Title: [SEQ RERUN] Conservation of Expected Evidence Tags: sequence_reruns Today's post, Conservation of Expected Evidence was originally published on 13 August 2007. A summary (taken from the LW wiki):

If you are about to make an observation, then the expected value of your posterior probability must equal your current prior probability. On average, you must expect to be exactly as confident as when you started out. If you are a true Bayesian, you cannot seek evidence to confirm your theory, because you do not expect any evidence to do that. You can only seek evidence to test your theory.

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This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Absence of Evidence is Evidence of Absence, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.

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This is one of those posts that drives the point home that "thought has rules".

I need a little help. Would anybody like to run through an example with a deck of cards? Say i hypothesize a deck of cards to be 1/2 hearts. If i draw from the top with replacement, how should i update when i see a heart or none heat according to this formalism? or say the hypothesis says that 90% of the cards are hearts, same question.

I understand the law when i interpret P(E) getting bigger, as becoming more confident that you saw a heart, or as having a higher expectation of seeing a heart, but i get confused when i thinkofit as actually having seen more hearts. can anyone help please?

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