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
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