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...