In practice, I think the effects of oneās actions decay to practically 0 after 100 years or so. In principle, I am open oneās actions having effects which are arbitrarily large, but not infinite, and continuity does not rule out arbitrarily large effects.
If you allow arbitrarily large values and prospects with infinitely many different possible outcomes, then you can construct St Petersburg-like prospects, which have infinite expected value but only take finite value in every outcome. These violate Continuity (if itās meant to apply to all prospects, including ones with infinitely many possible outcomes). So from arbitrary large values, we violate Continuity.
Weāve also discussed this a bit before, and I donāt expect to change your mind now, but I think actually infinite effects are quite plausible (mostly through acausal influence in a possibly spatially infinite universe), and I think itās unwarranted to assign them probability 0.
Reality forces us to compare outcomes, at least implicitly.
There are decision rules that are consistent with violations of Completeness. Iām guessing you want to treat incomparable prospects/ālotteries as equivalent or that whenever you pick one prospect over another, the one you pick is at least as good as the latter, but this would force other constraints on how you compare prospects/ālotteries that these decision rules for incomplete preferences donāt.
I just do not see how adding the same possibility to each of 2 lotteries can change my assessment of these.
You could read more about the relevant accounts of risk aversion and difference-making risk aversion, e.g. discussed here and here. Their motivations would explain why and how Independence is violated. To be clear, Iām not personally sold on them.
If you allow arbitrarily large values and prospects with infinitely many different possible outcomes, then you can construct St Petersburg-like prospects, which have infinite expected value but only take finite value in every outcome. These violate Continuity (if itās meant to apply to all prospects, including ones with infinitely many possible outcomes). So from arbitrary large values, we violate Continuity.
Sorry for the lack of clarity. In principle, I am open to lotteries with arbitrarily large expected utility, but not infinite, and continuity does not rule out arbitratily large expected utilities. I am open to lotteries with arbitrarily many outcomes (in principle), but not to lotteries with infinitely many outcomes (not even in principle).
Weāve also discussed this a bit before, and I donāt expect to change your mind now, but I think actually infinite effects are quite plausible (mostly through acausal influence in a possibly spatially infinite universe), and I think itās unwarranted to assign them probability 0.
I think empirical evidence can take us from a very large universe to an arbitrarily large universe (for arbitrarily strong evidence), but never to an infinite universe. An arbitrarily large universe would still be infinitely smaller than an infinite universe, so I would say the former provides no empirical evidence for the latter. So I am confused about why discussions about infinite ethics often mention there is empirical evidence pointing to the existence of infinity[1]. Assigning a probability of 0 to something for which there is not empirical evidence at all makes sense to me.
There are decision rules that are consistent with violations of Completeness. Iām guessing you want to treat incomparable prospects/ālotteries as equivalent or that whenever you pick one prospect over another, the one you pick is at least as good as the latter, but this would force other constraints on how you compare prospects/ālotteries that these decision rules for incomplete preferences donāt.
I have not looked into the post you linked, but you guessed correctly. Which constraints would be forced as a result? I do not think preferential gaps make sense in principle.
You could read more about the relevant accounts of risk aversion and difference-making risk aversion, e.g. discussed here and here. Their motivations would explain why and how Independence is violated. To be clear, Iām not personally sold on them.
Thanks for the links. Platoās section The Challenge from Risk Aversion argues for risk aversion based on observed risk aversion with respect to resources like cups of tea and money. I guess the same applies to Rethink Prioritiesā section. I am very much on board with risk aversion with respect to resources, but I still think it makes all sense to be risk neutral relative to total hedonistic welfare.
If you allow arbitrarily large values and prospects with infinitely many different possible outcomes, then you can construct St Petersburg-like prospects, which have infinite expected value but only take finite value in every outcome. These violate Continuity (if itās meant to apply to all prospects, including ones with infinitely many possible outcomes). So from arbitrary large values, we violate Continuity.
Weāve also discussed this a bit before, and I donāt expect to change your mind now, but I think actually infinite effects are quite plausible (mostly through acausal influence in a possibly spatially infinite universe), and I think itās unwarranted to assign them probability 0.
There are decision rules that are consistent with violations of Completeness. Iām guessing you want to treat incomparable prospects/ālotteries as equivalent or that whenever you pick one prospect over another, the one you pick is at least as good as the latter, but this would force other constraints on how you compare prospects/ālotteries that these decision rules for incomplete preferences donāt.
You could read more about the relevant accounts of risk aversion and difference-making risk aversion, e.g. discussed here and here. Their motivations would explain why and how Independence is violated. To be clear, Iām not personally sold on them.
Thanks, Michael.
Sorry for the lack of clarity. In principle, I am open to lotteries with arbitrarily large expected utility, but not infinite, and continuity does not rule out arbitratily large expected utilities. I am open to lotteries with arbitrarily many outcomes (in principle), but not to lotteries with infinitely many outcomes (not even in principle).
I think empirical evidence can take us from a very large universe to an arbitrarily large universe (for arbitrarily strong evidence), but never to an infinite universe. An arbitrarily large universe would still be infinitely smaller than an infinite universe, so I would say the former provides no empirical evidence for the latter. So I am confused about why discussions about infinite ethics often mention there is empirical evidence pointing to the existence of infinity[1]. Assigning a probability of 0 to something for which there is not empirical evidence at all makes sense to me.
I have not looked into the post you linked, but you guessed correctly. Which constraints would be forced as a result? I do not think preferential gaps make sense in principle.
Thanks for the links. Platoās section The Challenge from Risk Aversion argues for risk aversion based on observed risk aversion with respect to resources like cups of tea and money. I guess the same applies to Rethink Prioritiesā section. I am very much on board with risk aversion with respect to resources, but I still think it makes all sense to be risk neutral relative to total hedonistic welfare.
From Bostrom (2011), āRecent cosmological evidence suggests that the world is probably infiniteā.