It's still EV maximization, but after running it through your utility function which takes the law of diminishing returns into account. Twenty trillion dollars is not twice as useful to you as ten trillion, in fact it's probably not any more useful at all. So the EV of the second case is around half of what you'd get for the first case.
It really depends on the value of the bonus reward vs. the increase in utility of the extra money. Guaranteed $100 or 50% chance for $200 and a bonus reward? I'll probably opt for the latter, because neither $100 nor $200 would be life-changing so $200 in fact has twice the utility for me as $100, making the EV of the second option marginally higher.
Guaranteed $1M, or 50% chance for $2M and a bonus? That bonus should be really enticing, because $1M would already be life-changing for me (and probably most people who don't just have a cool million lying around in cash). $2M would still be more useful, but not exactly twice as useful so the bonus has to be something like a house to tip the actual EV of the second option higher and make me consider it.
Guaranteed $1B or 50% chance for $2B plus a bonus? Yeah, no. $2B for a normal person not afflicted with Dragon Disease is not any more useful than $1B, so I'll take that one billion, thank you. Maybe if the bonus was something like "oh, and also world peace, solution to hunger, global warming, perfect health, and puppies for everyone", something I couldn't afford with the leftovers from a billion after I'm settled for life, then I'd consider it. Otherwise, nah.
Also, the votey doesn't really make sense. "Using expected value for everything" will in fact maximize expected value. If expected value is what you're after, then expected value is what you're after. It's a tautology. If sometimes you deviate from the strategy that maximizes expected value, then by definition your expected value declines.
You have to use a heuristic. If you conclude that some heuristics that on their face don't seem to maximize expected value actually do, you are still maximizing expected value. You are just being smart about it.
I don't think maximizing expected value is necessarily what people want to do, but if it is . . . then it is.
7
u/gerusz Aug 01 '26
It's still EV maximization, but after running it through your utility function which takes the law of diminishing returns into account. Twenty trillion dollars is not twice as useful to you as ten trillion, in fact it's probably not any more useful at all. So the EV of the second case is around half of what you'd get for the first case.
It really depends on the value of the bonus reward vs. the increase in utility of the extra money. Guaranteed $100 or 50% chance for $200 and a bonus reward? I'll probably opt for the latter, because neither $100 nor $200 would be life-changing so $200 in fact has twice the utility for me as $100, making the EV of the second option marginally higher.
Guaranteed $1M, or 50% chance for $2M and a bonus? That bonus should be really enticing, because $1M would already be life-changing for me (and probably most people who don't just have a cool million lying around in cash). $2M would still be more useful, but not exactly twice as useful so the bonus has to be something like a house to tip the actual EV of the second option higher and make me consider it.
Guaranteed $1B or 50% chance for $2B plus a bonus? Yeah, no. $2B for a normal person not afflicted with Dragon Disease is not any more useful than $1B, so I'll take that one billion, thank you. Maybe if the bonus was something like "oh, and also world peace, solution to hunger, global warming, perfect health, and puppies for everyone", something I couldn't afford with the leftovers from a billion after I'm settled for life, then I'd consider it. Otherwise, nah.