And, in any case, there are arguments for the claim that we must assign probabilities to hypotheses like ‘The die lands on 1’ and ‘There will exist at least 10^16 people in the future.’ If we don’t assign probabilities, we are vulnerable to getting Dutch-booked
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.
(1) The human population will be at least 8 billion next year, (2) The human population will be at least 7 billion next year. If the probabilities of both hypotheses are undefined, then it would seem permissible to bet on either. But clearly you ought to bet on (2). So it seems like these probabilities are not undefined after all.
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
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