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Psy-Kosh 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.
Think of the probability you assign as a measure of how "not surprised" you would be at seeing a certain outcome.
Total probability of all mutually exclusive possibilities has to add up to 1, right?
So if you would be equally surprised at heads or tails coming up, and you consider all other possibilities to be negligible (Or you state your prediction in terms of "given that the coin lands such that one face is clearly the 'face up' face....") then you ought assign a probability of 1/2 to each. (Again, slightly less to account for various "out of bounds" options, but in the abstract, considered on its own, 1/2)
ie, the same probability ought be assigned to each, since you'd be (reasonably) equally surprised at each outcome. So if the two have to also sum to 1 (100%), then 1/2 (50%) is the correct amount of belief to assign.
Surprise is not isomorphic to probability. See this.
Ah, that makes a lot more sense: I was looking at the probability from the viewpoint of my guess (i.e. heads) instead of just looking at the all outcomes equally (no privileged references guesses), if you take my meaning. I also differentiated confidence in my prediction from the chance of my prediction being correct. How I managed to do that, I have no idea. Thanks for the reply.
Well, maybe you were thinking about "how confident am I that this is a fair coin vs that it's biased toward heads vs that it's biased toward tails" which is a slightly different question.
Given how 'confidence' is used in a social context that differentiation would feel quite natural.