“Why did I tell her? Did I foresee this? Was I even thinking?”, you ask.
Decision theory, they claimed, was a tool that would help me make my decisions.
In decisions under uncertainty, suppose that you have two possible actions, A1 and A2, and the worst outcome associated with A1 is at least as good as the best outcome associated with A2; suppose also that in at least one state of the world, A1′s outcome is strictly better than A2′s. Let us say in that case that A1 superdominates A2. Then rationality surely requires you to perform A1.
So how does this one go
She loves me She doesn’t
I profess my love Fairy tale Status quo
I hide my love Missed opportunity Status quo
Surely, rationality demanded that I tell her. Unless I was wrong about the outcomes. Or the probabilities weren’t 50-50.
So many uncertainties. Ah well! I flipped a coin. Heads I tell her. Tails I don’t.
It was Tails. I told her anyway.