I do seem to have some level of risk aversion when it comes to making these kinds of choices, but it’s not an extremely large level. The risk aversion seems to kick in most strongly when dealing with small probabilities of high payoffs. (In the “Set One” choice, I’d probably accept the 3% risk, though.)
If you had a choice between “$24000 with certainty” and “90% chance of $X”, is there really no value for X that would make you change your mind?
There are plenty of values of X for which I would change my mind in this case. The expected value of choosing X is X * 0.9. 24000 / 0.9 = 26666 + 1⁄3, so I’d take the riskier option if the payoff was $27,000 or above. (Why $27,000? No particular reason other than it’s convenient to round to.)
If you had a choice between “$24000 with certainty” and “X% chance of $24001″, what is the smallest value of X that would make you switch?
The value of X for which the expected utility is equal to $24,000 is 24000 / 24001 = 1 − 1/24001 = 0.999959… which is very close to 1. Possessing mere bounded rationality, I might as well round it up to 1 and say that betting $24,000 against $1, regardless of the offered odds, probably isn’t worth the time to set up and resolve the bet.
Now let’s look at set 4:
Choice 1: $24,000
Choice 2: A one in a million chance of $27 billion
Well… this is where my risk aversion kicks in. The decision-making heuristic that gets invoked is “events with odds of one in a million don’t happen to me”, the probability gets rounded down to zero, and I take the $24,000 and double my current net worth instead of taking the lottery ticket. I don’t know if this makes me silly or not.
This is very close to how I feel about it—I’m really tempted to take Set Four, Choice 1 on the assumption that “events with odds of one in a million don’t happen to me” too, but I’m not sure if that’s just pure scope insensitivity or an actually rational strategy.
Random musings:
I do seem to have some level of risk aversion when it comes to making these kinds of choices, but it’s not an extremely large level. The risk aversion seems to kick in most strongly when dealing with small probabilities of high payoffs. (In the “Set One” choice, I’d probably accept the 3% risk, though.)
There are plenty of values of X for which I would change my mind in this case. The expected value of choosing X is X * 0.9. 24000 / 0.9 = 26666 + 1⁄3, so I’d take the riskier option if the payoff was $27,000 or above. (Why $27,000? No particular reason other than it’s convenient to round to.)
The value of X for which the expected utility is equal to $24,000 is 24000 / 24001 = 1 − 1/24001 = 0.999959… which is very close to 1. Possessing mere bounded rationality, I might as well round it up to 1 and say that betting $24,000 against $1, regardless of the offered odds, probably isn’t worth the time to set up and resolve the bet.
Now let’s look at set 4:
Choice 1: $24,000 Choice 2: A one in a million chance of $27 billion
Well… this is where my risk aversion kicks in. The decision-making heuristic that gets invoked is “events with odds of one in a million don’t happen to me”, the probability gets rounded down to zero, and I take the $24,000 and double my current net worth instead of taking the lottery ticket. I don’t know if this makes me silly or not.
This is very close to how I feel about it—I’m really tempted to take Set Four, Choice 1 on the assumption that “events with odds of one in a million don’t happen to me” too, but I’m not sure if that’s just pure scope insensitivity or an actually rational strategy.