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DanielLC comments on Open thread, August 26 - September 1, 2013 - Less Wrong Discussion
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A few weeks ago I started assessing my own calibration, using tools such as the CFAR calibration game. I got fairly good and concluded that I am relatively well calibrated.
When given a question, my instincts would immediately throw out a number. I'd unpack it and adjust it in accordance to known biases. (Avoid representativeness, start from base rates, treat the initial number as a degree of support, factor in strength of evidence, etc.)
Yesterday, an assessment of probability came up in conversation. Immediately, my instincts threw out the number "80%". My thoughts went like this:
I opened my mouth to speak.
Then I shut my mouth.
I understand Löb's theorem on an intuitive level now.
I don't understand. What's wrong with 80%?
I achieved good calibration by paying attention to evidence and avoiding known biases as well as I was able. Once I had established reliable calibration, I experienced temptation to justify my first intuitive instinct by asserting my own calibration.
My calibration was based upon mediating my intuitions with reason. I can't invoke it to trust any old estimate that comes out of my mouth: if I did then I could say whatever I want and trust it to be calibrated (which would yield probability estimates out of touch with reality). Hence the parallels to Löb's theorem.