Is There a Curve of Best Fit?

https://astralcodexten.substack.com/p/crowds-are-wise-and-ones-a-crowd

The “wisdom of crowds” hypothesis claims that the average of many guesses is better than a single guess. Ask one person to guess how much a cow weighs, and they’ll be off by some amount. Ask a hundred people and take the average of their answers, and you’ll be off by less.

I was intrigued by a claim in this book review that:

You can play “wisdom of crowds” in single-player mode. Say you want to know the weight of a cow. Then take a guess. Now throw your guess out of the window, and take another guess. Finally, compute the average of your two guesses. The claim is that this average is better than your individual guesses.

This is spooky. We talk a lot about how to make accurate predictions here - and you can improve your accuracy on anything just by guessing twice and averaging, no additional knowledge required? It’s like God has handed us a creepy cow-weight oracle.

I wanted to test this myself, so I included some relevant questions in last year’s ACX Survey: