The ‘Dog vs Cat’ cluelessness dilemma (and whether it makes sense)

Instead I'm saying that in many decision-situations people find themselves in, although they could (somewhat) narrow their credence range by investing more thought, in practice the returns from doing that thinking aren't enough to justify it, so they shouldn't do the thinking.

(I don't think this is particularly important, you can feel free to prioritize my other comment.) Right, sorry, I understood that part. I was asking about an implication of this view. Suppose you have an intervention whose sign varies over the range of your indeterminate credences. Per the standard decision theory for indeterminate credences, then, you currently don’t have a reason to do the intervention — it’s not determinately better than inaction. (I’ll say more about this below, re: your digits of pi example.) So if by “the returns from doing that thinking aren’t enough to justify it” you mean you should just do the intervention in such a case, that doesn’t make sense to me.

Thanks for explaining!

I feel confusion about "where does the range come from? what's it supposed to represent?"

• Honestly this echoes some of my unease about precise credences in the first place!

Indeed. :) If “where do these numbers come from?” is your objection, this is a problem for determinate credences too. We could get into the positive motivations for having indeterminate credences, if you’d like, but I’m confused as to why your questions are an indictment of indeterminacy in particular.

Some less pithy answers to your question:

• They might come from the same sort of process people go through when generating determinate credences — i.e. thinking through various considerations and trying to quantify them. But, at the step where you find yourself thinking, “Hm, it could be 0.2, but it could also be 0.3 I guess, idk…”, you don’t force yourself to pick just one number.
• More formally, interval-valued credences fall out of Bradley’s (2017, sec 11.5.2) representation theorem. Even if your beliefs are just comparative judgments like “is A more/less/equally/[none-of-the-above] likely than B?” — which are realistic for bounded agents like us — if they satisfy all the usual axioms of probabilism except for completeness,^[1] they have the structure of a set of probability distributions.

I don't see probabilities as magic absolutes, rather than a tool

I’m confused about this “tool” framing, because it seems that in order to evaluate some numerical representation of your epistemic state as “helpful,” you still need to make reference to your beliefs per se. There’s no belief-independent stance from which you can evaluate beliefs as useful (see this post).^[2]

The epistemic question here is whether your beliefs per se should have the structure of (in)determinacy, e.g., do you think you should always be able to say “intervention XYZ is net-good, net-bad, or net-neutral for the long-term future”. That’s what I’m talking about when talking about “rational obligation” to have (in)determinate credences in some situation. It's independent of the kind of mere practical limitations on the precision of numbers in our heads you’re talking about.

Analogy: Your view here is like that of a hedonist saying, "Oh yeah, if I tried always directly maximizing my own pleasure, I'd feel worse. So pursuing non-pleasure things is sometimes helpful for bounded agents, by a hedonist axiology. But sometimes it actually is better to just maximize pleasure." Whereas I'm the non-hedonist saying, "Okay but I'm endorsing the non-pleasure stuff as intrinsically valuable, and I'm not sure you've explained why intrinsically valuing non-pleasure stuff is confused." (The hedonism thing is just illustrative, to be clear. I don't think epistemology is totally analogous to axiology.)

for the normal vNM kind of reasons

The VNM theorem only tells you you’re representable as a precise EV maximizer if your preferences satisfy completeness. But completeness is exactly what defenders of indeterminate beliefs call into question. Rationality doesn’t seem to demand completeness — you can avoid money pumps / Dutch books with incomplete preferences.

For a toy example, suppose that I could take action X, which will lose me $1 if the 20th digit of Pi is odd, and gain me $2 if the 20th digit of Pi is even. Without doing any calculations or looking it up, my range of credences is [0,1] -- if I think about it long enough (at least with computational aids), I'll resolve it to 0 or 1. But right now I can still make guesses about my expectation of where I'd end up

I think this fights the hypothetical. If you “make guesses about your expectation of where you’d end up,” you’re computing a determinate credence and plugging that into your EV calculation. If you truly have indeterminate credences, EV maximization is undefined.

I don't think I'd agree with that.

I’d like to understand why, then. As I said, if indeterminate beliefs are on the table, it seems like the straightforward response to unknown unknowns is to say, “By nature, my access to these considerations is murky, so why should I think this particular determinate ‘simplicity prior’ is privileged as a good model?”

1. ^{^}

   (plus another condition that doesn’t seem controversial)

2. ^{^}

   Technically, there are Dutch book and money pump arguments, but those put very little constraints on beliefs, as argued in the linked post.

I've looked into this and here's (this specific section of the post) a case against this cancelation postulate that builds upon the literature on the topic. :) For something that addresses Owen's above point in particular, see the second half of the section discussing Tomasik's argument (which is basically the same afaiu).

(Sharing this here on the off-chance this is also of interest to someone else finding themself lost in this comment thread someday).