SOC SCI H1G Lecture Notes - Lecture 18: Expected Return, Dutch Book, Belief Revision
30 Nov 2016
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Marilyn savant was right when she said you should shift, but her reasons were vague. The people (cid:449)ho disag(cid:396)eed did(cid:374)"t k(cid:374)o(cid:449) to pla(cid:455) (cid:271)(cid:455) the (cid:396)ules of the ga(cid:373)e o(cid:396) the(cid:455) (cid:449)e(cid:396)e just wrong. I start off with the old probability, p0(b1). The old probability given that evidence should be the new probability. The dynamics of probability change over time. A belief revision of knowledge: the sort of model of knowledge that quine and peirce suggests to us, also known as pragmatic theory of knowledge. Two examples: monty hall, medical evidence. Raise the stakes here a little bit. Let"s suppose that there is a relatively rare disease. Probability of disease, or p0(d), is 0. 0001. Probability that i have the disease is p0(d|t) = 0. 0098. Let"s suppose that the(cid:396)e is a (cid:396)elati(cid:448)el(cid:455) accurate test for the disease. P(t|d) = 0. 99: probability of testing positive given that you have the disease is pretty high.
