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Con­ser­va­tion of Ex­pected Evidence

TagLast edit: 19 Mar 2023 22:02 UTC by Diabloto96

Conservation of Expected Evidence is a consequence of probability theory which states that for every expectation of evidence, there is an equal and opposite expectation of counter-evidence [1]. Conservation of Expected Evidence is about both the direction of the update and its magnitude: a low probability of seeing strong evidence in one direction must be balanced by a high probability of observing weak counter-evidence in the other direction [2]. The mere expectation of encountering evidence–before you’ve actually seen it–should not shift your prior beliefs. It also goes by other names, including the law of total expectation and the law of iterated expectations.

A consequence of this principle is that absence of evidence is evidence of absence.

Consider a hypothesis H and evidence (observation) E. Prior probability of the hypothesis is P(H); posterior probability is either P(H|E) or P(H|¬E), depending on whether you observe E or not-E (evidence or counter-evidence). The probability of observing E is P(E), and probability of observing not-E is P(¬E). Thus, expected value of the posterior probability of the hypothesis is:

But the prior probability of the hypothesis itself can be trivially broken up the same way:

Thus, expectation of posterior probability is equal to the prior probability.

In other way, if you expect the probability of a hypothesis to change as a result of observing some evidence, the amount of this change if the evidence is positive is

If the evidence is negative, the change is

Expectation of the change given positive evidence is equal to negated expectation of the change given counter-evidence:

If you can anticipate in advance updating your belief in a particular direction, then you should just go ahead and update now. Once you know your destination, you are already there.

Sequences:

Notable Posts

See Also

Con­ser­va­tion of Ex­pected Evidence

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241 points
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Mis­takes with Con­ser­va­tion of Ex­pected Evidence

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Yes Re­quires the Pos­si­bil­ity of No

Scott Garrabrant17 May 2019 22:39 UTC
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Ab­sence of Ev­i­dence Is Ev­i­dence of Absence

Eliezer Yudkowsky12 Aug 2007 20:34 UTC
152 points
118 comments3 min readLW link

Up­date Your­self Incrementally

Eliezer Yudkowsky14 Aug 2007 14:56 UTC
101 points
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Con­ser­va­tion of ex­pected moral ev­i­dence, clarified

Stuart_Armstrong20 Jun 2014 10:28 UTC
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Con­ser­va­tion of Ex­pected Jury Probability

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[Question] Where is all this ev­i­dence of UFOs?

Logan Zoellner1 May 2023 12:13 UTC
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Rad­i­cal Probabilism

abramdemski18 Aug 2020 21:14 UTC
176 points
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Ex­pla­na­tion vs Rationalization

abramdemski22 Feb 2018 23:46 UTC
16 points
11 comments4 min readLW link

Some­what against “just up­date all the way”

tailcalled19 Feb 2023 10:49 UTC
29 points
10 comments2 min readLW link

An­trop­i­cal Prob­a­bil­ities Are Fully Ex­plained by Differ­ence in Pos­si­ble Outcomes

Ape in the coat9 Nov 2023 15:34 UTC
17 points
2 comments5 min readLW link

Un­known Probabilities

transhumanist_atom_understander27 Nov 2023 2:30 UTC
13 points
0 comments4 min readLW link

Co-Proofs

abramdemski21 May 2018 21:10 UTC
40 points
14 comments1 min readLW link

Bayesian Judo

Eliezer Yudkowsky31 Jul 2007 5:53 UTC
85 points
110 comments1 min readLW link

The Prin­ci­ple of Pre­dicted Improvement

Ronny Fernandez23 Apr 2019 21:21 UTC
69 points
17 comments3 min readLW link

Con­ser­va­tion of Ex­pected Ev­i­dence and Ran­dom Sam­pling in Anthropics

Ape in the coat3 Sep 2023 6:55 UTC
9 points
6 comments7 min readLW link

“Ab­sence of Ev­i­dence is Not Ev­i­dence of Ab­sence” As a Limit

transhumanist_atom_understander1 Oct 2023 8:15 UTC
16 points
1 comment2 min readLW link

I was raised by de­vout Mor­mons, AMA [&|] Solic­it­ing Advice

ErioirE13 Mar 2024 16:52 UTC
31 points
41 comments2 min readLW link