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

the trap Savage did and gave consistent answers. I suppose you have to wonder whether Savage clued him in.
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    In a 1953
Econometrica
article, published in French, Allais took issue with the axioms of
l’école Américaine
(meaning Detroit-born Jimmie Savage and his Brooklyn-born friend Milton Friedman). The Americans were saying that everyone’s got a price (utility) for everything. These subjective prices determine all decisions. Humans are more complex than that, Allais argued. Choices depend on context, and no single number can express how one feels about uncertain outcomes.
    This demonstration has since become known as Allais’ paradox. Don’t worry if you’re still unclear on what Allais was driving at and why it’s important. Let me give a remix of the paradox, conceived by Richard Zeckhauser of Harvard. You are a contestant on a popular new game show,
Your Money or Your Life
. Like most game shows, it simply recycles an old parlor game. Unfortunately for you, that old parlor game is Russian roulette.
    At the beginning of every show, Tiffany, the “Bullet Lady,” spins Fortune’s Wheel. The wheel is divided into six equal slices. The spin tells Tiffany how many bullets, from one to six, to load into a six-barrel gun and hand to the show’s host, Brian. After a brief commercial break, Brian spins the gun’s barrel and points it directly at your left temple. Just before he pulls the trigger, he proposes a financial arrangement that you will doubtless find interesting.
    You can buy a bullet.
Should you and Brian agree on a price, he will extract one bullet at random from the gun’s barrel and hand it to you in exchange for the money you give him. He will then spin the barrel again, point the gun at your temple again, and pull the trigger.
    Here’s the odd thing. You’d probably be willing to pay a higher price for a bullet when it’s the only one in the barrel. Buy that one bullet, and you’re 100 percent certain to survive (versus having a 1 in 6 chance of not making it to the commercial break). You’d pay a lot for that, right?
    Just for the sake of comparison, suppose there are four bullets in the barrel. Now how much would you pay to buy one bullet—to have just three bullets rather than four? Somehow this weakens the case for raising every last penny for that bullet. You might even feel you’d be willing to take your chances with the four bullets.
    Isn’t the human mind a funny thing? A bullet is a bullet, dead isdead. The reduction in probability of your demise is precisely the same in both cases. Why isn’t your price the same?
    Or imagine there are six bullets in the gun. You’re a corpse unless you buy a bullet. This may cause you to flip-flop again and conclude that the bullet is priceless, worth paying everything you’ve got.
    Both this game and Allais’ original puzzle reveal a
certainty effect
. There is often a huge subjective difference between an
absolute, 100 percent sure thing
and something that is only 99 percent likely. This difference is expressed in prices as well as choices. Meanwhile, the difference between a 10 and an 11 percent chance is shrugged off.
     
    To a select following of economists, psychologists, and philosophers, the Allais paradox became a sword in the stone. Great minds tested themselves against it, few managing to get much of a grip. In later years, Allais himself thought and wrote extensively about his puzzle. In true economist fashion, he tried to lay out axioms of human decision making and show that they were subtly incompatible, leading to contradiction.
    “His paradox was great,” one scholar said of Allais. “But if you read his own papers on what he thought the right theory was, they’re very hard to understand . . . He’s also cantankerous. There were a few conferences of a group called FUR, Foundations of Uncertainty and Risk, and I went to a couple of them. Allais would give this talk, and someone would say, ‘Your