/sci/ - Science & Math

[Anonymous No.9883876]

My probability theory professor:
>being rational by definition means always picking an option with the highest expected utility
Is this right?

[Anonymous No.9883944]

>>9883876
>no
A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator q. Numbers that are not rational are called irrational numbers. The real line consists of the union of the rational and irrational numbers. The set of rational numbers is of measure zero on the real line, so it is "small" compared to the irrationals and the continuum.

[Anonymous No.9884014]

>>9883876
Your professor is justifying genocide, i suggest you to report him to your local police station.

[Anonymous No.9884094]

>>9883876
Imagine a game with a very high probability of losing money, and a very low probability of winning a lot of money, enough money so that the expected utility is positive. You can only play once.

Is it rational to play? The expected utility is positive but you are most likely going to lose money.

[Anonymous No.9884134]

>>9884094
>The expected utility is positive
No because it is counter balanced by the fact that the probability to lose money is much higher, so your expected utility of playing might be lower than the one of not playing

[Anonymous No.9884136]

>>9884134
Also depends on the amounts of money involved , for example betting 1 cent with 1% odds of winning 100000 dollars, in that case it would be pretty rational for me to try it.

[Anonymous No.9884233]

>>9883876
It's a definition that you're using in the class, for specific purposes.
What do you mean by "Is this right?"

[Anonymous No.9884340]

>>9884233
>What do you mean by "Is this right?"
Well, suppose you follow this definition and I offer you a game. Bet all your money on a coin toss, if you win you get N dollars, if you don't, you lose all your money. I will always set N in such a way that your expected utility of playing one round is positive. Now, according to this definition you would be irrational not to play if offered. Suppose you play one round and I offer you to play again. I increase N so that expected utility of the game is still positive for you. Again, it would be irrational for you to decline. In fact, as long as I keep offering you to play you can never decline without being irrational, at least by this definition. Of course, since there is non-zero possibility of losing, eventually you will lose all your money - by doing the rational thing on every step.

[Anonymous No.9884357]

>>9884340
Expected utility is not necessarily equal to expected monetary payoff. You could very well have a complex utility function that isn't positive when the risk gets to big. Actually most utility models used in practice (e.g. In models used by insurance companies) assume that agents are risk averse and that this risk aversion increases when the risks get bigger.

Your professor just states the fact that you would always choose the option which gives higher expected utility. What choices you make due to that is entirely dependent on what the utility function is.

[Anonymous No.9884385]

>>9884357
>You could very well have a complex utility function that isn't positive when the risk gets to big
It doesn't have to be a fair coin, I can set the probability of losing arbitrarily low. If U is your utility function, x is how much money you bet, N is the payout and p is the probability of losing, what utility function can you have such that U(N)*(1-p) - U(x)*p cannot be made positive by setting p arbitrarily small and N arbitrarily large?

[Anonymous No.9884442]

Why doesn't he send me his paychecks then? I'm a utility monster.

[Anonymous No.9884473]

>>9883876
is it rational to play russian roulette with a large payoff?

[Anonymous No.9884715]

>>9883876
>Is this right?
Yes, but only for a "sufficiently complicated" definition of utility.

[Anonymous No.9885747]

>>9884385
Not him, you're treating the Utility like a monetary pay off sticking it in an expected value calculation. Yes expected monetary payoff can be positive but a utility function can be one which looks at, for example, the variability of your funds after the game as well as your necessity for these funds. The players rationale should justly include what they need and their consideration for the two possible outcomes, if they are satisfied with the current amount of money and the variance of the game is too great, cut it off.

[Anonymous No.9885759]

>>9884385
Also you've made the assumption that the function you've given us IS the utility function, that it is just the weighted average of your future utilities. Notice how you ask us to make that function positive? Because you've convinced yourself that monetary average is equivalent to expected utility. The thing you wrote is not necessarily the only utility function.

[Anonymous No.9885764]

>>9884473
If you're suicidal it definitely is.

[Anonymous No.9885766]

Your professor is crypto-nazi that wants to kill all humans with Magneto, infa 100%

[Anonymous No.9885802]

>>9885766
hui sosi, chmonya))0

[Anonymous No.9885918]

>>9884094
Rational doesn't just mean "a good idea", in the context of game theory it just refers to maximizing utility. Something can be rational but still be considered a stupid idea by most people.

[Anonymous No.9886001]

>>9884473
that depends on the utility of your life
if you think killing yourself comes at infinite cost, it is not rational
>>9883876
This is a kind of tautology in economics, utility is by definition the function that a rational actor maximizes.

[Anonymous No.9886024]

'utility' implies a value judgment and no value judgment is ever entailed by a purely factual statement. He may be acting rationally according to his personal system of values but if I don't agree with him in his judgments of value then I will see him as acting in a less than fully rational way.