https://astralcodexten.substack.com/p/mantic-monday-11121 Keynesian Beauty Contests

I have no source for this, someone told me about it at a meetup.

Suppose you want to run a forecasting tournament on whether nuclear war will destroy civilization by 2100. But nobody cares how much money they have in eighty years, plus if civilization is destroyed you can't collect your winnings.

There are lots of kludgey solutions to this, but one possibility is a Keynesian beauty contest. Get a lot of isolated teams, and make them predict what all the other teams will guess. Whoever gets closest to the average wins the prize.

Let's start with the good: in theory, this does solve the problem. Presumably the easiest way for the teams to all guess the same is to converge on the "right" answer. In some sense, the definition of probability is what a smart person who knows a certain amount of information should estimate, so if you ask someone to predict what a person just as smart as you who has the same information as you will estimate, that's like asking for your probability.