On Nov 23, 2007 11:46 AM, Thomas Dalton thomas.dalton@gmail.com wrote:
To put it another way, if losing £100 is infinitely bad, then you'd never engage in any risk, no matter how small, which had any chance of leading to such a result. This means, in essence, you'd never do anything at all.
I disagree that every action has a chance of losing everything you own.
It seems to me that even no action at all has that chance, although it depends in part on what you consider "everything you own". Your initial statement suggested a loss as a monetary figure, which is both easier to deal with and more appropriate to the situation at hand.
Nevertheless, we're not talking about real life, we're talking abstractly - you were asking about the game theory perspective. Game theory doesn't assign values to outcomes, it just gives results based on the values you assume. You can assume any values you like. If you assume the value of money is logarithmic, there is a definite difference between risks and gains, therefore they are not the same from a game theoretic point of view.
I don't deny that there is a definite difference, nor do I claim that they are completely the same. I deny that they are *completely* different. The magnitudes are different, but everything else is the same.
And I don't see what making the value "logaritmic" has to do with anything. If the value of money is equal to the base ten logarithm of the amount of money, then the difference between 0 and 100 is equal to the difference between 100 and 1000, and thus is not infinite at all.
From the point of view of a given value system, they might be equivalent or they might not, but that's part of the value system, not of game theory.
Agreed, at least for any sane value system. Applying a value system which gives infinite values to certain situations would probably destroy game theory.
For a more realistic value system that displays the same behaviour, assume there is a certain amount of money you need to live (to buy food, for example). If you have less than that, you die, if you have more than that, you get a few luxuries.
I can't make that assumption, because it is unrealistic.
It's is reasonable to assert that no amount of luxuries is worth death (plenty of people would disagree, but it's still reasonable).
It really isn't, though. No one lives their life with a sole purpose of avoiding death, or more meaningfully (as it's probably impossible to avoid death), with a purpose of extending their life as long as possible.
And even if someone did live their life with a purpose of extending it as long as possible, now you'd have to define the payout of living life for a certain amount of time. Is it worth a 1% chance of dying one year from now for a 99% chance of increasing your lifespan from 80 years to 90 years? You still can't separate potential risks from potential gains. No matter how much wealth you have, if you had more wealth, you could protect yourself against more possible ways of dying.
(This is similar to the advice given to casino goers of keeping their taxi fare home in a different pocket to their gambling money - however sure you are of a bet, it's not worth risking not being able to get home.)
While it may be valid advice in terms of the situations one is likely to find oneself in at a casino, it isn't literally true. The cost of having to hitchhike home might be great, but it's not infinite.