Is it irrational to have no precise credence at all about something like life on Europa?
A science journalist asked me last month, for a piece about the Europa missions, what probability I would put on there being life in its ocean. I said I had no idea. She pushed: “Just a number, roughly.” I said somewhere between one in a thousand and one in three, which she found hilarious and printed.
The orthodox Bayesian view, as I understand it, is that a rational agent has a precise credence in every proposition she considers, even if she cannot report it well. My range was then either a reporting failure or a rationality failure.
But I do not think I was hiding a precise number from myself. The evidence simply does not settle one. There are a few positions on the table that I know of:
- Precise credences are a requirement, and imprecision is a defect to be fixed.
- Credences can be intervals (or sets of probability functions), and that is the honest response to thin evidence.
- Dempster–Shafer style theories, where you can assign weight to evidence without forcing it into a single probability.
There is also the older distinction, often credited to Knight and Keynes, between risk you can quantify and uncertainty you cannot.
Which of these do people here find most defensible, and why? And does anyone know of traditions outside the Anglo-American literature that treat “I don't know” as a distinct state rather than as a low or middling degree of belief?