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RichardKennaway comments on Open Thread: November 2009 - Less Wrong
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I'd like to ask a moronic question or two that aren't immediately obvious to me and probably should be. (Please note, my education is very limited, especially procedural knowledge of mathematics/probability.)
If I had to guess what the result of a coin flip would be, what confidence would I place in my guess? 50% because that's the same as the probability or me being correct or 0% because I'm just randomly guessing between 2 outcomes and have no evidence to support either (well I guess there being only 2 outcomes is some kind of evidence)?
Likewise with a lottery. Would I place my confidence level (interval ? I don't know the terminology) of winning at 0% or 1/6,000,000? Or some other number entirely?
If this is something I could easily have figured out with Google or Wikipedia, my apologies. Also if my question is incoherent or flawed please let me know.
You might want to look at Dempster-Shafer theory, which is a generalisation of Bayesian reasoning that distinguishes belief from probability. It is possible to have a belief of 0 in heads, 0 in tails, and 1 in {heads,tails}.
It may be that, when looked at properly, DS theory turns out to be Bayesian reasoning in disguise, but a brief google didn't turn up anything definitive. Is anyone here more informed on the matter?
After looking at the reasoning in that article I was about to credit myself with being unintentionally deep, but I'm pretty sure that when I posed the question I was assuming a fair coin for the sake of the problem. Doh. Thanks for the interesting link.
(It's really kind of embarrassing asking questions about simple probability amongst all the decision theories and Dutch books and priors and posteriors and inconceivably huge numbers. Only way to become less wrong, I suppose.)