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To get rid of it entirely you have to declare that there is some point beyond which provides zero additional value no matter how much more money you add. No, y
by cperciva 11y ago
To get rid of it entirely you have to declare that there is some point beyond which provides zero additional value no matter how much more money you add.
No, you merely have to declare that there is some amount of utility which can never be obtained no matter how much money you have. (Or as the Simpsons put it: There's one thing you can't buy: A dinosaur.)
In mathematical terms, if your utility function is f(x) = 1 - 1/x, every marginal dollar adds utility; but the added utility is never enough to make the gamble profitable.
- AstralStorm 11y agoOh but you can but a dinosaur - a dead one. Given enough money you could potentially clone one too. Utility function analysis is arbitrary just as the article says. Compare this to ergodic theory (used for proper dynamic system analysis), where you can clearly derive the value function over number of plays, including infinite number. What an ergodic process is you can see here: https://en.wikipedia.org/wiki/Ergodic_process https://en.wikipedia.org/wiki/Ergodic_process By computing the limit of the ensemble average you will derive the logarithmic utility function. This works for finite resources as well, but then you can also derive the time it takes to bankrupt the bank, as well as probability of that ever happening.
- deleted 11y ago[deleted]