"What are my chances?"
"You mean, not good like one out of a hundred?"
"I'd say more like one out of a million."
"So... you're telling me there's a chance."
Whenever we have more than one option to choose between, we have to consider not only the relative value of each option but also the likelihood that we will be able to attain that option if we commit. Now, it makes no sense to choose something that is lower in both prob and value. But, if one option has a higher prob and a lower value, or vice versa, then we will have to rely on our values in deciding between them. Examples:
- In psychology, research describing how people choose based on the relative probability and value of an outcome is extensive. One theory says we are especially risk averse for moderate probability / low value gains and small probability / high value losses. (see here)
- In mate preference, choosing someone who is stable and dependable (sure bet) or someone with better looks and health (shot in the dark) is one of the universal trade offs across cultures. (see here)
- In finance, models of investors trade off between minimizing the variance of their stocks and maximizing their average return. Since individuals have a diminishing marginal return to each add'l dollar, they are risk averse and willing to give up expected returns to take the sure bet over the shot in the dark. (however see here for a critique on the risk premium when people benchmark relatively)
(Above photo and quote from the classic Dumb and Dumber scene)