On Nov 23, 2007 11:46 AM, Thomas Dalton <thomas.dalton(a)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.