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 de...
Apparently, at a recent EA summit Robin Hanson berated the attendees for giving to more than one charity. I think his critique is salient: given our human scope insensitivity, giving all your charity-money to one cause feels like helping with only *one* thing, even if that one organization does vastly more good, much more efficiently, than any other group, and so every dollar given to that organization does more good than an anything else that could be done with that dollar. More rational and more effective is to find the most efficient charity and give only to that charity, until it has achieved its goal so completely that it is no longer the most efficient charity.
That said, I feel that there are at least some circumstances under which it is appropriate to divide one's charity dollars: those that include risky investments.
If a positive singularity were to occur, the impact would be enormous: it would swamp any other good that I could conceivably do. Yet, I don't know how likely a positive singularity is; it seems to be a long shot. Furthermore, I don't know how much my charity dollars affect the probability one way or another. It may be that a p-singularity will either happen or it won't, and there's not much I can do about it. There's a huge pay-off but high uncertainty. In contrast, I could (for instance) buy mosquito nets for third world counties, which has a lower, but much more certain pay-off.
Some people are more risk-seeking than others, and it seems to be a matter of preference whether one takes risky bets or more certain ones. However, there are "irrational" answers, since one can calculate the expected pay-off of a gambit by mere multiplication. It is true that it is imprudent to bet one's life savings on an unlikely chance of unimaginable wealth, but this is because of quirks of human utility calculation: losses are more painful than gain are enjoyable, and there is a law of diminishing marginal returns in play (to most of us, a gift of a billion dollars is not very emotionally different than two billion, and we would not be indifferent between a 100% chance of getting a billion dollars and a 50% chance of getting two billion dollars on the one hand, and a 50% chance of getting nothing on the other. In fact, I would trade my 50/50 chance of a billion, for a 100% certainty of a 10 million). But, we would do well to stick to mathematically calculated expected-pay-offs, for any "games" that are small enough or frequent enough, that improbable flukes will be canceled out on the net.
Let's say you walk into the psychology department, Kahneman and Tversky offer you a trade off: you can save 50 lives, or you can "sell" some or all of those lives for a 0.005% increase in the probability of an outcome in which no one ever dies again and every problem that has ever plagued humanity is solved and post-humans impregnate the universe with life. That sounds fantastic, but at best you can only increase the probability of such an outcome by a quarter of a percent. Is any ratio of "lives saved" to "incremental increases in the probability of total awesomeness" rational? Is it just a matter of personal preference how much risk you personally decide to take on? Ought you to determine your conversion factor between human lives and increases in the probability of a p-singularity, and go all in based on whether the ratio that is offered you is above or below your own (i.e. you're getting a "good deal")?
I feel like there's a good chance that we'll screw it all up and be extinct in the next 200 years. I want to stop that, but I also want to hedge my bets. If it does all go boom, I want to have spent at least some of my resources making the time we have better for as many people as possible. It even seems selfish to to not help those in need so that I can push up the probability of an awesome, but highly uncertain future. That feels almost like making reckless investment with other people's money. But maybe I just haven't gotten myself out of the cognitive-trap that Robin accused us off.