If you had more evidence, you could make the comparison. But you currently have no clue which direction the comparison would go, in expectation over the evidence you might receive. So how are you supposed to compare them right now?

My best guess about which of 2 identical objects has a larger mass in expectation will be arbitrary is their mass only differs by 10^-6 kg, and I have no way of assessing this small difference. However, this does not mean the expected mass of the 2 objects is fundamentally incomparable

I worry you're reifying "expectations" as something objective here. The relative actual masses of the objects are clearly comparable. But if you subjectively can't compare them, then they're indeed incomparable "in expectation" in the relevant sense.

Besides the links Michael shared, I highly recommend this really short post.

However, the same goes for comparisons among the expected mass of seemingly identical objects with a similar mass if I can only assess their mass using my hands, but this does not mean their mass is incomparable.

I don't exactly understand what argument you're making here.

My core argument in the post is: Take any intervention X. We want to weigh up its impact for all sentient beings across the cosmos, where this "weighing up" is aggregation over all hypotheses. Now suppose we want to force ourselves to compare X with inaction, i.e., say either UEV(do X) > UEV(don't do X) or vice versa. We have such an extremely coarse-grained understanding (if any) of these hypotheses^[1] that, when we do the weighing-up, whether we say UEV(do X) > UEV(don't do X) or vice versa seems to depend on an arbitrary choice.

Can you say how your argument relates to mine?

1. ^{^}

   Relative to the amount of fine-grained detail necessary to evaluate the hypothesis, when what we value is "well-being of all sentient beings across the cosmos".

In normal situations, an agent can rationally come to a single probability distribution, but, Greaves argues that, in a situation with complex cluelessness, an individual should instead have a set of probability functions that they are “rationally required to remain neutral between.” I’m not entirely sure what this means.

You might be interested in this post I wrote explaining imprecision — hopefully answers "what this means".

I'm still not sure I understand why you find the arguments in the linked post, and post #3 of the sequence, uncompelling. Can you say more on that?

Given that the intervals are both derived from a representor P, the interval of EV diffs is {EV_p(A) - EV_p(B) | p in P}. See also here.

Ah I missed the "2 states of the world which are exactly the same" part, sorry. Then yeah the EVs would be the same. I'm not sure how this is supposed to support your original comment's argument though.

Depends on the details of what the intervals are supposed to represent. E.g.:

• Say you have a representor (imprecise probabilities) where EV_P(A) = EV_P(B) = [-1, 1].
• On one hand:
  • If:
    • for p1 in P, EV_p1(A) = -1 while EV_p1(B) = 1, and
    • for p2 in P, EV_p2(A) = 1 while EV_p2(B) = -1,
  • then A and B are incomparable.
• OTOH:
  • If for all p in P, EV_p(A) = EV_p(B), then A and B are comparable.
• (Ofc there are lots of other cases.)

Hi Vasco. I think Figure 3 here, and the surrounding discussion of how imprecision works, might answer your objection.

The idea is:

• Suppose two actions have precise EVs. You'll presumably grant that a tiny change in the (expected) location of electrons can flip the difference in EV from +epsilon to -epsilon.
• If so, then a tiny change in the (expected) location of electrons can flip the lower bound of an imprecise difference in EV from +epsilon to -epsilon.
• What makes two actions incomparable, under the imprecise EV model, is that the interval of EV differences crosses zero.
• So, it's unsurprising that a tiny change in the (expected) location of electrons can flip the two actions from "comparable" to "incomparable". 

Can you say which step in this argument you reject, and why?