Calculating an expected value
This is a tiny question that I wouldn’t be asking if I had paid more attention in economics class. Anyway, a friend of mine was at the mall with me and he needed to go to the mall parking to retrieve his car. However, if he played at the mall casino, the parking fee would be waived. Without much interest, I heard him calculate his options out loud, until he got to this part:
“The parking fee is $4. I might get that amount waived yet lose more than that at the casino. Or I could play at the casino and win, in which case my expected value is whatever I win plus $4...”
At that moment I felt I had to intervene:
“You don’t get to add the parking fee to your expected value if you win at the casino; you merely don’t substract it.”
But he kept insisting that he could add it. We didn’t meet later to check his numbers, but I was left with this question.
Was my objection accurate?
If you add a number to your utility in every possible scenario, it doesn’t change your behavior. So you can treat the parking fee as either a gain that can be had or as a loss that can be avoided, as long as you are consistent.
So the question is, for the other option besides gambling, where he just pays the parking fee, is he treating that as no money gained/lost, just part of the status quo before he made his decision, or is he treating it as a loss? If the former, then waiving the fee is a gain which he can add. If the latter, then waiving it is just a loss averted.
Something to keep in mind is the time cost of playing casino games, and the fact that the casino set up the game so that people would give them money. (Maybe they expect it to reel people in for more than the minimum amount of gambling and you know you are too smart for that, but maybe everyone “knows” that about themselves).
You are right in the sense that playing at the casino doesn’t give your friend an extra four dollars but since utility is relative it depends on your perspective. Allow me to explain
This demonstrates your view. C is the money lost or gained by playing at the casino.
Pay Parking outcome = −4$, Casino outcome = C
And this demonstrates your friends view
Pay Parking outcome = 0 , Casino outcome = C+4 (It’s the same as your view but +4 has been added to both sides)
If you apply a modifier (in this case +4) to all choices then the difference between them stays the same and a perfect utility maximizer will still make the same choice.
Humans are not perfect utility maximizers and so the modifier you apply to outcomes can have a effect on mood. For example a scenario where you have lost 50$ in order to keep $100. A possible view is that you
lost $50 (treating what you had before as 0 and setting utilities relative to that).
made $50. (treating the -$100 as 0 and setting utilities relative to that)
had no benefit (treating the best possible outcome as 0 and setting utilities relative to that)
Each option makes no difference to computer algortithm because it just cares about relative weights. A human however is going to be a lot happier if they view it as a gain instead of a loss.
Oh, and this seems more appropriate for an Open Thread than for Discussion.