Medicine provides many important-feeling examples that aren't politically charged.
Is it even possible to have an open question that lots of people would understand that wouldn't serve for signaling?
How about "The stock market will rise over the next month/year/decade", or "unemployment will go up", or some similar economics question?
I tentatively suggest there's a pattern here.
By default, and in practice for the great majority, no factual question can be regarded as popular or important unless it provides an opportunity for status signaling or mind killing.
However, if there is something like a prediction market, a tiny minority will adapt to become specialists in making accurate and profitable predictions.
This applies to sports and stock trades. Most people will be happy to be a [LOCAL SPORTS TEAM] fan, and will happily remained biased for signaling purposes, maybe making penny-ante bets to show loyalty. Professional bookmakers in Vegas and professional coaches of sports teams have to look at reality, or else find another job. Similarly, people in finance may have strong political opinions on their own time, but if they don't make money, they'll be out of a job.
This doesn't necessarily help if you're trying to "explain to people how beliefs should be expressed in probabilities" to the vast majority of people who don't have skin in the game. But you could appeal to their imagination.
Or if I were to try the existence of God, I predict half the population would say it's 100% certain God exists, and the other half would say the opposite.
That sounds like a massive overestimate of the percentage of atheists.
"What is the probability there is microbial-like life (other than from earth) in our solar system?"
I'm having difficulty giving this a good estimate, myself, actually.
Questions from DAGGRE with a current estimate between 10 and 90%:
Will Ayman al-Zawahiri still be recognized as the leader of al-Qaeda as of 31 december 2012?
Will there be an official announcement of a new sovereign debt restructuring program for Greece before June 1, 2012?
Will the forces of Alassane Outtara defeat the forces of Laurent Gbagbo in the Ivory Coast before 1 December 2012?
Will Croatia’s GDP grow more than 0 percent in calendar 2012?
Will €1 Euro buy less than $1.20 Australian dollars at any point before 1 January 2013?
Will there will be a 50%-effective malaria vaccine available for general use before 2015?
Some suggestions:
People care about their health, and there's a lot we don't know about even very popular, non-technical habits.
Does a daily aspirin help prevent cancer?
Is running better for your health than other exercise?
[Will you live longer if you switch from a typical American diet to a vegan diet?][oops. Okay, mindkillers are everywhere.]
(For specific probabilities, add parameters, e.g., 'live 3 months longer.' Or ask what parameter value the 50% probability should be at.)
If you can convince people to check a bookie's odds instead of asserting "WOO! Go team go! You're #1!" then I think you have succeeded in raising the sanity waterline...
Maybe whether we'll encounter intelligent life from another planet sometime within the next century?
You could ask: Was the Trojan War an actual historical event?
It is not actually an popular question, but it is a question about a popular subject. I wouldn't say it's important, but it fits all other criteria. You could fill the listener about the details.
Or if I were to try the existence of God, I predict half the population would say it's 100% certain God exists, and the other half would say the opposite.
So this might be the result of huge selection effects, but most "average or somewhat-above-agerage" people I've met, e.g. people at my high school, were agnostic, and weren't very mind-killed on the subject; in fact, they were mostly disinterested, and wary of both theistic and atheistic evangelism. I think the God question would work just fine for such people.
ETA: Ah, Vaniver already said similarly.
Reading the comments, I'm not sure we're addressing the question you're asking.
Prediction market proponents have put a lot of thought into how to turn mind-killing open-ended questions (far-mode) into resolvable bets (near-mode), often by use of conditional wagers (chance of Y, wager valid only if X happens). This is a good mechanism for applying percentages to such questions.
However, it completely bypasses the point I think you're trying to make, which is that all useful beliefs are of this form. Basically, you want a simple-example summary of Making Be...
It's a bit esoteric for many people, but nobody knows whether or not the LHC will find the Higgs boson...
How about nutrition related questions? The exact wording of the question is tricky, but something like
"Will a low fat diet help most people lose weight?" isn't the kind of thing that inspires 0% or 100% responses.
I agree that 1, 2, and 3 together eliminate all non-mindkilling topics. For a question to be well-known and unanswered, the world must not push back on it very hard (not important). Seemingly important unanswered questions are precisely the domain of religion, on one model ("why are we here?"). And it's been observed that the mindkilling aspects of debates increase inversely with their observable consequences.
I'm going to go out in the weeds, and simply point at places where probabilities are used all the time: betting.
Odds are well understood in these environments, and by picking a sport that a person is only peripherally interested in, most of the mindkilling effects should be reduced to a non-dangerous level.
"Is the fetus growing in [pregnant woman you both know]'s uterus a boy or a girl." There is a tremendous amount of people who think that order of birth, shape of belly, pulse on pinky, etc can be used to predict the baby's sex [anecdotally these results, combined with peoples' guesses come to 50/50, go figure!] , which if enough of them agreed could arguably be used to marginally move away from the base of 51/49. This probability could be updated after an ultrasound, but still not move to 100% as there are well documented error rates associated...
As an afterthought, I don't actually care about the "popular and important" part of it - I usually ask someone for the population of Indonesia, and then to make me a confidence interval. So if he says 2 million, I ask him for a 98% confidence interval and then show him that he was wrong. If you're interested in trying this, make your own 98% confidence interval [two numbers X,Y such that you are 98% sure that X < population of Indonesia < Y] and then Google it.
"Will the Artist win the Best Picture Oscar?" would probably have fit your criteria in the runup to the Academy Awards. Not sure what the current analogy is - probably some similarly 'unimportant' yet highly publicised award/reality show exit.
I think when you have a question that fits the first three criteria, it always devolves into mindkilling. (Operating systems are a good example.)
The only time this doesn't happen is when the question is not popular/important. If you want to find an example, you're going to have to let go of either #2 or #5.
If we observe, most things that are factual questions are indisputable by intelligent people; for example, "Is the Earth round?" is a question that anyone who is fortunate enough to have some basic intelligence and an elementary school education is unlikely to argue. However, in order to have an opinionated question, one opens the can of worms that is mind killing and biased. For example, if you had two towns side by side, populated by young adults of equal intelligence and equal education, and they each had a sports team that competed against the other town's, those people living in each town would claim their team to be superior, without evidence other than "I live in this town." Hence, bias.
Is string theory more closely correct than any other current theory of physics?
I, at least, have essentially no way to judge this question and so don't really know what probability to assign it. Perhaps 1/n where n is the number of viable theories of physics? Plus a bit since it does seem to have more expert backing than anything else.
How/where memories are stored. It was salient for me, but even so it seems to satisfy all your conditions, except perhaps "important" since it doesn't impact most decisions that aren't whether to sign up for cryonics.
(I would like there to be no replies to this comment saying "Memory is probably stored in X via process Y" because yes, probably. That's the point.)
"Safe" for whom? This could mean several different things:
As with "organic food", the halo/horns effect is strong with this one.
Unfortunately, this question has become entangled with political/personal identity issues, and thus has become quite mind-killing.
Suppose you were to calculate expected value (e.g. expected change in final utility) based on your probability estimates. How certain would you be in that number? If not 100%, adjust the number accordingly to take that % into account. Now, how certain are you in that number? Rinse and repeat.
People are not terribly good at transmitting and receiving, across adversary relation, what exactly they are 100% sure about. But it is clear that one has to end up with some value, that one has to trust completely; one could e.g. side with consensus, and trust that co...
When I explain to people how beliefs should be expressed in probabilities, I would like to use an example like "Consider X. Lots of intelligent people believe X, but lots of equally intelligent people believe not-X. It would be ridiculous to say you are 100% sure either way, so even if you have a strong opinion about X, you should express your belief as a probability."
Trouble is, I'm having a hard time thinking of an example to plug into X. For an example to work, it would need the following properties:
Factual question. So no value-laden questions like "Is abortion morally acceptable?" or counterfactual questions like "Would the US have won a war with the Soviet Union in 1960?"
Popular and important question. The average person should be aware it's an issue and care about the answer. So no "My aunt's middle name is Gladys" or "P = NP."
High uncertainty. Reasonable people should be reluctant to give a probability >90% or <10%
No opportunity to gain status by signaling overwhelming support for one side. So cryonics is out, because it's too easy to say "That's stupid, I'm 100% sure cryonics won't work and no intelligent person could believe it." I'm assuming in any debate where you can gain free status by assigning crazy high probabilities to the "responsible" position, people will do just that - so no psi effects, Kennedy assassination, or anything in that cluster. I need a question with no well-accepted "responsible" position.
Minimal mindkilling effect. My previous go-to example has been global warming, but I keep encountering people who say that global warming 100% for sure exists and the only people who could possibly doubt it are oil company shills. Or if I were to try the existence of God, I predict half the population would say it's 100% certain God exists, and the other half would say the opposite.
So what are the important questions that average (or somewhat-above-average) people will likely agree are complicated open questions where both sides have good points? And if there aren't many such questions, what does that say about us?