Read Online Priceless: The Myth of Fair Value (and How to Take Advantage of It) by William Poundstone - Free Book Online Page B
Authors: William Poundstone
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problem with that, Allais told Savage: his theory was dead
wrong
.
Proving theories wrong was a hobby with Allais. His parents had owned a cheese shop, and he had worked eighty-hour weeks—while holding down administrative posts with the French bureau of mines—writing the iconoclastic economic works that secured his renown, and ultimately a Nobel Prize. Allais did not limit himself to disproving wrong ideas in economics. He was just then embarking on a grand quest to disprove Einstein’s theory of relativity. Allais devised a special pendulum that would one day show Einstein’s error, or so he believed. He would spend much of the 1950s attempting to demonstrate that Einstein had cribbed relativity (for what it’s worth) from that great Frenchman Henri Poincaré.
Proving that Savage’s theory was wrong was much simpler. Like a troll in a fairy tale, Allais posed three riddles.
I will use a streamlined version of the questions Allais published the following year, putting the money amounts in dollars. Though not identical to the riddles Allais posed to Savage, they will give you the flavor of his argument.
Riddle one: Which of the following would you rather have?
(a) A sure $1 million
—
or
—
(b) This gamble: We spin a wheel of fortune with 100 slots. You have an 89 percent chance of winning $1 million, a 10 percent chance of winning $2.5 million, and a 1 percent chance of winning nothing at all.
Allais believed that most people would choose (a), the sure million, over (b), which offers a small chance of ending up with nothing. Apparently, Savage agreed.
Riddle two: This time your choice is
(a) An 11 percent chance of winning $1 million
—
or
—
(b) a 10 percent chance of winning $2.5 million.
Allais thought that most people would choose (b). There isn’t much difference in the chances. You might as well go for the higher prize in(b). Again Savage concurred. In so doing, he fell into the Frenchman’s trap.
This brings us to Riddle 3. In front of you is a sealed box. Which would you rather have?
(a) An 89 percent chance of winning whatever is in the box, and an 11 percent chance of winning $1 million instead
—
or
—
(b) An 89 percent chance of winning what’s in the box, a 10 percent chance of winning $2.5 million, and a 1 percent chance of winning nothing at all.
This was a direct thrust at the American’s jugular. As Allais knew, one of Savage’s axioms of reasonable decision making says (in essence) that when deciding between a burger with diet soda or pizza with diet soda, you can ignore the diet soda because you’re getting it in either case. The only thing that matters is whether you like burgers or pizza better. In general, according to Savage, deciders should ignore the common elements of choices and choose based on the differences.
This sounds reasonable to just about everyone. Allais spotted a subtle flaw. By Savage’s logic, the choice in Riddle 3 shouldn’t depend on what’s in the box. Whether you choose (a) or (b), you get the same 89 percent chance at winning the same box.
This doesn’t mean that the box’s contents are unimportant. The box could contain a billion dollars, or a deadly tarantula, or the phone number of that cool person you met on the subway. But according to Savage, the box shouldn’t bear on the choice between (a) and (b). That choice should be based solely on whether it’s better to have an 11 percent chance of $1 million or a 10 percent chance of $2.5 million.
In other words, the answer to Riddle 3 should be the same as to Riddle 2. That’s not all. Suppose we open the box and discover a million dollars in there. Then the choice in Riddle 3 ends up being identical to that in Riddle 1. In short, the answer to all three riddles should be the same, either (a) or (b) with no flip-flopping. Allais had tricked Savage into betraying his own rule.
A few months later, Allais gave a similar pop quiz to Milton Friedman. Friedman did
not
fall into
wrong
.
Proving theories wrong was a hobby with Allais. His parents had owned a cheese shop, and he had worked eighty-hour weeks—while holding down administrative posts with the French bureau of mines—writing the iconoclastic economic works that secured his renown, and ultimately a Nobel Prize. Allais did not limit himself to disproving wrong ideas in economics. He was just then embarking on a grand quest to disprove Einstein’s theory of relativity. Allais devised a special pendulum that would one day show Einstein’s error, or so he believed. He would spend much of the 1950s attempting to demonstrate that Einstein had cribbed relativity (for what it’s worth) from that great Frenchman Henri Poincaré.
Proving that Savage’s theory was wrong was much simpler. Like a troll in a fairy tale, Allais posed three riddles.
I will use a streamlined version of the questions Allais published the following year, putting the money amounts in dollars. Though not identical to the riddles Allais posed to Savage, they will give you the flavor of his argument.
Riddle one: Which of the following would you rather have?
(a) A sure $1 million
—
or
—
(b) This gamble: We spin a wheel of fortune with 100 slots. You have an 89 percent chance of winning $1 million, a 10 percent chance of winning $2.5 million, and a 1 percent chance of winning nothing at all.
Allais believed that most people would choose (a), the sure million, over (b), which offers a small chance of ending up with nothing. Apparently, Savage agreed.
Riddle two: This time your choice is
(a) An 11 percent chance of winning $1 million
—
or
—
(b) a 10 percent chance of winning $2.5 million.
Allais thought that most people would choose (b). There isn’t much difference in the chances. You might as well go for the higher prize in(b). Again Savage concurred. In so doing, he fell into the Frenchman’s trap.
This brings us to Riddle 3. In front of you is a sealed box. Which would you rather have?
(a) An 89 percent chance of winning whatever is in the box, and an 11 percent chance of winning $1 million instead
—
or
—
(b) An 89 percent chance of winning what’s in the box, a 10 percent chance of winning $2.5 million, and a 1 percent chance of winning nothing at all.
This was a direct thrust at the American’s jugular. As Allais knew, one of Savage’s axioms of reasonable decision making says (in essence) that when deciding between a burger with diet soda or pizza with diet soda, you can ignore the diet soda because you’re getting it in either case. The only thing that matters is whether you like burgers or pizza better. In general, according to Savage, deciders should ignore the common elements of choices and choose based on the differences.
This sounds reasonable to just about everyone. Allais spotted a subtle flaw. By Savage’s logic, the choice in Riddle 3 shouldn’t depend on what’s in the box. Whether you choose (a) or (b), you get the same 89 percent chance at winning the same box.
This doesn’t mean that the box’s contents are unimportant. The box could contain a billion dollars, or a deadly tarantula, or the phone number of that cool person you met on the subway. But according to Savage, the box shouldn’t bear on the choice between (a) and (b). That choice should be based solely on whether it’s better to have an 11 percent chance of $1 million or a 10 percent chance of $2.5 million.
In other words, the answer to Riddle 3 should be the same as to Riddle 2. That’s not all. Suppose we open the box and discover a million dollars in there. Then the choice in Riddle 3 ends up being identical to that in Riddle 1. In short, the answer to all three riddles should be the same, either (a) or (b) with no flip-flopping. Allais had tricked Savage into betraying his own rule.
A few months later, Allais gave a similar pop quiz to Milton Friedman. Friedman did
not
fall into
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