[NeoTar]

I wonder how humans would respond to a prompt '(without mechanical assistance) with 80% probability say Left, and with 20% say Right' across a population.

I can think of a few levels that people might try to think about the problem: Level 0: Ignore the probabilities and just pick whichever you feel like, (would tend to 50:50) Level 1: Say the most with the greatest probability - Left (would tend to 100:0) Level 2: Consider that most people are likely to say Left, so say Right instead (would tend to 0:100) Level 3: Try to think about what proportion of people would say Left, and what would say Right, and say whichever would return the balance closest to 80:20...

Presumably your result would depend on how many people thinking on each level you have in your sample...

[cortesoft]

This sounds a lot like a Keynesian Beauty Contest (https://en.wikipedia.org/wiki/Keynesian_beauty_contest), where you are trying to make a selection based on what you think other people are going to choose.

If I really wanted to give an accurate answer in this case, I would probably choose some arbitrary source of a number (like my age or the number of days that have gone by so far this year), figure out the modulo 5 of that number, then say 'Right' if the modulo is 0, and 'Left' otherwise.

Obviously there are some flaws in this approach, but I think it would be as accurate as I could get.

[spiffytech]

I've seen people do this with Twitter polls with tens of thousands of respondants. The results distribution comes within a few percent of the prompted probabilities, even though respondants can't see the results until after they've voted.

[michaelt]

Level 4: Clearly, the Schelling point requires a number everyone knows, which is evenly distributed across the population, modulo 10. Let's use year of birth modulo 10. For me that's 2, so I'll say Left.

[patapong]

Fun question! I think the following would be a viable strategy without communication:

Think of an observable criterion that matches the target distribution. For example, for 80-20:

- "Is the minute count higher than 12?" (This is the case in 80% of cases)

- "Do I have black hair?" (This is apparently also the case in 80% of cases)

Then, answer according to this criterion.

If everyone follows the same strategy, even if the criteria selected differs between each individual, the votes should match the target probability. Unless I am making a logical mistake :)