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How Much Evidence Does It Take? — LessWrong

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Previously, I defined evidence as “an event entangled, by links of cause and effect, with whatever you want to know about,” and entangled as “happening differently for different possible states of the target.” So how much entanglement—how much rational evidence—is required to support a belief? Let’s start with a question simple enough to be mathematical: How hard would you have to entangle yourself with the lottery in order to win? Suppose there are seventy balls, drawn without replacement, and six numbers to match for the win. Then there are 131,115,985 possible winning combinations, hence a randomly selected ticket would have a 1/131,115,985 probability of winning (0.0000007%). To win the lottery, you would need evidence selective enough to visibly favor one combination over 131,115,984 alternatives. Suppose there are some tests you can perform which discriminate, probabilistically, between winning and losing lottery numbers. For example, you can punch a combination into a little bla

x Rationality: A-Z — LessWrong Noticing Confusion Bayes' Theorem Epistemology Frontpage 196 How Much Evidence Does It Take? by Eliezer Yudkowsky 24th Sep 2007 4 min read 34 196 Previously, I defined evidence as “an event entangled, by links of cause and effect, with whatever you want to know about,” and entangled as “happening differently for different possible states of the target.” So how much entanglement—how much rational evidence—is required to support a belief? Let’s start with a question simple enough to be mathematical: How hard would you have to entangle yourself with the lottery in o

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