Free Priceless: The Myth of Fair Value (and How to Take Advantage of It) by William Poundstone Page B

similar phenomenon pertains to losing bets. How much would you pay to get out of a situation in which you have a 1 in 12 chance of losing $63? People were typically willing to pay
more
than the average loss. The dollar amount of the penalty loomed more important than the probability in their decision making.
    This suggests an explanation for why people buy insurance. They are willing to pay “too much” for coverage because they worry more about the dollar value of catastrophes than the remoteness of the odds.
    Lichtenstein and Slovic asked some of their subjects to rate the “attractiveness” of bets on a scale of 1 to 5. They found that the ratings correlated most strongly with the probability of winning. People liked bets that were easy to win.
    Okay, fine. But the
prices
assigned to bets correlated with the amount to win. It was as if people had two ways of valuing bets, and they were subtly in conflict.
     
    “I remember we were in Paul’s office, I can’t tell you what year it was,” Lichtenstein said. “We were getting an idea of what subjects were paying attention to. I don’t recall who said it first, or whether we said it at the same time. But it struck us that we could design bets that would encourage subjects to do one thing under one response mode and another under another response mode. When we saw it and said it aloud, we were sure it was going to work—and it did.”
    Their brainstorm was that prices might not reflect what people want.They could invent a pair of bets—call them A and B—such that most people would say they preferred A, but, when asked to assign prices to them, they would give a higher value to B.
    The strangeness of this might be easier to appreciate if you pretend that A and B are fancy gift boxes wrapped in paper and bows. I don’t know for sure what’s in either box. I have had a chance to shake them and form some opinion about what’s inside. Okay, I’ve decided that I’m willing to pay $40 for Box A and $70 for Box B. I’ve also decided that I’d rather have Box A.
    This is crazy! My prices don’t jibe with my desires or actions. Lichtenstein and Slovic found something crazier yet. For certain types of gambles,
most
people have valuations just like this.
    They called this a “preference reversal,” and here’s an example. In the figure below, the two circles represent dartboards. Pick one; then a “dealer” is going to toss a dart at the center of your chosen target, so that the dart is equally likely to land anywhere within the circle. That determines how much (if anything) you win. Which target would you rather use?

    The target on the left offers an 80 percent chance of winning $5 (otherwise nothing). The one on the right has a 10 percent chance of winning $40, and otherwise nothing.
    The expected value happens to be the same for both bets ($4), so thatprovides no grounds for choosing. Yet a majority prefer the target on the left. Lichtenstein and Slovic termed gambles like the one on the left
P
(for
probability
) bets. A P bet offers a high chance of winning. The bet on the right is a
$
(
money
) bet offering a bigger prize and a lesser chance of winning it. When asked to choose, most people prefer P bets to $ bets.
    There is nothing peculiar about that. Choosing the P bet increases the odds of walking away a winner. What
is
odd is that the same subjects regularly assign higher prices to $ bets, like the one on the right above. The prices contradict the preferences.
    In the actual experiments, a dozen distinct bets were used. They were somewhat more complicated than the examples above, in that the player stood a chance of losing money as well as winning it. (This is more like familiar sports or casino bets: you have to put up some money to play and risk losing it.) The experimental subjects were first shown bets two at a time and asked to choose which they preferred. Then they were shown the same set of bets one at a time and asked to price them. In this part,