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A comment on Bernoulli: Exposition of a New Theory on the Measurement of Risk (1738) [pdf].

Re:Bernoulli: Exposition of a New Theory on the Measurement ... by jcr on Friday July 17, 2015 @07:19AM (#9902179)
I thought this (ancient) paper was interesting enough to submit to HN since it's an English translation of the 1738 Latin treatise. I've seen it mentioned in a lot of places, but until tonight, I had never read the original (albeit a translation).

https://en.wikipedia.org/wiki/Utility

>"The St. Petersburg paradox was first proposed by Nicholas Bernoulli in 1713 and solved by Daniel Bernoulli in 1738. D. Bernoulli argued that the paradox could be resolved if decision-makers displayed risk aversion and argued for a logarithmic cardinal utility function. The first important use of the expected utility theory was that of John von Neumann and Oskar Morgenstern, who used the assumption of expected utility maximization in their formulation of game theory."

[ Parent | on HN ]
Re:Bernoulli: Exposition of a New Theory on the Measurement ... by crznp on Friday July 17, 2015 @08:53AM (#9902455)
The St Petersburg Paradox [1] has numerous solutions. While D. Bernoulli's solution is interesting in that it introduces the concept of Utility, it isn't the most satisfying to me.

The simplest solution is to recognize that a real world casino has an upper bound to what it can pay, and you can't realistically get more than that. With that upper bound, the expected payout is now finite, and actually pretty small, even for absurdly large upper bounds on the maximum payout (such as "all the money in the world").

[1] https://en.wikipedia.org/wiki/St._Petersburg_paradox

[ Parent | on HN ]
Re:Bernoulli: Exposition of a New Theory on the Measurement ... by applecore on Friday July 17, 2015 @12:14PM (#9903437)
Even if you had a 100% guarantee that the casino would pay with no upper bound, it still isn't worth paying more than few dollars for a lottery ticket.
[ Parent | on HN ]
Re:Bernoulli: Exposition of a New Theory on the Measurement ... by lisper on Friday July 17, 2015 @12:40PM (#9903579)
> if you had a 100% guarantee that the casino would pay with no upper bound

That's kind of like saying "If you could travel faster than the speed of light..." Paying without an upper bound is no less a violation of the laws of physics in a finite universe.

[ Parent | on HN ]