Chapter 5 Review Questions
5.1 Why might people dislike compound lotteries or uncertainty?
It is clear that people do not like compound lotteries or uncertainty (see also chapter nine).
Why this is so, is an open question. In our evolutionary past uncertainty may have been a
‘dangerous’ thing that is best avoided. Hence we avoid it. In essence we take risk aversion to
a higher level. One way to capture this in a slightly more formal way is that our subjective
beliefs are pessimistic. In situations of uncertainty we fear the worst. If we couple
pessimism with risk aversion then it is not surprising that we avoid uncertainty. But, why do
we avoid compound lotteries? Cognitively a compound lottery may look like uncertainty.
Even though we know the probabilities a second order lottery may seem ‘further away’ and
so harder to objectify. Framing and context may, therefore, be important. Also note the
diversity of behavior observed in Table 5.2. In short, this is a field ripe for further study!
5.2 Ellsberg (1961) suggested another box in which there are 90 balls. You know that 30 of
the balls are red and the other 60 are some mix of black and yellow. One ball will be randomly
drawn from the box. Would you prefer to ‘bet the ball is red’ or ‘bet the ball is black’? Would
you prefer to ‘bet the ball is red or yellow’ or ‘bet the ball is black or yellow’? Were your
choices consistent with subjective expected utility maximization?
Many people prefer to:
•
•
Bet on red rather than bet on black.
Bet on black or yellow rather than red or yellow.
Let us try to make sense of this using subjective expected utility. Suppose you believe there
are black balls in the box and 60
yellow balls.
If you bet on red you have a 30/90 0.33 chance of winning. If you bet on black you
have a /90 chance of winning. That you bet on red suggests you think
30.
If you bet on black or yellow you have a 60/90
on red or yellow you have a 30 60
/90 1
bet on black or yellow suggests you think 0.67 1
30.
0.67 chance of winning. If you bet
/90 chance of winning. That you
/90. This implies /90 0.33 or
Clearly this is inconsistent. It illustrates the general dislike of uncertainty. Many prefer
the certainty of knowing how many red balls there are and how many black or yellow balls
there are. It also illustrates how pessimism with uncertainty can be quite extreme. When
considering a bet on black a person might think ‘but none of the balls might be black’. When
considering a bet on red or yellow a person might think ‘but none of the balls might be
yellow’. This pessimism does not make sense when looking at as a whole but may appear
sensible on a case by case basis.
5.3 Why might someone who is ambiguity averse delay making a decision? How does
this relate to procrastination because of a present bias?
Most decisions involve an element of uncertainty. If we are reluctant to make choices in the
presence of uncertainty then we may delay. For example, if someone is uncertain what will
happen if she joins a gym she may delay joining the gym. If she is uncertainty what will
happen if she cancels gym membership she may delay cancelling the membership. This
delay may look like procrastination but is quite different.
In the case of procrastination the person knows what they want to do – there is
certainty – but they delay because of present bias. In the case of uncertainty the person
does not know what to do and so delays. How could we distinguish the two? If a person
delays in a situation in which they are well informed then we should suspect present bias. If
the person makes no attempt to gain new information then we should suspect present bias.
In reality, present bias and uncertainty likely combine. In both the gym and
telephone examples of chapter four, for instance, people did eventually cancel membership
or change calling plan – it just took longer than we might expect. At first both present bias
an uncertainty might cause them to delay. Over time, they become better informed as it
becomes more and more clear they will not use the gym but will use the phone a lot. As
they learn the amount of uncertainty is reduced. Ultimately, they only have present bias to
contend with.
5.4 There are no experiments to test for confirmatory bias in economic behavior. Design one.
And then do one to test for the law of small numbers.
The key things we need are: (1) for subjects to get some prior belief; (2) be exposed to
information; (3) see whether prior beliefs bias the interpretation of the information. For
example suppose subjects need to put a willingness to pay on a product like a microwave.
Some are given the initial impression the product is cheap others that it is expensive.
Subjects are then exposed to information about the product such as consumer reviews.
Does willingness to pay become more polarized by the additional information? To test for
the law of small numbers we can give some subjects more information than others.
5.5 Why might people be over‐influenced by what others do in some situations, and under‐
influenced in others?
In some situations the actions of an individual can tell a lot about what that person knew, in
others it can tell us little. This is captured in an information cascade. The first people to act
have no choice but to follow their private information: so one you can infer a lot from their
actions. Those that follow may just be learning from others: you can infer nothing from their
actions. We, however, have a bias towards thinking the number of people doing something
matters.
For example, if an investor called Alice buys a load of Facebook shares we should infer
she knows something. If Bill and Claire see what Alice does and then buy a load of facebook
shares we should infer much less about what they know. They could just be buying shares
because they saw Alice buy shares. Because of bias, we are likely to infer less than we
should from Alice’s actions and infer more than we should from Bill and Claire’s actions.
5.6 Can we trust people’s opinions? Why might people trust friends over expert advice?
Consider a signaling game like the sender‐receiver cheap talk game of chapter two. Recall
that someone tells you which option is best and then you get to choose. You should be
thinking what are the incentives of the sender? Does he have an incentive to give me good
advice, or to manipulate me? You should also be thinking how much the sender knows
about your preferences? Does he know what is the best for me, or is he guessing?
This should give you lots of reasons to not trust people’s opinion. The salesman may
be trying to manipulate you. Your friend may be misinformed on what you like and dislike. It
pays to be skeptical. We can also see why a friend’s evidence may be trusted more than an
expert. The friend has less incentive to manipulate and probably knows your preferences
better. In trusting friends opinions we may, however, fall foul of the law of small numbers.
How much does your fried really know? An expert may be more informed.
5.7 Consider reasons why confirmatory bias and the law of small numbers may matter in
health care.
Consider a doctor who gets a handful of patients during his career with a particular heart
condition. State of the art advice is to do treatment A. This has a 40 percent success rate
where success is measured as increased mobility. The doctor, however, has a prior that
treatment B is better. He uses treatment B on the first three of his patients. It is somewhat
ambiguous what counts as increased mobility. Partly because of confirmatory bias he
interprets a successful outcome for all three of his patients. Because of the law of small
numbers he then interprets this 100 percent success rate as evidence treatment B is better.
So, he carries on using treatment B.
5.8 How can we address the problems caused by biases in the interpretation of new
information in health care, and more generally?
A key thing in health care is to make practitioners aware of bias. Practitioners are clearly
highly educated people and once made aware of bias they can, hopefully, better avoid it.
Applying this approach more generally is more complicated but still a viable option.
Consider for example a ‘conflict zone’ such as that in Northern Ireland or Palestine. A
realization that the other side may interpret new information in a completely different way
can help to relieve tension.
We also should think about the way information is presented. For example, we have
seen that ambiguity is not good. So, can we reduce the ambiguity of new information? Can
we ‘humanize’ the results of statistical studies? For example, saying a treatment saves 40
out of every 100 patients looks very different to the success rate is 0.4. In short, we need to
think what causes bias and then try to avoid it.
5.9 When should someone buy an asset that is rising in price? When should they sell it?
If you are looking for short run gains then the strong evidence is that this question has no
answer. Or at least the answer is to sell whenever you want. Day to day asset prices are
unpredictable. You cannot know which way market sentiment is going to go and so the price
may turn at any moment. If you are looking over the long term then there is more hope of
making a good choice. If an asset is below fundamental value then you will, on average, over
the long term gain from buying it. And, if it is above fundamental value you will gain from
selling it.
5.10 Why do we see bubbles and crashes in the housing market?
A house is an investment as well as a home. In the US and the UK, less so in Europe, it is a
popular investment. People track house prices, house price changes make the front page of
the newspapers. These are the kinds of things we need for a bubble. If people see house
prices rising then they want to ‘get in on the game’. They increase the asking price of their
existing house. They are willing to pay more for a new house because the price is ‘sure’ to
rise further still. Mortgage companies also want to get in on the game by offering very
attractive deals. The bubble grows a‐pace. But, unfortunately, the end must come at some
point as reality sinks in.
5.11 What do you think happens if some traders have experience of bubble and crash but
some do not?
If we accept that experienced traders learn from past bubbles then they should prevent a
future bubble. To see why: Suppose that inexperienced traders are happy to pay above
fundamental value if the price is rising. The experienced traders realize this is a bubble. But,
rather than stay away they would be happy to sell, or short sell, stocks to the inexperienced
traders. Competition between experienced traders to sell to inexperienced traders will keep
prices low. The bubble never gets going. Note that this does rely on the option to short sell.
So, the argument applies to the stock market but not the housing market.
5.12 How does the buy sell imbalance relate to the ostrich effect?
The buy sell imbalance says that investors are more likely to buy than sell a stock that has
been in the news. The ostrich effect says that investors are more likely to look up their
investments when the news is good. If the news is good the investor will presumably be
more focused on buying than selling – we get a buy sell imbalance. If the news is bad the
investor will not look up his investments and so will not sell – we get a buy sell imbalance.
5.13 Come up with a list of reasons why a person’s opinion of electoral candidates may be
biased. On what basis should the person decide who to vote for?
This could be a long list! We typically only see candidates through the media or self
promotion. This means that the information coming to us is highly biased in itself. Our bias
will amplify that. Consider, for example, confirmatory bias. A democrat is likely to interpret
most a Republican candidate says negatively. A Republican is likely to interpret most a
Republican candidate says positively. Attitudes will thus become polarized. We also may be
highly influenced by one event during the election that shapes our opinion. For example, we
back a candidate that does well during a television debate. In doing this we can fall foul to
the law of small numbers. We may also conform to what friends, family, colleagues think.
Ideally a person would become informed on policy of each candidate and vote accordingly.
Many websites now make this easy by comparing candidates. Such websites are, however,
not all that popular! Most people tend to vote on a gut instinct.