One topic investigated by behavioral economists but not covered in the text relates to how individuals assess probabilities of random events occurring repeatedly. The hot-hand fallacy is the fallacy that a randomly generated event is more likely to occur again if it has just been observed to have occurred multiple times. For instance, a poker player that has had a streak of “hot hands” might believe that he is on a winning streak and will again be dealt a “hot hand” in the next game. The gambler’s fallacy, on the other hand, occurs when people believe that, once a randomly generated event has occurred, it is less likely to occur again. For instance, a lottery player might observe that a particular number has just won in a lottery and conclude that it is less likely that this number will win in the next run of the same lottery.
A: Both types of fallacies arise, for instance, for naive investors in stocks.
(a) When a stock falls in value, people often hold onto it based on the argument that “what goes down must come up”. What fallacy is this an example of?
(b) When a stock rises in value, people sometimes hold onto it because “the company must be doing well and will thus continue to rise in value.” What fallacy is at play now?
(c) If you know that lots of other people believe that stocks which have risen in value will rise again in the near future, might this affect your investment choices even if you do not yourself operate under any particular illusion about probabilities of random events?
(d) In the period leading up to the housing market crash in 2007, housing values were increasing at dramatic rates — by as much as 20 to 25% annually in some markets. Lots of people invested with the expectation that this would continue. Can you use the hot-hand fallacy to explain such financial “bubbles”?
(e) The empirical evidence suggests that investors generally are less likely to dispose of losing stocks than they are of disposing winning stocks. Is there another aspect of behavioral economics, one that is explicitly covered in the text, which might explain this (rather than either of the fallacies we have mentioned in this exercise)?
(f) In lotteries where people guess what number will be chosen, the total money pot gets split between the winners. In light of the fact that the gambler’s fallacy appears to be strong among lottery players, why might it be best to choose last week’s winning number when playing the lottery this week?
B: One of my friends had four children, each a boy. She had really been hoping for a girl for some time and reasoned that she should try again — after all, having four boys in a row was an unlikely enough event—what were the chances of the even less likely event of 5 boys in a row?
(a) How many possible gender sequences are there for a woman who gives birth to 4 children? What does this imply for the probability that the sequence will be “all boys”?
(b) What is the probability that her first 5 births are all boys?
(c) What is the probability that the sequence of a woman’s first 4 children is boy-girl-boy-girl? What about any other gender sequence?
(d) What is the probability that my friend’s next (and fifth) child will be a boy? How does it compare to the probability that a woman who has had the boy-girl-boy-girl sequence will have a girl as her fifth child?
(e) My friend used the evidence that four boys in a row was an unlikely event—and five boys in a row would be an even more unlikely event, as her reason for why she thought she had a good chance of her fifth child being a girl. What part of her reasoning is correct, and what part is incorrect? 1