Investor Presentaiton
Bernoulli's utility is the first of many resolutions
The St. Petersburg Paradox works by placing very large weight on
very rare outcomes-outcomes that cannot happen in practice.
▷ Bernoulli's resolution reduces the relative weight of those outcomes.
▷ However, the log transformation does not solve the problem of
infinite expectations in general.
In fact, the game can be adjusted to produce infinite expectations by
simply increasing the payout. (e.g. set wn = 22")
Scientists continue to write about the paradox. Other resolutions:
▷ Poisson: Arbitrarily large payouts are unrealistic; the world has finite
wealth. If payouts are capped, the expected winnings are small.
e.g. Suppose a casino only has $100 million. Then the game must
stop before round 27 since 227 > 100,000,000
If game must stop before round 27, the expected winnings are $27.
▷ Condorcet: Expected winnings do not tell you the value of any one
bet, only the value of repeating a bet many times.
►If the game is repeated a large enough number of times, the average
winnings across all plays will exceed any predetermined price.View entire presentation