Information Cascades Todd Kaplan

Restaurant You go to a unfamiliar city such as Tel Aviv. Where do you decide to eat? Restaurant A and B both look nice on the outside and have a similar menu. A has a small crowd. B is empty. Which do you go to? Is this still the case when from the outside B looks slightly better? How about if some clerk at the hotel said he heard B was good?

Dance. You are at a dance. Some good-looking guy asks the woman next to you to dance. She says no. He then asks another woman next to you to dance. She says no. Now he asks you to dance. You say … Some not-so-good-looking middle-aged guy asks you to dance first. You say …

Job Interview Haifa wants to hire an economist. Sam has a boring CV but we hear that he is interviewing at Bar-Ilan and BGU. We decide we must have missed something and give him a job talk. The talk is somewhat lame, but he is in a good field. We hear that Bar-Ilan and BGU made him and offer. In addition Tel Aviv is interviewing him. We decide to make Sam an offer.

Don’t look up. In the 60s, some experimenters had groups of people 1-15 look up in the sky. They then watched to see if anyone else looked up as well. With one looking up, most ignored him. With 5 looking up, many stopped. With 15, 45% stopped and kept looking up.

Information cascade In all these cases, decisions are made sequentially. People deciding later can infer information of those deciding earlier. A cascade develops when people deciding later ignore their information relying on the earlier information.

Information vs. Network. This relates to network externalities. Is the reason a bestselling book picks up momentum because: People like to read the same book. If so many people read a book it must be good.

Experiment Two urns: B and R. B contains 2 blue balls and 1 red ball. R contains 2 red balls and 1 blue ball. Person 1 privately sees one randomly drawn ball. He guesses which urn. Person 2 privately sees one randomly drawn ball AND what person 1 guessed. She guesses which urn. Etc..

What should happen. If person 1 sees R what does he choose? If person 1 sees B what does he choose? If person 2 sees 1 choose R and sees R what does she choose? If person 2 sees 1 choose R and sees B what does she choose? If person 3 sees 1 choose R and 2 choose R and sees B what does she choose? Does this ever stop?

Bayes’ rule Knowing Bayes’ rule can save your life. You might have a rare disease (1 out of 10,000). You decide to get tested and tests are accurate 99 percent of the time (regardless of whether the results come back positive or negative). If your test results come back positive, what are your chances that you actually have the disease? (a) .99, (b) .90, (c) .10, or (d) .01?

Bayes’ rule P(sick|positive)=P(positive & sick)/P(positive)=P(positive &sick)/(P(positive and sick)+P(positive and not sick)). Why could knowing Bayes’ rule save your life? In early 1990s, HIV test had a 4 percent rate of false positives. 1 in 250 males had HIV. Roughly a positive result meant you had still less than 10% chance of having the disease. Known case of suicide as a result of receiving news.

Bayes’ Rule P(A|B)=P(A & B)/P(B)=P(A)*P(B|A)/P(B)=P(A&B)/P(B)= P(A&B)/(P(B|A)*P(A)+P(B|not A)*P(not A)). What is the prob of the urn being B given sequence b? What is the prob of the urn being B given sequence bb? What is the prob of the urn being R given sequence bb? What is the prob of the urn being B given bbr? What is the prob of the urn being B given brbbr?

Breaking a Cascade What do you do if you see the following sequence: bbbbbbbbbbbrr and then get an r.

Information Cascade An information cascade starts if there is too much variance from the average.

Lessons It is rational to look at the decisions of others. Cascades can be wrong. Opposite of the Wisdom of Crowds effect. Francis Galton found crowd at a county fair accurately guessed the weight of an ox Average of individual guesses were closer to the ox’s true butchered weight than the estimates of most individuals and cattle experts.

Lessons Cascades can be based on very little information. Cascades can be fragile. Financial crisis.. Could causes have been an information cascade? People ignore common sense because everyone else does. Question one should ask is which effect is stronger: information cascade or wisdom of crowds?