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Actually, the logarithmic utility of money was introduced by one of the Bernoullis in the mid-1700's, several decades before Jeremy Bentham called his philosophy "utilitarianism". I think utilitarianism was, in fact, an attempt at "rationalising" ethics and the philosophy was always an attempt at doing what the modern mathematical theory of utility does.

Those whom the Gods wish to destroy They first make mad. -- Euripides
by Migeru (migeru at eurotrib dot com) on Fri Oct 20th, 2006 at 09:53:56 AM EST
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You learn something new every day.

What I still want to do is moderate this 'technical measure' distinction. Utility as it is used in economics does contain all kinds of philosophical assumptions about mindstates, etc. You can't talk about the declining marginal utility of consumption without making this utility partly a subjective measure of gratification, for instance.

by nanne (zwaerdenmaecker@gmail.com) on Fri Oct 20th, 2006 at 10:11:02 AM EST
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Wikipedia:
In probability theory and decision theory the St. Petersburg paradox describes a particular 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 theory (which takes only the expected value into account) would recommend a course of action that no (real) rational person would be willing to take. The paradox can be resolved when the decision model is refined via the notion of marginal utility or by taking into account the finite resources of the participants.

The paradox is named from Daniel Bernoulli's presentation of the problem and his solution, published in 1738 in the Commentaries of the Imperial Academy of Science of Saint Petersburg (Bernoulli 1738). However, the problem was invented by Daniel's cousin Nicolas Bernoulli who first stated it in a letter to Rémond de Montmort from 9th of September 1713.

Daniel was the first to solve the problem by showing that even though the expected payoff of the game is infinite, the expected log-payoff (i.e., the expected utility of playing the game) is finite.

Those whom the Gods wish to destroy They first make mad. -- Euripides
by Migeru (migeru at eurotrib dot com) on Fri Oct 20th, 2006 at 10:16:53 AM EST
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You can't talk about the declining marginal utility of consumption without making this utility partly a subjective measure of gratification, for instance.

I agree.  Bernoulli himself said:

"There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount."

And Gabriel Cramer, a few years before Bernoulli, refers to the role of "good sense":

"the mathematicians estimate money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it."


Truth unfolds in time through a communal process.
by marco on Fri Oct 20th, 2006 at 10:49:18 AM EST
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