4.5 Probability in psychology and economicsxxx rather than construct a theory of rational behavior, more interesting to giveexamples of “predictably irrational” behavior. In this section I give two famousexamples and one less famous example.In reading literature on this topic, it is important to keep in mind that thereis rather little direct evidence from real-world behavior (xxx partly becauseit’s hard to control for other variables). Most xxx comes from studying people’sanswers to hypothetical questions (“which of these alternative would you choose. . . . . . ?”) and the extent to which people’s actual actions correspond to theiranswers to a questionnaire is rather uncertain (xxx teenage smokers).xxx to get startedSuppose you are a manufacturer, selling an item to consumers at a currentprice, say $100. What would happen if you lowered the price, say to $90? Well,you expect the number of sales to increase – maybe a little, maybe a lot –but you expect it to increase rather than decrease. This seems self-evident,but what’s going on from a customer’s viewpoint? Well, a conceptually simpleexplanation is that each customer places a dollar value to the item, and thenbuys it if the price is less than the dollar value. It’s important for realism thatthe dollar value is subjective – what a venti latte or an Xbox 360 or a Coachhandbag is worth to you depends on your subjective tastes. Continuing theexplanation, the number of sales of the item at $100 is the number of peoplewho value the item at $100 or more; decreasing the price to $90 increases thenumber of sales by the number of people who value it between $90 and $100.Obviously this story can’t be literally true – it would require you to assigna personal value to every item available for sale, and who has time for that? –but the issue is to what extent people’s behavior is consistent with this story.xxx segue4.5.1 The endowment effectAt time of writing I own a 12 year old car with a blue book value of $2,800.Would I sell it for $2,800? No, because it’s been reliable, it’s running well rightnow, it’s convenient that I don’t need to worry about minor dings, and I don’twant the hassle of looking for a new car. In fact I wouldn’t consider selling itfor less than 5, 000. Now suppose I needed a car and you owned the car justdescribed: would I be willing to buy it from you for $2,800? No, because I don’tpositively want an old car, I wouldn’t know how reliable it is, I would need todeal with paperwork for this purchase knowing that soon I would have to dealwith buying a new car – and in fact I wouldn’t be willing to pay you mo re than$500.Why this factor of 10 difference between two prices for the same object? Aneconomist would say that part of the difference is indeed the (rational) reasonsabove, but another part is that it’s an illustration of the (irrational)endowment effect: people place a higher value on objects theyown than objects they do not own. [54]44To demonstrate this effect in the real world one wants a situation where one caneliminate possible extraneous reasons. A very ingenious example is described atgreater length in [1]: below is the summary from [54].Duke University has a very small basketball stadium and the numberof available tickets is much smaller than the number of people whowant them, so the university has developed a complicated selectionprocess for these tickets that is now a tradition. Roughly one weekbefore a game, fans begin pitching tents in the grass in front ofthe stadium. At random intervals a university official sounds anair-horn which requires that the fans check in with the basketballauthority. Anyone who doesn’t check in within five minutes is cutfrom the waiting list. At certain more important games, even thosewho remain on the list until the bitter end aren’t guaranteed a ticket,only an entry in a raffle in which they may or may not receive a ticket.After a final four game in 1994, economists Ziv Carmon and DanAriely called all the students on the list who had been in the raffle.Posing as ticket scalpers, they probed those who had not won a ticketfor the highest amount they would pay to buy one and received anaverage answer of $170. When they probed the students who hadwon a ticket for the lowest amount they would sell, they received anaverage of about $2,400. This showed that students who had wonthe tickets placed a value on the same tickets roughly fourteen timesas high as those who had not won the tickets.xxx segueIn some setting one can view the endowment effect as an underlying reasonfor risk aversion. Suppose two items (A and B) have the same market price,and the same “personal value” to me, and suppose I own A but not B. Supposethere is an available action that(with chance 0.4) I lose item A(with chance 0.6) I gain item B.According to the expected (market) value criterion, I should take this action.But most p eople wouldn’t: the endowment effect says the psychological cost oflosing A may be considerably greater than the psychological value of gaining B.4.5.2 An experiment: risk aversion in games of chancexxx a classic experiment, rep eated by two students (Rose Cendak and RebeccaGraff) in my Berkeley course. The subjects are not told the purpose of theexperiment; can you the reader guess?• Subjects: college educated, non-quantitative majors.• Equipment: bingo balls (1 – 39) and 10 Monopoly $500 bills.• Draw balls one at a time; subject has to bet $500 on whether next ballwill be higher or lower than last ball; prompt subject to talk (recorded)about thought process. Repeat for 5 bets.45• Say: we’re doing this one last time; this time you have option to bet allyour money. Prompt talk.As I said, it’s not at all obvious what the purpose of the experiment is, so thisis your opportunity to try to guess the purpose.The point is that we’re interested, not so much in people’s actions, as intheir reasons for their actions. In the first part, everyone behaves and explainsrationally: if this ball is 27 then (because 27 is more than half of 39) it’s morelikely that the next ball is less than 27, so subjects bet that way. In the lastpart, what explanations do people give for their choice of whether or not to betall their money? In my students’ experiment, about 2/3 of the subjects gaveexplanations involving chances to win and or risk-aversion: we counted these as“rational” reasons. But the other 1/3 gave reasons