Alternatively, one might adjust ambiguous probability assignments to reduce their variance. For example, in a Bayesian framework, the posterior expectation of some value is a function of both the prior expectation and evidence that one has for the true value. When the evidence is scant, the estimated value will revert to the prior.[30] Therefore, Bayesian posterior probability assignments tend to have less variance than the original ambiguous estimate, assigning lower probabilities to extreme payoffs.[31]
Would you say this is being ambiguity averse in terms of aiming for a lower EV option, or would you say that this is just capturing the EV of the situation more precisely and still aiming for the highest EV option?
Eg. maybe in your story by picking option 2 Pat is not being truly ambiguity averse (aiming for a lower EV option) but has a prior that someone is more likely to be traying to scam her out of $5 than give her free money and is thus still trying to maximise EV.
This is a great question. As I see it, there are at least 3 approaches to ambiguity that are out there (which are not mutually exclusive).
a. Ambiguity aversion reduces to risk aversion about outcomes. You might think uncertainty is bad because leaves open the possibility of bad outcomes. One approach is to consider the range of probabilities consistent with your uncertainty, and then assume the worst/​ put more weight on the probabilities that would be worse for EV. For example, Pat thinks the probability of heads could be anywhere from 0 to 1. If it’s 0, then she’s guaranteed to lose $5 by taking the gamble. If it’s 1, then she’s guaranteed to win $10. If she’s risk averse, she should put more weight on the possibility that it has a Pr(heads) = 0. In the extreme, she should assume that it’s Pr(heads) = 0 and maximin.
b. Ambiguity aversion should lead you to adjust your probabilities The Bayesian adjustment outlined above says that when your evidence leaves a lot of uncertainty, your posterior should revert to your prior. As you note, this is completely consistent with EV maximization. It’s about what you should believe given your evidence, not what you should do.
c. Ambiguity aversion means you should avoid bets with uncertain probabilities You might think uncertainty is bad because it’s irrational to take bets when you don’t know the chances. It’s not that you’re afraid of the possible bad outcomes within the range of things you’re uncertain about. There’s something more intrinsically bad about these bets.
Would you say this is being ambiguity averse in terms of aiming for a lower EV option, or would you say that this is just capturing the EV of the situation more precisely and still aiming for the highest EV option?
Eg. maybe in your story by picking option 2 Pat is not being truly ambiguity averse (aiming for a lower EV option) but has a prior that someone is more likely to be traying to scam her out of $5 than give her free money and is thus still trying to maximise EV.
Hi weeatquince,
This is a great question. As I see it, there are at least 3 approaches to ambiguity that are out there (which are not mutually exclusive).
a. Ambiguity aversion reduces to risk aversion about outcomes.
You might think uncertainty is bad because leaves open the possibility of bad outcomes. One approach is to consider the range of probabilities consistent with your uncertainty, and then assume the worst/​ put more weight on the probabilities that would be worse for EV. For example, Pat thinks the probability of heads could be anywhere from 0 to 1. If it’s 0, then she’s guaranteed to lose $5 by taking the gamble. If it’s 1, then she’s guaranteed to win $10. If she’s risk averse, she should put more weight on the possibility that it has a Pr(heads) = 0. In the extreme, she should assume that it’s Pr(heads) = 0 and maximin.
b. Ambiguity aversion should lead you to adjust your probabilities
The Bayesian adjustment outlined above says that when your evidence leaves a lot of uncertainty, your posterior should revert to your prior. As you note, this is completely consistent with EV maximization. It’s about what you should believe given your evidence, not what you should do.
c. Ambiguity aversion means you should avoid bets with uncertain probabilities
You might think uncertainty is bad because it’s irrational to take bets when you don’t know the chances. It’s not that you’re afraid of the possible bad outcomes within the range of things you’re uncertain about. There’s something more intrinsically bad about these bets.