imperfect Information, I: Probability

A.           Everyone is familiar with probability to some degree, from rolling dice, playing cards, and so on. 

B.           Basic postulate of probability theory: events range from impossible (probability=0) to certain (probability=1).

C.           Probability language allows us to quantify uncertainty.

D.           Even though people rarely put a precise number on each event, they almost always have some probabilities in the back of their minds. 

E.           When people are asked difficult questions, they often say "I don't know."  But what if they HAD to guess?  Note: in real life, you have to guess all of the time.

F.            Common sophism: "No one can 'know' X."

1.            If this means "No one can know X with certainty," then it's obvious but uninteresting.

2.            If this means "No one has any idea at all about X," then it is clearly false.

II.            The Economics of Imperfect Information, II: Search Theory

A.           Must economists assume "perfect information"?  Not at all: there is an extremely general theory of economic action under uncertainty, known as "search theory."

B.           Basic assumptions of search theory:

1.            More time and effort spent "searching" increase your probability of successful discovery.

2.            Searching ability differs between people.

3.            People can make a reasonable guess about the probabilities of different events and their ability to influence those probabilities.

C.           Main conclusion: People search so that the marginal cost of searching equals the expected marginal gain of searching.

D.           The (endless) applications:

1.            Prospecting for gold.

2.            Searching for a job.

3.            Dating.

III.          Political Knowledge and Rational Ignorance

A.           Instead of assuming that voters are perfectly informed, search theory suggests that we look at the marginal cost and expected marginal gain of acquiring political knowledge.

B.           Easy part: The marginal cost is whatever time you would have to spend reading the newspaper, watching the news, going to politicians' websites, etc.  A simple approximation for this marginal cost is simply your after-tax hourly wage.

C.           Harder part: What are the marginal benefits of political knowledge?

D.           Naive answer: The marginal benefits are better government performance stemming from a more informed electorate.

E.           But the naive answer is wrong.  Why?  The logic of collective action.  Just because I personally become more informed, will government performance appreciably rise?  No.

F.            Your decision become a more informed voter is as unlikely to actually improve government performance as your solitary vote is to change the electoral outcome.  For all practical purposes, the MB of political information is 0!

G.           With positive MC and 0 MB, what is the privately optimal quantity of political information to acquire?  None.

H.           This conclusion is so amazing economists gave it a name: rational ignorance.  When knowledge gives you no practical benefit, and time is money, ignorance (the decision not to acquire knowledge) is rational.

1.            Thus, while voters' lack of political knowledge tends to baffle political scientists, to economists it is amazing that anyone knows anything about politics at all.

I.             So why do voters know anything at all?

1.            Other benefits - not looking stupid in front of your boss

2.            Negative cost - curiosity ("politics is fun"); ubiquity of information

IV.          Empirical Evidence on Political Knowledge

A.           Are voters really "rationally ignorant" with regard to politics?  A mountain of empirical evidence says "yes."

B.           From Dye and Zeigler:  Quiz of adult Americans finds that...



Know President's term is 4 years


Can name governor of home state


Can name vice president


Know which party has U.S. House majority


Know there are two U.S. senators per state


Can name their Congress member


Aware Bill of Rights is first ten amendments to U.S. Constitution


Can name both of their U.S. senators


Can name current U.S. secretary of state


Know term of U.S. House members is 2 years


Can name one of their state senators


C.           Moving to specific policies, voters look far worse; once you reach foreign policy, the level of ignorance is shocking.

D.           Voters are however fairly able to correctly answer questions about affairs, scandals, personalities, and so on.

E.           If voters' goal was to pick sensible policies, this would be a crazy way to allocate mental energy.  But if the main reason voters pay attention to politics is personal entertainment, this pattern is easy to understand.

F.            When you give random adult Americans a complete political exam and look at the distribution of scores, it has the familiar bell-shaped curve; it isn't a right triangle.  But the mean score is shockingly low compared to the idealized "civics textbook" picture of the electorate.

G.           We will be exploring the practical significance of voter ignorance throughout the course.  But for now, it is worth pointing out two things:

1.            People are rational ignorant about many things besides politics.  I am rationally ignorant about car mechanics, the activities of the firms I invest in, and so on.  My performance on exams about these subjects would also be "shockingly low."

2.            But there is a big difference here: For my car or my portfolio, I can just look at the bottom line.  Does my car work?  What has my rate of return been?  The key question to explore as we go on: Do voters have a similar bottom line to check?  Or are voters more analogous to quack brain surgeons?

V.           Informed Voting as a Public Good

A.           The preceding argument only shows that it is privately optimal to know little about politics: If you weigh your costs and your benefits, it doesn't help you.

B.           Going back to public goods theory, it seems that acquiring political information must be a public good.  Everyone benefits when the electorate is more informed, since sensible policies are more likely to prevail.  But these benefits go to the informed and uninformed alike, leaving no private incentive to gather information.

C.           As with other public good problems, then, we can draw the S of political knowledge curve, the D curve showing private willingness to pay for political knowledge, and the SB curve showing the total social benefits of political knowledge.  The equilibrium quantity lies well below the efficient quantity.

D.           What could be done to raise the level of voter information?  The usual approach is to bombard public service messages at the populace, but people are pretty good at tuning out unwanted information.

E.           Another would be to restrict the franchise based on an exam of political knowledge.  Why?  Because the public good is not exactly average political knowledge; it is average political knowledge of people who vote.  You can supply it by improving the existing electorate OR redefining the electorate to include only the informed.

F.            In today's world this is almost unheard of.  But why is this idea so unpopular?

VI.          Education and Voter Ignorance

A.           The strongest predictor of political knowledge is education - not income. 

B.           As usual, the claim that "everyone is knowledgeable about something and has something to contribute" is false.  In fact, political knowledge of all sorts is highly correlated: People who know a lot about foreign policy usually know a lot about domestic policy, the Constitution, etc.

C.           Interesting factoid: Even though education levels greatly increased over the last 50 years, political knowledge scores remained quite constant.

1.            This suggests that education might merely be a proxy for IQ. 

2.            Alternately, TV and other forms of entertainment might have counterbalanced rising education levels.

D.           One alternative to voter competency testing, then would simply be to restrict the vote to college graduates.  This would drastically raise voters' average information levels.

E.           Probably the second-best predictor of political knowledge, controlling for other variables, is gender.  Males out-perform females on tests of political knowledge, even when their education, income, age, and other characteristics are the same.

VII.        Voter Ignorance, Principal-Agent Problems, and Optimal Punishment

A.           Economists have thought a great deal about "principal-agent problems."  An agent is a person a principal hires to act in his (the principal's) interest.

B.           When information is imperfect, the principal needs to figure out some way to "align" the agent's incentives with his own.

1.            Ex: Shareholders, managers, and stock options.

2.            Ex: Why an athlete might want to give his agent a high percentage of his earnings.

C.           If information is available but costly, a natural way to align incentives is random monitoring combined with harsh punishment. 

1.            Ex: You only check in on your secretary once per day, but you fire her if you catch her playing Tetris.  This risk might entirely keep her from playing video games at work because she doesn't know when you'll show up.

D.           We can easily extend principal-agent thinking to politics.  The voters are principals - they want politicians to do a good job, keep their promises, etc.  Politicians are the agents with their own agenda.

E.           How does rational ignorance affect the principal-agent problem?  One answer is that politicians shamelessly and repeatedly violate voter trust because voters don't pay attention to what politicians do anyway.

F.            This story may be largely true, but it does not necessarily follow.  Even if voters are poorly informed, they could still induce good behavior with harsh punishment.  If the media catches a politician taking a $1 bribe, voters could decide to never vote for him again, or even give him jail time.

1.            Ex: Abuse of the franking privilege.

G.           While this sounds unrealistic, for offenses voters care about, it happens.  Voters really hate racist politicians, so they ruin the career of any politician who lets the wrong word slip out.  The media is always listening, so politicians carefully watch what they say.

H.           What is interesting is that politicians seem far more likely to ruin their careers with a slip of the tongue, an affair, youthful drug use, petty bribery, or other indiscretions than by aggressively pursuing foolish policies - or even breaking campaign promises.

1.            Ex: Al Gore's calling card

I.             Main point: Rationally ignorant voters remain able to control politicians in spite of their ignorance.  If they wanted highly honest politicians, they would harshly punish dishonesty whenever they happened to notice it.

VIII.       The Principle of Aggregation

A.           When you roll a single die, you are highly uncertain about how the roll will turn out.  It is equally likely to be anything between 1 and 6.

B.           But when you roll ten dice and add the sum, your level of uncertainty is far lower.  It is very likely to lie between 30 and 40, and virtually certain not to be 10 or 60.

C.           Why?  Because when you roll more dice, you are likely to get some high rolls and some low rolls, which tend to "cancel each other out."  You may get 3 6's, but also 3 1's.

D.           Exams work on the same principle.  If an exam consisted in a single question (or 1 question where each part builds on the last!), an excellent student could easily still mess it up and get an F.  But if an exam has 100 questions, good and bad luck tends to cancel out, leaving a reliable measure of student knowledge.

1.            Imagine basing SAT scores solely on, say, the first question.  A little bad luck would keep a good student out of college; a little good luck would admit a bad student into college.

E.           Even in the hard sciences, experimenters will frequently measure the same object several times, and record the average height, weight, or whatever.  The idea is to reduce the importance of random measurement errors.

F.            This observation - that random errors tend to cancel out as sample size increases - is known as "the principle of aggregation."  (Or in mathematics and statistics as "the law of large numbers.")  When you add up a bunch of random errors, they tend to cancel out, leaving you would a surprisingly good overall measure.

G.           Some aggregation examples

1.            Reaction time experiments

2.            Altruism experiments

3.            Public opinion on NATO

IX.          Voter Ignorance and the "Miracle of Aggregation"

A.           A number of economists and political scientists have admitted the ignorance of individual voters, but still defend the quality of the electorate's decisions.

B.           Why?  The principle of aggregation. 

1.            Individual voters are poorly informed, and thus their votes are highly random. 

2.            But elections are based on aggregate opinions of millions of voters.

3.            Thus, even if there is a large component of randomness in individual voting, the principle of aggregation ensures, for all practical purposes, that outcomes still make sense.

C.           Another way to understand this point: Suppose than 90% of all voters are uninformed and vote randomly.  The remaining 10% are perfectly informed.

D.           In a two-party race, then, the principle of aggregation gives each politician approximately 45% of the vote no matter what they do.

E.           But they need 50% to win.  Nothing they do matters to the uninformed.  So who must the politicians cater to?  The informed voters!  In this example, whichever candidate wins the support of a majority of informed voters also wins the election.

F.            This result has been named "the miracle of aggregation."  It seems miraculous because it implies that a highly uninformed electorate may - at the aggregate level - act "as if" it were perfectly informed.  Lead into gold indeed.

G.           If true, this is an amazing result.  But as we shall see, it hinges critically on the assumption that errors are random, as opposed to systematic.

X.           Uncertainty and Platform Convergence

A.           Suppose that politicians are uncertain about the exact location of the median voter.  What then?

B.           If politicians care solely about winning, they move to wherever they think the median voter is most likely to be located.

C.           However, if politicians care about both winning and policy, uncertainty gives them some slack.  With full certainty, you either compromise your principles or lose.  With some uncertainty, in contrast, you can make a trade-off between your probability of winning and your ideological purity.

D.           If the two parties have opposing ideologies, then uncertainty provokes each to move somewhat away from the position they believe the median voter is most likely to hold. 

E.           This allows for a moderate degree of platform divergence, as each party lowers its chance of winning in order to be true to their cause.