Questions

1. In this chapter, brief mention was made of the false
consensus as a form of the availability heuristic.
Consider an entrepreneur who has developed a product
that she finds very useful in her own life. What
might the false consensus have to say regarding her
beliefs that the product is marketable to a more general
audience? How might these beliefs affect her decision
to invest in a new business venture distributing the
product, and what impact will this have on the riskiness
of her investment? Suppose we were to examine a
large sample of entrepreneurs who each had developed
products around their own needs. Given the false
consensus, what types of entrepreneurs are most likely
to succeed?
2. In 2003 Andy Pettitte pitched for the New York
Yankees baseball team, a team that won the American
League pennant and qualified for the World Series. In
the postseason, the Yankees played a series of games
with each of three teams: Minnesota, Boston, and
Florida. In each series, Pettitte pitched the second game
and won. A prominent sportswriter noticed this and
wrote an article touting this notable streak of wins
when pitching the second game of a series. Over the
season, Pettitte had pitched in 29 games and won 21 of
them. Is this a streak? Why might the sportswriter
believe this is a streak? How could you profit from this
perception? Model the sportswriter’s beliefs supposing
that the individual has two mental urns. One urn
(average) has three balls, with two marked “win” and
one marked “lose.” Suppose the other urn (streak) also
has three balls but all are marked “win.” Suppose that
the urns are never refreshed. What is the lowest
probability of a streak that would lead the sportswriter
to interpret this series of wins as a streak? Suppose
instead that the urns are refreshed after every two
games. Now what must the unconditional probability
of a streak be before one would believe one was
observing a streak?
3. Suppose there is an unconditional probability of a bull
market of 0.8, and a 0.2 probability of a bear market.
In a bull market, there is a 0.7 probability of a rise in
stock prices over a one-week period and 0.3 probability
of a fall in stock prices over the same period.
Alternatively, in a bear market there is a 0.4 probability
of a rise in stock prices in a one-week period and a 0.6
probability of a decline in stock prices in a one-week
period. Suppose, for simplicity, that stock price
movements over a week are independent draws. In the
last 10 weeks, we have observed four weeks with rising
prices and six weeks with declining prices. What is
the probability that you are observing a bear market?
Suppose a cable news analyst behaves according to
Grether’s generalized Bayes’ model of belief updating,
with βP =1.82 and βL = 2.25. What probability would
the news analyst assign to a bear market? Finally,
suppose a competing news analyst behaves according
to Rabin’s mental urn model, refreshing after every
two weeks of data. Suppose further that this analyst has
10 balls in each urn with distributions of balls labeled
“rise” and “fall” corresponding to the true probabilities.
What probability will he assign to a bear market? What
if the analyst had 100 balls in each urn?
4. Many lotteries divide the winnings evenly among all
those selecting the winning number. Knowing this,
how could one use the gambler’s fallacy to increase the
expected earnings from playing the lottery? Under