# 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