Hi Max! Again, I agree the longtermist and garden-variety cases may not actually differ regarding the measure-theoretic features in Vaden’s post, but some additional comments here.
But it would be a pretty strange objection to say that me giving a probability of 60% is meaningless, or that I’m somehow not able or not allowed to enter such bets.
Although “probability of 60%” may be less meaningful than we’d like / expect, you are certainly allowed to enter such bets. In fact, someone willing to take the other side suggests that he/she disagrees. This highlights the difficulty of converging on objective probabilities for future outcomes which aren’t directly subject to domain-specific science (e.g. laws of planetary motion). Closer in time, we might converge reasonably closely on an unambiguous measure, or appropriate parametric statistical model.
Regarding the “60% probability” for future outcomes, a useful thought experiment for me was how I might reason about the risk profile of bets made on open-ended future outcomes. I quickly become less convinced I’m estimating meaningful risk the further out I go. Further, we only run the future once, so it’s hard to actually confirm our probability is meaningful (as for repeated coin flips). We could make longtermist bets by transferring $ btwn our far-future offspring, but can’t tell who comes out on top “in expectation” beyond simple arbitrages.
This defence is that for any instance of probabilistic reasoning about the future we can simply ignore most possible futures
Honest question being new to EA… is it not problematic to restrict our attention to possible futures or aspects of futures which are relevant to a single issue at a time? Shouldn’t we calculate Expected Utility over billion year futures for all current interventions, and set our relative propensity for actions = exp{α * EU } / normalizer ?
For example, the downstream effects of donating to Anti-Malaria would be difficult to reason about, but we are clueless as to whether its EU would be dwarfed by AI safety on the billion yr timescale, e.g. bringing the entire world out of poverty limiting political risk leading to totalitarian government.
The Dutch-Book argument relies on your willingness to take both sides of a bet at a given odds or probability (see Sec. 1.2 of your link). It doesn’t tell you that you must assign probabilities, but if you do and are willing to bet on them, they must be consistent with probability axioms.
It may be an interesting shift in focus to consider where you would be ambivalent between betting for or against the proposition that “>= 10^24 people exist in the future”, since, above, you reason only about taking and not laying a billion to one odds. An inability to find such a value might cast doubt on the usefulness of probability values here.
I don’t believe this relies on any probabilistic argument, or assignment of probabilities, since the superiority of bet (2) follows from logic. Similarly, regardless of your beliefs about the future population, you can win now by arbitrage (e.g. betting against (1) and for (2)) if I’m willing to take both sides of both bets at the same odds.
Correct me if I’m wrong, but I understand a Dutch-book to be taking advantage of my own inconsistent credences (which don’t obey laws of probability, as above). So once I build my set of assumptions about future worlds, I should reason probabilistically within that worldview, or else you can arbitrage me subject to my willingness to take both sides.
If you set your own set of self-consistent assumptions for reasoning about future worlds, I’m not sure how to bridge the gap. We might debate the reasonableness of assumptions or priors that go into our thinking. We might negotiate odds at which we would bet on “>= 10^24 people exist in the future”, with our far-future progeny transferring $ based on the outcome, but I see no way of objectively resolving who is making a “better bet” at the moment