# Questions

1. Confirmation bias leads people to interpret the same

information in very different ways. Given such a bias is

pervasive, one must be careful in forming initial opinions.

If confirmation bias is pervasive, what might this

say about the quality of information sources that are

available for controversial topics in which people often

hold sharply diverging views? When people claim

strong evidence for their opinion, should we believe

them? Is there a way to obtain unbiased assessments?

2. Suppose you hold a stock and are considering whether

to sell it or keep it. You initially believe that the

probability the stock will rise in value in the long run is

0.7. You decide you will sell the stock when the

probability of a long run drop in value reaches 0.5.

Then, over the course of time you watch the changes in

the value of the stock day to day, each day’s outcome

serving as a forecast of future value. Further, suppose

that P RISE rise =0.6 where RISE indicates a longrun

future rise in value and rise indicates an observed

daily rise in value. Correspondingly,P FALL fall = 0.6,

where FALL indicates a long-run decline in future values

of the stock and fall indicates a daily observed decline in

value. Suppose the probability that you misperceive a

signal given it contradicts your current belief is q= 0.4.

How many daily declines would you need to observe

before you would sell the stock according to Rabin and

Schrag’s model of confirmation bias? What would

a Bayesian’s beliefs be regarding the probability of a

decline at that point? How many daily declines would

you need to observe in order to sell if you had perfect

perception q= 0 ?

3. In this chapter, we motivated the rational model of

information search by showing that rational people

should prefer information that is accurate no matter

how it relates to their current hypothesis. People should

continue to seek new information until they are certain

enough of the answer that the cost of new information

is not justified by the degree of uncertainty. Confirmation

bias can lead to overconfidence, where people

fail to recognize the level of uncertainty they face.

What implications are there for information search by

those displaying confirmation bias? When will they

cease to search for information? What might this imply

regarding people who have chosen to cease their

education efforts at various phases? What education

policy might be implied by this result?

4. Governments often require people to obtain insurance;

for example, all drivers are required to carry auto

insurance to cover damages to others in the event of a

crash. Homeowners are often required by banks to

carry insurance on their home. Why do these requirements

exist? Would they be necessary if people truly

recognized the risk they faced? One characteristic of an

overconfident person is that she is continually surprised

when what she thought was unlikely or

impossible comes to pass. What would happen in these

cases if people were not required to insure? What

problems might arise if governments also prepared for

emergencies in a way that displayed overconfidence?

What mechanisms could prevent overconfidence in

government action?

5. Suppose we consider producers in a competitive

market. Hence all producers are price takers and earn

profit π =pq−c q , where p is a random variable.

Thus, the mean of profit is E π =μpq −c q , and

variance of profit is VAR π = σ2p

q2. Further, suppose

that each producer has an expected utility of wealth

function that can be approximated as

E u π =E π − RA 2 VAR π and that each

behaves so as to maximize expected utility of wealth.

Consider that some producers are overconfident and

others are not. Which will produce more (larger q)?

Which will obtain a higher profit on average? Suppose

that the mean price declines over time. What is the

condition for shut down? Will rational or overconfident

producers shut down first? What does this say

about the rationality of firms in a competitive

environment?