The value of the St. Petersburg paradox
- From: pauldepstein@xxxxxxx
- Date: Sun, 22 Jun 2008 06:39:34 -0700 (PDT)
I'm skeptical about the pedagogical or theoretical value of the St.
Petersburg paradox. For one thing, it's seen to be a non-paradox
right away because the world's money supply is clearly finite.
The below is copy-pasted from Wikipedia's entry on the paradox: "In
economics, the St. Petersburg paradox is a paradox related to
probability theory and decision theory. It is based on a particular
(theoretical) lottery game (sometimes called St. Petersburg Lottery)
that leads to a random variable with infinite expected value, i.e.
infinite expected payoff, but would nevertheless be considered to be
worth only a very small amount of money. The St. Petersburg paradox is
a classical situation where a naïve decision criterion (which takes
only the expected value into account) would recommend a course of
action that no (real) rational person would be willing to take. "
Yes, good points are made in this paragraph. But I believe that the
basic point could be made much more simply, and hence that the paradox
isn't as clever or interesting as people think.
For example, suppose you had the opportunity to make exactly one (non-
transferrable) bet where your odds of winning would be 1 in 1000 and
where you would win 1 billion US dollars if successful but nothing if
unsuccesful. Surely, exactly as in the St. Petersburg paradox, most
people wouldn't be prepared to pay very much to take on this bet
either, even though the expected value of this bet is 1 million
dollars.
Does anyone agree with me that this paradox is not as important an
illustration as many seem to think it is?
Paul Epstein
.
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