For example, if I said to my wife “I think there’s an 8% chance we’ll get divorced in the next five years,” the very act of sharing that prediction might cause that number to go up! She might reasonably interpret it as a sign that I don’t believe in the partnership. Then, she might respond with her own prediction of 14%, leading me to update in the same way, in a back-and-forth pattern that ends up in divorce. This cascade of updates is only irrational in that speaking purely in terms of high-level probabilities is the wrong tool for the job of coordination
I don’t have the math proof at hand but, I would figure that it is also irrational in another way. If both people are perfectly rational and honest, I expect that communicating wouldn’t make them both worse off.
Zack Davis (the wise): 20 years ago I read in the Sequences that P[link]