You’re saying that you prefer the option with an expected value of 1000 utils over the option with an expected value of 1100 utils. If we were talking about dollars, you could explain this by saying that you are risk averse, i.e. that the more dollars you have, the less you want each individual dollar. Utils are essentially a measurement of how much you want a particular outcome, so an outcome that is worth 1,000,100 utils is something you want 1000.1 times more than you want an outcome worth 1000 utils. If you don’t want to take this bet, that means you don’t actually want the 1,000,100 outcome enough for it to be worth 1,000,100 utils.
For the purposes of expected utility calculations, don’t think of utils as a measure of happiness; think of them as a measure of the strength of preferences.
(shrug) Sure. As long as I don’t try to understand utils as actually existing in the world, as being interpretable as anything, and I just treat them as numbers, then sure, I can do basic math as well as the next person.
And if all we’re saying is that it’s irrational to think that (.999 100) + (.001 1,000,100) <> 1100, well, OK, I agree with that, and I withdraw my earlier assertion about being utility risk averse. I agree with everyone else; that’s pretty much impossible.
My difficulty arises when I try to unpack those numbers into something real… anything real. But it doesn’t sound like that’s actually part of the exercise.
So, let’s say you have 1000 utils when you are offered the bet that Perplexed proposed. You have two possible choices:
You don’t take the bet. You continue to possess 1000 utils with probability 1. Expected value: 1000.
You take the bet.
There is a .999 probability that you will lose and be left with 100 utils.
There is a .001 probability that you will win, giving you a total of 1,000,100 utils.
Expected value: (.999 * 100) + (.001 * 1,000,100) = 1100.
You’re saying that you prefer the option with an expected value of 1000 utils over the option with an expected value of 1100 utils. If we were talking about dollars, you could explain this by saying that you are risk averse, i.e. that the more dollars you have, the less you want each individual dollar. Utils are essentially a measurement of how much you want a particular outcome, so an outcome that is worth 1,000,100 utils is something you want 1000.1 times more than you want an outcome worth 1000 utils. If you don’t want to take this bet, that means you don’t actually want the 1,000,100 outcome enough for it to be worth 1,000,100 utils.
For the purposes of expected utility calculations, don’t think of utils as a measure of happiness; think of them as a measure of the strength of preferences.
(shrug) Sure. As long as I don’t try to understand utils as actually existing in the world, as being interpretable as anything, and I just treat them as numbers, then sure, I can do basic math as well as the next person.
And if all we’re saying is that it’s irrational to think that (.999 100) + (.001 1,000,100) <> 1100, well, OK, I agree with that, and I withdraw my earlier assertion about being utility risk averse. I agree with everyone else; that’s pretty much impossible.
My difficulty arises when I try to unpack those numbers into something real… anything real. But it doesn’t sound like that’s actually part of the exercise.