There are two very different sorts of scenarios with something like “imprecise probabilities”.
The first sort of case involves uncertainty about a probability-like parameter of a physical system such as a biased coin. In a sense, you’re uncertain about “the probability that the coin will come up heads” because you have uncertainty about the bias parameter. But when you consider your subjective credence about the event “the next toss will come up heads”, and integrate the conditional probabilities over the range of parameter values, what you end up with is a constant. No uncertainty.
In the second sort of case, your very subjective credences are uncertain. On the usual definition of subjective probabilities in terms of betting odds this is nonsense, but maybe it makes some sense for boundedly introspective humans. Approximately none of the decision theory corpus applies to this case, because it all assumes that credences and expected values are constants known to the agent. Some decision rules for imprecise credence have been proposed, but my understanding is that they’re all problematic (this paper surveys some of the problems). So decision theory with imprecise credence is currently unsolved.
Examples of the first sort are what gives talk about “uncertain probabilities” its air of reasonableness, but only the second case might justify deviations from expected utility maximization. I shall have to write a post about the distinction.
But when you consider your subjective credence about the event “the next toss will come up heads”, and integrate the conditional probabilities over the range of parameter values, what you end up with is a constant. No uncertainty.
Really? You can estimate your subjective credence without any uncertainty at all? You integration of the conditional probabilities over the range of parameter values involves only numbers you are fully certain about?
I don’t believe you.
Approximately none of the decision theory corpus applies to this case
So this decision theory corpus is crippled and not very useful. Why should we care much about it?
So decision theory with imprecise credence is currently unsolved.
Yes, of course, but life in general is “unsolved” and you need to make decisions on a daily basis, not waiting for a proper decision theory to mature.
I think you overestimate the degree to which abstractions are useful when applied to reality.
The fact that the assumptions of an incredibly useful theory of rational decisionmaking turn out not to be perfectly satisfied does not imply that we get to ignore the theory. If we want to do seemingly crazy things like diversifying charitable donations, we need an actual positive reason, such as the prescriptions of a better model of decisionmaking that can handle the complications. Just going with our intuition that we should “diversify” to “reduce risk”, when we know that those intuitions are influenced by well-documented cognitive biases, is crazy.
This has been incredibly unproductive I can’t believe I’m still talking to you kthxbai
Ignore the last sentence and take the rest for what it’s worth :) I did the equivalent of somewhat tactlessly throwing up my hands after concluding that the exchange stopped being productive (for me at least, if not for spectators) a while ago.
There are two very different sorts of scenarios with something like “imprecise probabilities”.
The first sort of case involves uncertainty about a probability-like parameter of a physical system such as a biased coin. In a sense, you’re uncertain about “the probability that the coin will come up heads” because you have uncertainty about the bias parameter. But when you consider your subjective credence about the event “the next toss will come up heads”, and integrate the conditional probabilities over the range of parameter values, what you end up with is a constant. No uncertainty.
In the second sort of case, your very subjective credences are uncertain. On the usual definition of subjective probabilities in terms of betting odds this is nonsense, but maybe it makes some sense for boundedly introspective humans. Approximately none of the decision theory corpus applies to this case, because it all assumes that credences and expected values are constants known to the agent. Some decision rules for imprecise credence have been proposed, but my understanding is that they’re all problematic (this paper surveys some of the problems). So decision theory with imprecise credence is currently unsolved.
Examples of the first sort are what gives talk about “uncertain probabilities” its air of reasonableness, but only the second case might justify deviations from expected utility maximization. I shall have to write a post about the distinction.
Really? You can estimate your subjective credence without any uncertainty at all? You integration of the conditional probabilities over the range of parameter values involves only numbers you are fully certain about?
I don’t believe you.
So this decision theory corpus is crippled and not very useful. Why should we care much about it?
Yes, of course, but life in general is “unsolved” and you need to make decisions on a daily basis, not waiting for a proper decision theory to mature.
I think you overestimate the degree to which abstractions are useful when applied to reality.
The fact that the assumptions of an incredibly useful theory of rational decisionmaking turn out not to be perfectly satisfied does not imply that we get to ignore the theory. If we want to do seemingly crazy things like diversifying charitable donations, we need an actual positive reason, such as the prescriptions of a better model of decisionmaking that can handle the complications. Just going with our intuition that we should “diversify” to “reduce risk”, when we know that those intuitions are influenced by well-documented cognitive biases, is crazy.
This has been incredibly unproductive I can’t believe I’m still talking to you kthxbai
Ah.
Thank you for clarity.
I’m not sure what I’m should take away from that exchange.
Ignore the last sentence and take the rest for what it’s worth :) I did the equivalent of somewhat tactlessly throwing up my hands after concluding that the exchange stopped being productive (for me at least, if not for spectators) a while ago.
Anything in particular you are wondering about? :-)
Just my original question. I’m not sure if diversification to mitigate charitable risk is a matter of preference or numeric objectivity.
Try making up your own mind..? :-)
Someone told me not to.
(this is a joke)
At this point you’re supposed to fry your circuits and ’splode.