Without multiple repetition, risk aversion is, I would argue, an extremely sensible strategy for utility maximisation.
If you value safety, you should simply include that in the utilify function you are considering.
So again, naively maximising expectation could leave one disappointed.
That is if you equate money with utility. However, these things have different names for a good reason. Look into diminishing marginal utility for more details.
While I am not claiming that instinct is always correct about what will make us happy in the long run, using to simple a method to try and overwrite ourselves will not help.
Your post shows that you don’t understand what you are criticising very well. Perhaps try harder to find a sympathetic interpretation.
Utility functions usually map from expected future states to utilities. You seem to be doing something else—since you have utilities in the arguments to the utility function. Put some dollars in there instead and you get:
a utility function where U(10% chance of 10 dollars) < U(1 dollar)
...which is absolutely fine and correctly represents risk aversion.
No, though I was using 10 utiles as shorthand for “an event that, were it to occur, would give you 10 utiles”. So without that shorthand it would be something like:
Let A and B be two future states and assume without loss of generality that U(A) = 0 utiles and U(B) = 10 utiles. Then if U(10% chance of B, 90% chance of A) < 1 utile.
But that would have been ugly in the context.
a utility function where U(10% chance of 10 dollars) < U(1 dollar)
This could be the same utility function that I am talking about, but it could also be one of a risk neutral agent with a diminishing marginal utility for money.
This could be the same utility function that I am talking about, but it could also be one of a risk neutral agent with a diminishing marginal utility for money.
Those are intimately-linked concepts, as I understand it:
Quantified utility models simplify the analysis of risky decisions because, under quantified utility, diminishing marginal utility implies “risk aversion”.
If you value safety, you should simply include that in the utilify function you are considering.
That is if you equate money with utility. However, these things have different names for a good reason. Look into diminishing marginal utility for more details.
Your post shows that you don’t understand what you are criticising very well. Perhaps try harder to find a sympathetic interpretation.
I think you are missing a “don’t” there.
Which would give you a utility function where U(10% chance of 10 utiles) < 1 utile
Utility functions usually map from expected future states to utilities. You seem to be doing something else—since you have utilities in the arguments to the utility function. Put some dollars in there instead and you get:
...which is absolutely fine and correctly represents risk aversion.
No, though I was using 10 utiles as shorthand for “an event that, were it to occur, would give you 10 utiles”. So without that shorthand it would be something like:
Let A and B be two future states and assume without loss of generality that U(A) = 0 utiles and U(B) = 10 utiles. Then if U(10% chance of B, 90% chance of A) < 1 utile.
But that would have been ugly in the context.
This could be the same utility function that I am talking about, but it could also be one of a risk neutral agent with a diminishing marginal utility for money.
Those are intimately-linked concepts, as I understand it:
http://en.wikipedia.org/wiki/Marginal_utility#Revival