Links should be fixed! Thanks for pointing this out.

Thanks for pointing this out. It should work now.

Sorry—you're right that this doesn't work. To clarify, I was thinking that the method of picking the color should be fixed ex-ante (e.g. "I pick red as the color with 50% probability"), but that doesn't do the trick because you need to pool the colors for ambiguity to arise.

The issue is that the problem the paper identifies does not come up in your example. If I'm offered the two bets simultaneously, then an ambiguity averse decision maker, like an EU decision maker, will take both bets. If I'm offered the bets sequentially without knowing I'll be offered both when I'm offered the first one, then neither an ambiguity-averse nor a risk-averse EU decision-maker will take them.  The reason is that the first one offers the EU decision-maker a 50% chance of winning, so given risk-aversion its value is less than 50% of $1. So your example doesn't distinguish a risk-averse EU decision-maker from an ambiguity-averse one.

So I think unfortunately we need to go with the more complicated examples in the paper. They are obviously very theoretical. I think it could be a valuable project for someone to translate these into more practical settings to show how these problems can come up in a real-world sense.

Thanks! Helpful follow-ups.

On the first point, I think your intuition does capture the information aversion here, but I still think information aversion is an accurate description. Offered a bet that pays $X if I pick a color and then see if a random ball matches that color, you'll pay more than for a bet that pays $X if a random ball is red. The only difference between these situations is that you have more information in the latter: you know the color to match is red. That makes you less willing to pay. And there's no obvious reason why this information aversion would be something like a useful heuristic.

I don't quite get the second point. Commitment doesn't seem very relevant here since it's really just a difference in what you would pay for each situation. If one comes first, I don't see any reason why it would make sense to commit, so I don't think that strengthens the case for ambiguity aversion in any way. But I think I might be confused here.

Yeah, that's the part I'm referring to. I take his comment that expectations are not random variables to be criticizing taking expectations over expected utility with respect to uncertain probabilities.

I think the critical review of ambiguity aversion I linked to us sufficiently general that any alternatives to taking expectations with respect to uncertain probabilities will have seriously undesirable features.

Thanks for writing this. I think it's very valuable to be having this discussion. Longtermism is a novel, strange, and highly demanding idea, so it merits a great deal of scrutiny. That said, I agree with the thesis and don't currently find your objections against longtermism persuasive (although in one case I think they suggest a specific set of approaches to longtermism).

I'll start with the expected value argument, specifically the note that probabilities here are uncertain and therefore random valuables, whereas in traditional EU they're constant. To me a charitable version of Greaves and MacAskill's argument is that, taking the expectation over the probabilities times the outcomes, you have a large future in expectation. (What you need for the randomness of probabilities to sink longtermism is for the probabilities to correlate inversely and strongly with the size of the future.) I don't think they'd claim the probabilities are certain.

Maybe the claim you want to make, then, is that we should treat random probabilities differently from certain probabilities, i.e. you should not "take expectations" over probabilities in the way I've described. The problem with this is that (a) alternatives to taking expectations over probabilities have been explored in the literature, and they have a lot of undesirable features; and (b) alternatives to taking expectations over probabilities do not necessarily reject longtermism. I'll discuss (b), since it involves providing an example for (a).

(b) In economics at least, Gilboa and Schmeidler (1989) propose what's probably the best-known alternative to EU when the probabilities are uncertain, which involves maximizing expected utility for the prior according to which utility is the lowest, sort of a meta-level risk aversion. They prove that this is the optimal decision rule according to some remarkably weak assumptions. If you take this approach, it's far from clear you'll reject longtermism: more likely, you end up with a sort of longtermism focused on averting long-term suffering, i.e. focused on maximizing expected value according to the most pessimistic probabilities. There's a bunch of other approaches, but they tend to have similar flavors. So alternatives on EU may agree on longtermism and just disagree on the flavor of it.

(a) Moving away from EU leads to a lot of problems. As I'm sure you know given your technical background, EU derives from a really nice set of axioms (The Savage Axioms). Things go awry when you leave it. Al-Najjar and Weinstein (2009) offer a persuasive discussion of this (H/T Phil Trammell). For example, non-EU models imply information aversion. Now, a certain sort of information aversion might make sense in the context of longtermism. In line with your Popper quote, it might make sense to avoid information about the feasibility of highly-specific future scenarios. But that's not really the sort of information non-EU models imply aversion to. Instead, they imply aversion to info that would shift you toward the option that currently has a lot of ambiguity about it because you dislike it based on its current ambiguity.

So I don't think we can leave behind EU for another approach to evaluating outcomes. The problems, to me, seem to lie elsewhere. I think there are problems with the way we're arriving at probabilities (inventing subjective ones that invite biases and failing to adequately stick to base rates, for example). I also think there might be a point to be made about having priors on unlikely conclusions so that, for example, the conclusion of strong longtermism is so strange that we should be disinclined to buy into it based on the uncertainty about probabilities feeding into the claim. But the approach itself seems right to me. I honestly spent some time looking for alternative approaches because of these last two concerns I mentioned and came away thinking that EU is the best we've got.

I'd note, finally, that I take the utopianism point well and wold like to see more discussion of this. Utopian movements have a sordid history, and Popper is spot-on. Longtermism doesn't have to be utopian, though. Avoiding really bad outcomes, or striving for a middling outcome, is not utopian. This seems to me to dovetail with my proposal in the last paragraph to  improve our probability estimates. Sticking carefully to base rates and things we have some idea about seems to be a good way to avoid utopianism and its pitfalls. So I'd suggest a form of longtermism that is humble about what we know and strives to get the least-bad empirical data possible, but I still think longtermism comes out on top.
 

This this this! As a PhD student in economics, I'm always pushing for the same thing in academia. People usually think saying nice job is useless, because it doesn't help people improve. It's important for people to know what they're doing right, though. It's also important for people to get positive reinforcement to keep going down a path, so if you want someone to keep persevering (which I hope we generally do), it's good to give them a boost when they do a good job.

I'm excited to see this! One thing I'd mention on the historian path and its competitiveness is you could probably do a lot of this sort of work as an economic historian with a PhD in economics. Economic historians study everything from gender roles to religion and do ambitious if controversial quantitative analyses of long-term trends. While economists broadly may give little consideration to historical context, the field of economic history prides itself on actually caring about history for its own sake as well, so you can spend time doing traditional historian things, like working with archival documents (see the Preface to the Oxford Encyclopedia of Economic History for a discussion of the field's norms).

The good thing here is it probably allows for greater outside options and potentially less competitiveness than a history PhD given the upsides of an economics PhD. You could also probably do similar work in political science.

>> Our impression is that although many of these topics have received attention from historians (examples: 1, 2, 3, 4, 5), some are comparatively neglected within the subject, especially from a more quantitative or impact-focused perspective.

I'd also note that some of these cites I don't think are history—2 and 4 are written by anthropologists. (I think in the former case he's sometimes classified as a biologist, psychologist, or economist too.)

I really do hope we have EAs studying history and fully support it, and I just wanted to give some closely related options!

Great post, and thanks for writing it. One note: if polarization is defined as "more extreme views on each issue" (e.g. more people wanting extremely high or extremely low taxes), then it does not seem to be happening according to some research. The sort of polarization happening in the U.S. is more characterized as ideological sorting. That is, views on any particular issue (abortion, affirmative action, gun control) don't have more mass on the extremes than before, but the views in each political party are less mixed.

This is nonetheless important, and I don't think it radically changes much of what you said. Affect toward the opposite party is still much more negative than before. But it might suggest we should be more concerned about the conflict between the parties itself (e.g. abusing constitutional norms, cancellation) and less concerned about their policies per se.