Good points well made. I'm not sure what you mean by "my expected log score is maximized" (and would like to know), but in any case it's probably your average world rather than your median world that does it?

Very interesting!

From eyeballing the graphs, it looks like the average Brier score is barely below 0.25. This indicates that GPT-4 is better than a dart-throwing monkey (i.e. predicting a random %age, score of 0.33), and barely better than chance (always predicting 50%, score of 0.25).

It would be interesting to see the decompositions for those two naive strategies for that set of questions, and compare to the sub-scores GPT-4 got.

You could also check if GPT-4 is significantly better than chance.

dieontrasted

Typo?

people who are focused on providing—and incentivized to provide—estimates of the expected number of cases

Can you say more about this? Would users forecast a single number? Would they get scored on how close their number is to the actual number? Could they give confidence intervals?

I think that's how I'd use this as well.

I don't think that solves the problem though. There are a lot of people, and many of them believe very unlikely models. Any model we (lesswrong-ish) people spend time discussing is going to be vastly more likely than a randomly selected human-thought-about model. I realise this is getting close to reference class tennis, sorry.

Cool idea. Any model we actually spend time talking about is going to be vastly above the base rate, though. Because most human-considered models are very nonsensical/unlikely.

At first I was dubious about the framing of a "shifting" n-dimensional landscape, because in a sense the landscape is fixed in 2n dimensions (I think?), but you've convinced me this is a useful tool to think about/discuss these issues. Thanks for writing this!

Epistemic status: gross over-simplification, and based on what I remember from reading this 6 months ago.

This paper resolved many quesitons I had left with MWI. Relevantly here, I think it argues that the number of worlds doesn't grow because there was already an infinity of them through space.

Observing an experiment is then equivalent to locating yourself in space. Worlds splitting is the process where identical regions of the universe become different.

The scoring system incentivizes predicting your true credence, (gory details here).

I think Metaculus rewarding participation is one of the reasons it has participation. Metaculus can discriminate good predictors from bad predictors because it has their track record (I agree this is not the same as discriminating good/bad predictions). This info is incorporated in the Metaculus prediction, which is hidden by default, but you can unlock with on-site fake currency.