Suspiciously balanced evidence

But isn't it strange that there are so many questions for which the evidence we have is so very balanced?

But there aren’t. We just focus on the very tiny subset of questions for which that is the case, because those are the ones that are interesting.

If you look at prediction datasets like PredictionBook or GJP or other calibration datasets (or even prediction markets with their longshot biases), which cover a wide variety of questions (far wider than most policy or political debates, and typically with neutral valence such that most predictors are disinterested), it seems like people are generally uncalibrated in the direction of extremes, not 50%.

So that's evidence against people actually holding beliefs which are biased to be too close to 50%, and suggests something else is doing on, like topic filtering or attempting to appear rhetorically reasonable / nonfanatical. (The second definitely seems like a concern. I notice that people seem to really shy away from publicly espousing strong stands like when we were discussing the Amanda Knox case, or putting a 0/100% on PB even when that is super obviously correct just from base rates; there's clear status/signaling dynamics going on there.)

I have a confession to make, I can make no sense of probability as degree of belief. The measure-theoretic definition (due to Kolmogoroff?) suits me and I have never progressed beyond it. I can do naught but beg your forgiveness.

It is literally impossible for untrained humans to pay attention to settled questions for more than a tiny amount of time. We are hardwired for glossing over them, conscious attention are very expensive compute cycles.

A big part of the answer for me is something like this Scott Alexander post [LW · GW] about the probability of X within your model versus the probability that your model is miscalibrated in a relevant way. Given how shaky our models of the world are, this alone makes it hard for me to push past 99% on many questions, especially those that require predicting human decisions.

I assign a greater than 1% probability for each of these questions that all of the information I've taken in about the situation is completely wrong in some fashion. It's quite possible that I actually have no idea how the stock market, for example, works. There's lots of misinformation floating around each of these questions.

Generally, .1<p<.9 comes from not having a good gears-level model for the situation, for me. .9<p<.99 comes from concerns around the trustworthiness of data or from insufficiently tested models.

An additional possibility: everything already adds up to normality, we're just failing to notice because of how we're framing the question [LW · GW] (in this case, whether or not holding middling probability estimates for difficult and controversial statements is correct).

One more good explanation: Numbers are hard. Think of a few things that you would definitely give >99%. I can just about rank them, but I have no idea how many nines are supposed to be there.
And one more not-so-good one: We aren't actually trying to figure it out. We just want to participate in a discussion game, and this one involves numbers called propability, and they are usually between .1 and .9. A good sign that this is happening (and propably in part a reason for the range restriction) is when the "winning criterion" is whether the propability is above or below 50%.

I'm seeing a lot of replies saying, in effect, "duh, obviously #1: we only bother thinking about the questions whose answers are still somewhat open to doubt". Maybe that's the whole story, but I still don't think so: some questions remain in the category of "questions many people think about and aren't close to certain of the answers to" even as a lot of evidence accumulates.

(But maybe #1 is more of the story than I was inclined to think.)

I don't know if it's a good or not-good explanation, but in a lot of discussions of these examples, a different question will be answered than you're asking. But also #1, and also some ok-version-of-not-so-good: we cap our probability estimates with plausibility heuristics. If I'd be surprised but not shocked to see something, it's not less than 5% probability. If I'd be shocked, but not question everything I know, it's not less than 0.1% (for reference classes with a few-per-lifetime incidence of resolution).

"Human activity has caused substantial increases in global mean surface temperature over the last 50 years and barring major policy changes will continue to do so over at least the next 50 years -- say, at least half a kelvin in each case."

Generally, people seem to answer about whether policy changes are possible or useful, even when they claim to be discussing causality and prediction. This topic is rife with arguments-as-soldiers, and it's unsurprising that probability estimates are hard to find.

"On average, Christians in Western Europe donated a larger fraction of their income last year to non-religious charitable causes than atheists."

Wow, never thought about this, but I have trouble with the categorizations - I know a whole lot of semi-Christians (and Jews and Muslims) who could be counted in either camp, and a whole lot of charities which have religious origins but are currently not affiliated. In any case, I'd wonder why you were asking and how my prediction would change any behavior.

"Over the next 10 years, a typical index-fund-like basket of US stocks will increase by more than 5% per annum above inflation."

This one is better. Define the basket and inflation index and I'll make a bet. S&P 500 vs US CPI, I'd say about 15% to beat it by 5% per year (62% over the decade). Even so, I'd expect the joint prediction about inflation and return on investment to cause confusion. This is one where my proposed plausibility heuristic is putting a cap on my confidence level. For "reasonable" numbers, I don't think I can be more than 95% confident.

"In 2040, most global electricity generation will be from renewable sources."

Definition of "renewable" makes this one tricky, and questions about whether to include energy that could be electric or not (heating, for instance). Is nuclear included? I think we could narrow it down to a specific prediction that one could have a prediction market on. I don't know enough to bet, myself. And I won't be shocked in either direction, so my estimates can't be very strong.

There are a few questions on which the evidence is really one-sided - like the common ancestry of huamns and chimps.

Good explanation #3- we perceive probabilities differently from their objective values (i.e., a question of calibration). Our responses to questions will be both a function of our "underlying" subjective probabilities and also the mapping of that to the response format. In the link, for example, responding with (p) 10% to 90% feels like being from (w(p)) 20% to 70% sure.

" But isn't it strange that there are so many questions for which the evidence we have is so very balanced? "

What if we asked what type of informational distributions would produce a more skewed balances?

I would expect an enormous bias in terms of how much attention is paid to "interesting" questions - propositions we could sensibly rate near-1 or near-0 are boring because they're so obviously true or so obviously absurd that they feel mundane - like they're hardly a question in the first place.

It'd feel like cheating by way of degenerate examples to enumerate every common object and say "I'm extremely sure that at least one of those exists", but that is still a lot of propositions (even more propositions available if we dare to venture that two of each thing might exist)

Or for another partial explanation: on a question that is in any actual doubt, it's difficult to gather sufficient evidence to push a probability estimate very far into the tails. There are only so many independent observations one can make in a day.