Daniel Bernoulli, 1738*

“Peter tosses a coin and continues to do so until it should land heads.

He agrees to give Paul one ducat if he gets heads on the very first throw,

two ducats if he does it on the second,

four if on the third,

eight if on the fourth, and so on,

so that with each additional throw the number of ducats he must pay is doubled.

Suppose we seek to determine the value of Paul’s expectation.”

*Published in Papers of the Imperial Academy of Sciences in Petersburg

John Maynard Keynes, 1921*

“Is it certain that a larger good, which is extremely improbable, is precisely equivalent ethically to a smaller good which is proportionately more probable?

We may doubt whether the moral value of speculative and cautious action respectively can be weighed against one another in a simple arithmetic way

just as we have already doubted whether a good whose probability can only be determined on a slight basis of evidence can be compared by means merely of the magnitude of this probability with another good whose likelihood is based on completer knowledge.”

* “The application of probability to conduct”

Cash Value vs. Utility (or “Moral Worth”)

Laplace (1814): “It is apparent that one franc has much greater value for him who possesses only a hundred than for a millionaire.”

He distinguished between fortune physique and fortune morale.

Bernoulli thought the utility of a person’s wealth increased as the logarithm of its cash value.