# Absence of Evidence Is Evidence of Absence

54 12 August 2007 08:34PM

From Robyn Dawes's Rational Choice in an Uncertain World:

Post-hoc fitting of evidence to hypothesis was involved in a most grievous chapter in United States history: the internment of Japanese-Americans at the beginning of the Second World War.  When California governor Earl Warren testified before a congressional hearing in San Francisco on February 21, 1942, a questioner pointed out that there had been no sabotage or any other type of espionage by the Japanese-Americans up to that time.  Warren responded, "I take the view that this lack [of subversive activity] is the most ominous sign in our whole situation. It convinces me more than perhaps any other factor that the sabotage we are to get, the Fifth Column activities are to get, are timed just like Pearl Harbor was timed... I believe we are just being lulled into a false sense of security."

Consider Warren's argument from a Bayesian perspective.  When we see evidence, hypotheses that assigned a higher likelihood to that evidence, gain probability at the expense of hypotheses that assigned a lower likelihood to the evidence.  This is a phenomenon of relative likelihoods and relative probabilities.  You can assign a high likelihood to the evidence and still lose probability mass to some other hypothesis, if that other hypothesis assigns a likelihood that is even higher.

Warren seems to be arguing that, given that we see no sabotage, this confirms that a Fifth Column exists.  You could argue that a Fifth Column might delay its sabotage.  But the likelihood is still higher that the absence of a Fifth Column would perform an absence of sabotage.

Let E stand for the observation of sabotage, H1 for the hypothesis of a Japanese-American Fifth Column, and H2 for the hypothesis that no Fifth Column exists.  Whatever the likelihood that a Fifth Column would do no sabotage, the probability P(E|H1), it cannot be as large as the likelihood that no Fifth Column does no sabotage, the probability P(E|H2).  So observing a lack of sabotage increases the probability that no Fifth Column exists.

A lack of sabotage doesn't prove that no Fifth Column exists.  Absence of proof is not proof of absence.  In logic, A->B, "A implies B", is not equivalent to ~A->~B, "not-A implies not-B".

But in probability theory, absence of evidence is always evidence of absence.   If E is a binary event and P(H|E) > P(H), "seeing E increases the probability of H"; then P(H|~E) < P(H), "failure to observe E decreases the probability of H".  P(H) is a weighted mix of P(H|E) and P(H|~E), and necessarily lies between the two.  If any of this sounds at all confusing, see An Intuitive Explanation of Bayesian Reasoning.

Under the vast majority of real-life circumstances, a cause may not reliably produce signs of itself, but the absence of the cause is even less likely to produce the signs.  The absence of an observation may be strong evidence of absence or very weak evidence of absence, depending on how likely the cause is to produce the observation.  The absence of an observation that is only weakly permitted (even if the alternative hypothesis does not allow it at all), is very weak evidence of absence (though it is evidence nonetheless).  This is the fallacy of "gaps in the fossil record"—fossils form only rarely; it is futile to trumpet the absence of a weakly permitted observation when many strong positive observations have already been recorded.  But if there are no positive observations at all, it is time to worry; hence the Fermi Paradox.

Your strength as a rationalist is your ability to be more confused by fiction than by reality; if you are equally good at explaining any outcome you have zero knowledge.  The strength of a model is not what it can explain, but what it can't, for only prohibitions constrain anticipation.  If you don't notice when your model makes the evidence unlikely, you might as well have no model, and also you might as well have no evidence; no brain and no eyes.

Part of the sequence Mysterious Answers to Mysterious Questions

Next post: "Conservation of Expected Evidence"

Previous post: "Your Strength as a Rationalist"

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Comment author: 12 August 2007 09:24:48PM 16 points [-]

Perhaps this criticism of the California governor assumes an over-naive probabilistic modelling, with only two events ("no acts of espionage" => "fifth column exists [or not]"). In reality, there existed some non-public information about an existing japanese spy network (MAGIC decodes; informants) that is unlikely to have been mentioned in a public hearing.

Perhaps the reasoning was more like this: "We know that they are already here. We know that some fraction of the population sympathizes with the mother nation. If the fifth column did not exist in an organized form, we might have seen some sabotage already. Since there hasn't been any, maybe they are holding back for a major strike."

Comment author: 13 August 2007 12:01:42AM 17 points [-]

Frank: It is impossible for A and ~A to both be evidence for B. If a lack of sabotage is evidence for a fifth column, then an actual sabotage event must be evidence *against* a fifth column. Obviously, had there been an actual instance of sabotage, nobody would have thought that way- they would have used the sabotage as more "evidence" for keeping the Japanese locked up. It's the Salem witch trials, only in a more modern form- if the woman/Japanese has committed crimes, this is obviously evidence for "guilty"; if they are innocent of any wrongdoing, this too is a proof, for criminals like to appear especially virtuous to gain sympathy.

Comment author: 27 November 2010 01:42:34AM 2 points [-]

BTW, what would you consider evidence for a genuine attempt to lull the government into a false sense of security (in an analagous situation)?

Comment author: 08 December 2010 10:35:50PM *  12 points [-]

Lack of sabotage is obviously evidence for a fifth column trying to lull the government, given the fifth column exists, since the opposite - sabotage occuring - is very strong evidence against that.

However lack of sabotage is still much stronger evidence towards the fifth column not existing.

Comment author: 29 January 2011 12:46:21AM 7 points [-]

The takeaway is that if you are going to argue that X group is dangerous because they will commit Y act, you cannot use a lack of Y as weak evidence that X exists, because then Y would be strong evidence that X does not exist, and Y is what you are afraid X is going to do!

You would be much better off using the fact that no sabotage occurred as weak evidence that the 5th column was preventing sabotage.

If there is other evidence that suggests the 5th column exists and that they are dangerous, that is the evidence that should be used. Making up non-evidence (which is actually counter evidence) is not the way to go about it. There are ways of handling court cases that must remain confidential (though it would certainly make the court look bad, it is the right way to do it).

Comment author: 19 August 2011 12:40:30AM 3 points [-]

As I understand it, there were at least three hypotheses under consideration: a) No members (or a negligibly small fraction) of the ethnic group in question will make any attempt at sabotage. b) There will be attempts at sabotage by members of the ethnic group in question, but without any particular organization or coordination. c) There is a well-disciplined covert organization which is capable of making strategic decisions about when and where to commit acts of sabotage.

The prior for A was very low, and any attempt by the Japanese government to communicate with saboteurs in the States could be considered evidence against it. Lack of sabotage is evidence for C over B.

Comment author: 27 February 2015 09:21:07AM 1 point [-]

I think you're right, but there's an adjustment (an update, isn't it called?) warranted in two directions.

The absence of sabotage decreases the likelihood of the fifth column existing at all.

But if there is a fifth column, it could be reasonably predicted that there would be evidence of sabotage unless there was an attempt to keep a low profile. If they were to favor this hypothesis for other reasons, as in the classified data mentioned by Frank, then the lack of apparent sabotage would also increase the probability that if the unlikely fifth column DID exist, it would be one which is keeping a low profile. I grant, of course, at the same time, the decreased probability of there being any kind of fifth column in the first place.

Comment author: 13 August 2007 01:35:15AM 2 points [-]

A and ~A are not each evidence for B, if B is "there is a fifth column active". In some ways, as I said, they already knew B - it was true. There were questions of degree - how organized? how ready? how many? - for which A and ~A each provide some hints at.

Comment author: 13 August 2007 02:16:42AM 3 points [-]

Earl Warren tumbled headlong into the standard conspiracy theory attractor with, I might add, no deleterious effect on his career. This man was later the 14th Chief Justice of the US Supreme Court and has probably had more lasting effect on US society than any single figure of the 20th century. Thanks for the post.

Comment author: 13 August 2007 06:13:04AM 2 points [-]

http://en.wikipedia.org/wiki/Japanese_American_internment#Was_the_internment_justified_by_military_necessity.3F

But that's not the point. The point is that Earl Warren's reasoning was invalid. It didn't matter what other evidence he had (Warren certainly did not know about the ultra-classified MAGIC decodes). The particular observation of no sabotage was evidence against, and could not legitimately be worked into evidence for.

Comment author: [deleted] 10 June 2011 08:07:44AM *  3 points [-]

Can we be sure that he did not just assign a very strong prior distribution to the existence of Fifth Column? In that case, if we model Warren's decision as binary hypothesis testing with a MAP rule, say, then maybe it occurred to Warren that the raw conditional probabilities satisfied this inequality P(no sabotage | imminent Fifth Column threat) < P(no sabotage | no imminent Fifth Column threat).

But perhaps, for Warren, P(imminent Fifth Column threat) >> P( no imminent Fifth Column threat).

In this scenario, he reasoned that it was so likely that there was a Fifth Column threat that it outweighed the ease with which (absence of Fifth Column) can account for (absence of sabotage), and led him to choose the hypothesis that a Fifth Column was a better explanation for lack of sabotage.

In that case, the issue becomes the strength in the prior belief. Similar reasoning can be applied to McCarthy, or to those suggesting we're due for another terrorist attack.

I guess what I am saying is like this: maybe someone just believes we're due for another terrorist attack very strongly (perhaps for irrational reasons, but reasons that have nothing to do with a witnessed lack of terrorist attacks). Then you present them with the evidence that no terrorist activity has been witnessed, say. Instead of this updating their prior to a better posterior that assigns less belief to imminence of terrorist attacks, they actually feel capable of explaining the absence of terrorist activities in light of their strong prior.

I do agree that it would then be nonsensical to take that conclusion and treat it like a new observation. As if: Fifth Column -> they absolutely must exist and be planning something -> invent a reason why strength of belief in prior is justified -> Fifth Column's existence explains absence of sabotage -> further absence of sabotage now feeds back as ever-more-salient corroborating evidence of original prior.

Perhaps more focus should be placed on the role of the prior in all of this, rather than outright misinterpretations of evidence.

Comment author: 13 August 2007 06:25:34AM 2 points [-]

I suspect a part of the appeal of this saying comes from a mental unease with conflicting evidence. It is easier to think of the absence of evidence as not evidence at all, rather than as evidence against where the evidence in favor just happens to be much stronger. Perhaps it is a specific case of a general distaste for very small distinctions, especially those close to 0?

Ad hominem argumentation is another example of evidence which is usually weak, but is still evidence.

Comment author: 26 June 2012 10:27:04PM 2 points [-]

I suspect a part of the appeal of this saying comes from a mental unease with conflicting evidence.

I am quite sure you're onto something here. A similar effect occurs when people try to argue that a given intervention has no downsides at all; none at all? Really? It will be absolutely free and have beneficial effects on everyone in the world? Why aren't we doing it already then?

People aren't used to thinking in terms of cost-benefit analysis, where you say "Yes, it has downsides A, B, C; but it also has upsides W, X, Y, Z, and on balance it's a good idea." They think that merely by admitting that the downsides exist you have given up the game. (Politics is the mind-killer?)

Comment author: 26 August 2013 03:27:45PM 3 points [-]

We aren't doing it already because the Bad People have power and if we did it, it would frustrate their Evil (or at least Morally Suspect) Purposes. Frustrating such purposes doesn't count as a downside. Depending on who you are talking to, taking money from rich people, allowing people who make stupid choices to die, or preventing foreigners who want to from entering your country isn't just a bad thing that's outweighed by its good consequences; it simply doesn't warrant an entry in the "costs" column at all.

Comment author: 26 August 2013 06:18:47PM *  0 points [-]

Why aren't we doing it already then?

An aside, but I always hated this argument. It proves way too much. (Cryonics, for example.)

Comment author: 13 August 2007 02:32:09PM 10 points [-]

The particular observation of no sabotage was evidence against, and could not legitimately be worked into evidence for.

You are assuming that there are only two types of evidence, sabotage v. no sabotage, but there can be much more differentiation in the actual facts.

Given Frank's claim, there is a reasoning model for which your claim is inaccurate. Whether this is the model Earl Warren had in his head is an entirely different question, but here it is:

We have some weak independent evidence that some fifth column exists giving us a prior probability of >50%. We have good evidence that some japanese americans are disaffected with a prior of 90%+. We believe that a fifth column which is organized will attempt to make a *significant* coordinated sabotage event, possibly holding off on any/all sabotage until said event. We also believe that the disaffected who are here, if there is *no* fifth column would engage is small acts of sabotage on their own with a high probability.

Therefore, if there are small acts of sabotage that show no large scale organization, this is weak evidence of a lack of a fifth column. If there is a significant sabotage event, this is *strong* evidence of a fifth column. If there is no sabotage at all, this is weak evidence of a fifth column. Not all sabotage is alike, it's not a binary question.

Now, this is a nice rationalization after the fact. The question is, if there had been rare small acts of sabotage, what is the likelihood that this would have been taken by Warren and others in power as evidence that there was no fifth column. I submit that it is very unlikely, and your criticism of their actual logic would thus be correct. But we can't know for certain since they were never presented with that particular problem. And in fact, I wish that you, or someone like you, had been on hand at the hearing to ask the key question: "Precisely what would you consider to be evidence that the fifth column does *not* exist?"

Of course, whether widespread internment was a reasonable policy, even if the logic they were using were not flawed, is a completely separate question, on which I'd argue that *very* strong evidence should be required to adopt such a severe policy (if we are willing to consider it at all), not merely of a fifth column, but of widespread support for it. It is hard to come up with a plausible set of priors where "no sabotage" could possibly imply a high probability of that situation.

Comment author: 13 August 2007 10:06:38PM -1 points [-]

I would agree that the lack of sabotage cannot be argued as support for accepting an increase in the probability of the existence of a fifth column. But it may not be sufficient to lower the probability that there is a fifth column, and certainly may not be sufficient to lower a prior of greater than 50% to below 50%, even assuming that one is a Bayesian.

Comment author: 13 August 2007 11:56:26PM 0 points [-]

If sabotage increases the probability, lack of sabotage necessarily decreases the probability.

Comment author: 14 August 2007 04:15:03PM 3 points [-]

When you hear someone say "X is not evidence ...", remember that the Bayesian concept of evidence is not the only concept attached to that word. I know my understanding of the word evidence changed as I adopted the Bayesian worldview. My recollection of my prior use of the word is a bit hazy, but it was probably influenced a good deal by beliefs about what a court would admit as evidence.(This is a comment on the title of the post, not on Earl Warren's rationalization).

Comment author: 26 June 2012 10:29:29PM 1 point [-]

That's a good point. And clearly court standards for evidence are not the same as Bayesian standards; in court lots of things don't count that should (like base rate probabilities), and some things count more than they should (like eyewitness testimony).

Comment author: 14 August 2007 06:52:10PM -2 points [-]

If sabotage increases the probability, lack of sabotage necessarily decreases the probability.

That's true in the averages, but different types of sabotage evidence may have different effects on the probability, some negative, some positive. It's conceivable, though unlikely, for sabotage to on average decrease the probability.

Comment author: 13 April 2009 06:37:03PM 0 points [-]

This is all fine and good, but it does not address what "evidence" is. I cannot gather evidence of extra solar planets (either evidence for or against existence) with my naked eyes. So in this experiment, even though I see no "evidence" of extra solar planets by looking up into the sky, I still do not have evidence of absense, because in fact I have no evidence at all.

Evidence, from the aspect of probability theory, is only meaningful when the experiment is able to differential between existence and absence.

Then the real question becomes: do we have evidence that our experiment is able to yield evidence? And the only way to prove this to the affirmative, is to find something. You cannot *know* you experiment is designed correctly.

Comment author: 28 October 2010 12:28:37AM 0 points [-]

Really, the issue here is whether evidence has to increase probability (of existence or nonexistence) by a positive amount or a non-negative amount. The difference between those two sets is the very important "zero."

You are interested in the question: "Are there extra-solar planets?", with possibilities "Yes" and "No". You wonder how to answer the question, and decide to try the experiment "look with my naked eyes." You sensibly decide that if you can see any extra-solar planets, then it's not less likely that there are extra-solar planets, and if you can't see extra-solar planets, then it's not more likely that there are extra-solar planets. The strength of those effects is determined by the quality of the experiment; in this case, that strength is 0.

The specific fallacy in question is saying that all outcomes of an experiment make a claim more likely- that is inconsistent with how probability works. Similarly, one can argue that you should have a good estimate of the quality of an experiment before you get the results. That estimate doesn't have to be perfect- you can look at the results and say "I'm going to doublecheck to make sure I didn't screw up the experiment"- but changing your bet after you lose should not be allowed.

Comment author: 26 June 2012 10:31:38PM -1 points [-]

There is another way: Look really really hard with tools that would be expected to work. If you find something? Yay, your hypothesis is confirmed. If you don't? You'd better start doubting your hypothesis.

You already do this in many situations I'm sure. If someone said, "You have a million dollars!" and you looked in your pockets, your bank accounts, your stock accounts (if any), etc. and didn't find a million dollars in them (or collectively in all of them put together), you would be pretty well convinced that the million dollars you allegedly have doesn't exist. (In fact, depending on your current economic status you might have a very low prior in the first place; I know I would.)

Comment author: 26 August 2013 03:30:30PM 3 points [-]

The fact that you can't see them when you look outside is evidence against their presence, it's just extremely weak evidence. See also the Raven paradox.

Comment author: 26 August 2013 06:02:14PM 0 points [-]

To be fair, it's amazing how people will interpret "evidence" as "strong evidence".

Comment author: 26 August 2013 06:20:31PM 2 points [-]

But it's completely unamazing how many people will interpret "evidence" as "strong enough evidence to be worth taking notice of", because that is how the word is actually used outside circumscribed mathematical contexts.

Comment author: 26 August 2013 06:26:25PM -1 points [-]

Yup. To be honest, it's not actually that amazing that it's interpreted as "strong evidence", or "this thing is probably true", because arguments are soldiers and all that.

Comment author: 26 August 2013 06:49:24PM *  2 points [-]

It's not about arguments being soldiers, but basic Gricean maxims. In everyday talk you don't call something "evidence" unless it actually matters that it is evidence, and it only matters if it is strong enough to be worth attending to.

Just because there is this other, mathematically defined concept called "evidence", according to which every purple M&M is evidence for the blackness and whiteness of crows, you don't get to say that everyone else is wrong for not using the word the way you redefined it. Instead, you must recognise that this is a different concept, called by the same name, and take care to distinguish the two meanings.

What next, insisting that black paint isn't black?

Comment author: 26 August 2013 07:15:52PM *  2 points [-]

It's always better to rename overloaded terms, or at least to make clear which meaning (the colloquial or the technical) one defaults to. Quibbling over what to name which doesn't solve any issues and is mostly just kicking the can down the road, but allow me to say that if there's one place on which I always default to the technical definition, it's LW. Where else if not here?

I understand that the LW fraction which aims to prioritize accessibility and strives to avoid jargon, may also strive to avoid counter-intuitive technical definitions for the sake of commonly used interpretations. I just don't subscribe to their methods.

Comment author: 26 August 2013 09:42:36PM -1 points [-]

Sorry, I wasn't clear. I agree that it's reasonable, except when discussing prob. math, to assume "evidence" means "evidence worth mentioning". I noted that, while not "reasonable" exactly, it's even natural that it tends to be interpreted as "this is my side, I offer evidence in tribute", from an evopsych perspective :/

Comment author: 27 August 2013 06:39:57AM 1 point [-]

Right, and in fact the very idea of "extremely weak evidence" is really only worth paying attention to because it resolves various seeming paradoxes of evidence, such as the extrasolar planets and raven problems above.

Comment author: 16 February 2010 11:40:26AM 1 point [-]

If all you have is some generic crime data, then more crime in a region can indicate that the Mafia is strong. On the other hand, Mafias keep their own neighborhoods, and the Mafia sometimes can suppress police activity through corruption, so a very low crime rate can indicate that the Mafia is strong.

Of course, background details would suggest which of these is indicated by the evidence

Comment author: 03 June 2010 08:34:06PM *  2 points [-]

The crime rate has gone up. This means that everything is getting worse and the police are ineffective.

The crime rate has gone up. This means that the police are getting better at catching formerly clandestine criminal behavior.

Comment author: 19 August 2011 12:49:34AM 2 points [-]

It would be possible to distinguish between those hypotheses by looking at the ratio of crimes reported to crimes successfully prosecuted.

Comment author: 02 July 2010 03:47:34AM 1 point [-]

Seems reasonable to me; if there's the expected amount of crime in an area, then it's not too worthy of special attention. If there's a higher than usual amount of crime, then it's clearly worthy of special attention.

However, if there's a lower than usual amount of crime, then it's also worthy of special attention, because that indicates that something odd is happening there (or, it indicates that something has genuinely reduced the amount of crime and not just the metric, which is worth investigating and hopefully replicating).

Comment author: 25 November 2010 02:55:31PM 4 points [-]

Hi Eliezer, That's another great post, I very much enjoyed reading even though there are gaps in my understanding. I'm new here so I have lots to learn. I wonder if you could kindly explain what you mean by: "Your strength as a rationalist is your ability to be more confused by fiction than by reality; if you are equally good at explaining any outcome you have zero knowledge. " Thanks, Lou

Comment author: 25 November 2010 05:52:34PM *  5 points [-]

Welcome to Less Wrong!

A belief is useless unless it makes predictions. Making Beliefs Pay Rent gives a couple examples of "beliefs" that are useless because they don't make any predictions.

A belief from which you can derive any prediction is just as useless. Your Strength as a Rationalist and the beginning of A Technical Explanation of Technical Explanation give examples of people trying too hard to make their beliefs explain their observations; they fail to discover that their beliefs are incorrect.

Comment author: 15 December 2010 07:18:32PM *  9 points [-]

Warren seems to be arguing that, given that we see no sabotage, this confirms that a Fifth Column exists.

This article makes a very good point very well. If E would be evidence for a hypothesis H, then ~E has to be evidence for ~H.

Unfortunately, I think that it is unfair to read Warren as violating this principle. (I say "Unfortunately" because it would be nice to have such an evocative real example of this fallacy.)

I think that Warren's reasoning is more like the following: Based on theoretical considerations, there is a very high probability P(H) that there is a fifth column. The theoretical considerations have to do with the nature of the Japanese–American conflict and the opportunities available to the Japanese. Basically, there mere fact that the Japanese have both means and motive is enough to push P(H) up to a high value.

Sure, the lack of observed sabotage (~E) makes P(H|~E) < P(H). So the probability of a fifth column goes down a bit. But P(H) started out so high that H is still the only contingency that we should really worry about. The only important question left is, Given that there is a fifth column, is it competent or incompetent? Does the observation of ~E mean that we are in more danger or less danger? That is, letting C = "The fifth column is competent", do we have that P(C | ~E & H) > P(C | H)?

Warren is arguing that ~E should lead us to anticipate a more dangerous fifth column. He is saying that an incompetent fifth column would probably have performed minor sabotage, which would have left evidence. A competent fifth column, on the other hand, would probably still be marshaling its forces to strike a major blow, which would be inconsistent with E. Hence, P(C | ~E & H) > P(C | H). That is why ~E is a greater cause for concern than E would have been.

Whether all of these prior probabilities are reasonable is another matter. But Warren's remarks are consistent with correct Bayesian reasoning from those priors.

Comment author: 29 January 2011 01:21:46AM -1 points [-]

Warren stated in the quote that the lack of any subversive activity was the most convincing factor of all the evidence he has that the 5th Column would soon commit subversive activity.

The problem here should be pretty obvious.

As soon as any subversive activity occurs, the evidence that the 5th Column is going to commit subversive activity clearly just went down! And since the lack of evidence was the strongest evidence for this fact, the fact that the "lack of evidence" is now 0 (either evidence exists, or no evidence exists, there are no degrees for this type of evidence) makes it impossible for the 5th Column to have committed the subversive activity!

The absurdity of this reasoning should be obvious, and it should be thrown out immediately. The lack of subversive activity was clearly not evidence that the 5th Column was planning something. It could not be. You might think the 5th Column was planning something based on other evidence, and that is perfectly fine, but your reasoning for the risk of a subversive activity cannot be based on the lack of any subversive activity. It must be based on other evidence or it invalidates itself.

Comment author: 30 January 2011 01:14:24AM *  9 points [-]

Warren stated in the quote that the lack of any subversive activity was the most convincing factor of all the evidence he has that the 5th Column would soon commit subversive activity.

I just don't see that in the quote. Here is the Warren quote from the OP:

"I take the view that this lack [of subversive activity] is the most ominous sign in our whole situation. It convinces me more than perhaps any other factor that the sabotage we are to get, the Fifth Column activities are to get, are timed just like Pearl Harbor was timed... I believe we are just being lulled into a false sense of security."

His claim isn't that subversive activity will start soon. The claim is that subversive activity will be "timed just like Pearl Harbor was timed". I read this to mean that he anticipates a centrally-orchestrated, synchronized, large-scale attack, of the sort that could only be pulled off by a disciplined, highly-competent fifth column.

If they had seen small, piece-meal efforts at sabotage, then that would have been evidence against a competent fifth column. That is, P(there is a competent fifth column | there has been piece-meal sabotage) < P(there is a competent fifth column).

Therefore, not seeing such efforts is evidence for a competent fifth column: P(there is a competent fifth column | there has been no piece-meal sabotage) > P(there is a competent fifth column). This is a direct algebraic consequence of Bayes's formula.

Of course, seeing no piece-meal sabotage is also evidence for there being no fifth column at all. But if your prior for "no fifth column" is sufficiently low, it still makes sense to spend most of your effort on interpreting what the no-sabotage evidence says about the nature of the fifth column, given that it exists. And what it says, given that there is a fifth column, is that the fifth column is probably marshaling its forces to strike a major blow. (Or at least, that's what the no-sabotage evidence says under the right prior.)

As soon as any subversive activity occurs, the evidence that the 5th Column is going to commit subversive activity clearly just went down!

Scattered and piecemeal acts of sabotage would show that the fifth column is incompetent. So such activity would make "our situation" less "ominous". This is consistent with Warren's view. Such sabotage wouldn't make the probability of subversive activity go down, but Warren doesn't say that it would. But such sabotage would make the probability of sabotage comparable to Pearl Harbor go down. That is Warren's claim.

And since the lack of evidence was the strongest evidence for this fact, the fact that the "lack of evidence" is now 0 (either evidence exists, or no evidence exists, there are no degrees for this type of evidence) ...

This is where we disagree. It's not a matter of "sabotage" vs. "no sabotage". Incompetent sabotage is different from competent sabotage. Warren has a prior that assigns a high prior probability to the existence of a fifth column. His priors about how fifth-columns work, as a function of their competence, are evidently such that our significantly-probable states, in increasing order of ominousness, are

• having seen incompetent sabotage,

• having seen no sabotage yet,

• having seen competent sabotage.

Warren believed that we were in the middle state.

The absurdity of this reasoning should be obvious, and it should be thrown out immediately. The lack of subversive activity was clearly not evidence that the 5th Column was planning something. It could not be. You might think the 5th Column was planning something based on other evidence, and that is perfectly fine, but your reasoning for the risk of a subversive activity cannot be based on the lack of any subversive activity. It must be based on other evidence or it invalidates itself.

In my previous comment, I gave a Bayesian explanation of how the lack of subversive activity could be evidence that we are in a more dangerous situation than we would have been if we had seen evidence of subversion. That is, given the right priors, the lack of subversive activity could be "ominous". Can you point to an error in my reasoning?

Comment author: 31 January 2011 09:26:33PM 0 points [-]

While I think your reading is consistent with a very generous application of the principle of charity, I'm not certain it's appropriate in this case to so apply. Do you have any evidence that Warren was reasoning in this way rather than the less-charitable version, and if so, why didn't he say so explicitly?

It really seems like the simpler explanation is fear plus poor thinking.

Comment author: 23 March 2011 04:20:30PM *  1 point [-]

Do you have any evidence that Warren was reasoning in this way rather than the less-charitable version, and if so, why didn't he say so explicitly

Sorry for taking so long to reply to this.

I think that a close and strict reading supports my interpretation. I don't see the need for an unduly charitable reading.

First, I assume the following context for the quote: Warren had argued for (or maybe only claimed) a high probability for the proposition that there is a Japanese fifth column within the US. Let R be this italicized proposition. Then Warren has argued that p(R) >> 0.

Given that context, here is how I parse the quote, line-by-line:

[A] questioner pointed out that there had been no sabotage or any other type of espionage by the Japanese-Americans up to that time.

I take the questioner to be asserting that there has been no observed sabotage or any other type of espionage by Japanese-Americans up to that time. Let E be this proposition.

Warren responds:

I take the view that this lack [of subversive activity] is the most ominous sign in our whole situation.

I take Warren to be saying that the expected cost of not interring Japanese-Americans is significantly higher after we update on E than it was before we updated on E. Letting D be the "default" action in which we don't inter Japanese-Americans, Warren is asserting that EU(D | E) << EU(D).

The above assertion is the conclusion of Warren's reasoning. If we can show that this conclusion follows from correct Bayesian reasoning from a psychologically realistic prior, plus whatever evidence he explicitly adduces, then the quote cannot serve as an example of the fallacy that Eliezer describes in this post.

Now, we may think that that "psychologically realistic prior" is very probably based in turn on "fear plus poor thinking". But Warren doesn't explicitly show us where his prior came from, so the quote in and of itself is not an example of an explicit error in Bayesian reasoning. Whatever fallacious reasoning occurred, it happened "behind the scenes", prior to the reasoning on display in the quote.

Continuing with my parsing, Warren goes on to say:

It [this lack of subversive activity] convinces me more than perhaps any other factor that the sabotage we are to get, the Fifth Column activities are to get, are timed just like Pearl Harbor was timed... I believe we are just being lulled into a false sense of security.

Let Q be the proposition that there is a Japanese fifth column in America, and it will perform a timed attack, but right now it is lulling us into a false sense of security.

I take Warren to be claiming that p(Q | E) >> p(Q), and that p(Q | E) is sufficiently large to justify saying "I believe Q".

It remains only to give a psychologically realistic prior distribution p such the claims above follow — that is, we need that

• p(R) is sufficiently large to justify saying "R has high probability",
• p(E) = 1 - epsilon,
• EU(D | E) << EU(D),
• p(Q | E) >> p(Q),
• p(Q | E) is sufficiently large to justify saying "I believe Q".

This will suffice to invalidate the Warren quote as an example for this post.

It is a mathematical fact that such priors exist in an abstract sense. Do you think it unlikely that such a prior is psychologically realistic for someone in Warren's position? I think that selection effects and standard human biases make it very plausible that someone in his position would have such a prior.

If you're still skeptical, we can discuss which priors are psychologically realistic for someone in Warren's position.

Comment author: 18 January 2011 02:17:31AM 0 points [-]

I have to think that there is another question to be considered: What are the odds that Japanese-Americans would commit sabotage we could detect as sabotage? If the odds are very high that detectable sabotage would occur, then the absence of sabotage would be evidence in favor of something preventing sabotage. A conspiracy which collaborates with potential saboteurs and encourages them to wait for the proper time to strike then becomes a reasonable hypothesis, if such a conspiracy would believe that an initial act of temporally focused sabotage would be effective enough to have greater utility than all the acts of sabotage which would otherwise occur before the time of the sabotage spree.

Comment author: 29 January 2011 01:28:20AM 0 points [-]

That is a good question, but it doesn't help Warren's reasoning.

His reasoning was not that there was a high probability that they had committed acts of subversion that were undectectible. His reasoning was that because there was no evidence of subversion, this was evidence of future subversion.

This line of reasoning invalidates itself as soon as the first evidence of subversion is discovered, since the reason subversion was imminent was because there was no evidence of subversion.

In its most simple form, Warren was saying: "Because there is no evidence that the ball is blue, the ball is blue."

Comment author: 02 February 2011 02:46:09AM 0 points [-]

I don't make any claims about undetected sabotage, I believe it to be statistically meaningless for these purposes. The detection clause was intended to make my statements more precise. Undetectable sabotage only modifies the odds of detectable sabotage, because it's clearly preferable to strike unnoticed. The conditional statement "If the odds are very high..." eliminates all scenarios where those odds are not very high, which brings this down to Warren assuming an ordering factor in the absence of random events. If you'd like to include undetected sabotage, then you also need to consider the odds that untrained saboteurs would be capable of undetectable sabotage.

Warren wasn't saying "Because there is no evidence that the ball is blue, the ball is blue." He was saying "The sun should be in the sky. I cannot see the sun. Therefore, it has been eaten by a dragon." He was wrong, as it turned out, the eclipse was caused by the moon, and the dragon he feared never existed. But if the dragon he predicted did exist, the world might look much like it did at the time of the predictions.

Comment author: 15 February 2011 05:19:56AM *  1 point [-]

The problem with this scenario, as presented, is that it assumes that "sabotage" is a binary variable. If that were the case, the pool of possibilities would consist of: (1) Fifth Column exists & sabotage occurs, (2) Fifth Column exists & sabotage does not occur, and (3) Fifth Column does not exist & sabotage does not occur (presuming that sabotage, as defined in the scenario, could only be accomplished by Fifth Column). In that case, necessarily, lack of sabotage could only reduce the probability of (1), and therefore could only reduce the probability of the existence of Fifth Column.

However, sabotage is not a binary variable. Presumably, there is some intermediate level of sabotage (call it "amateur sabotage") that one might expect to see in the absence of a well-organized Fifth Column. In this case, we need to add 2 possibilities to the pool: (4) Fifth Column exists & amateur sabotage occurs and (5) Fifth Column does not exist & amateur sabotage occurs.

Given the above, the complete absence of sabotage would reduce the probability not only of (1), but also of (4) and (5). Depending on the prior probability of (5) occurring relative to the probabilities of (1) and (4), Warren's argument may be perfectly reasonable.

Comment author: 24 February 2011 01:07:19PM *  -1 points [-]

If absence of proof is not proof of absence, but absence of evidence is evidence of absence, what makes proof different from evidence?

Example: we currently have no evidence supporting the existence of planets orbiting stars in other galaxies, because our telescopes are not powerful enough to observe them. Should we take this as evidence that no galaxy except ours has planets around its stars?

Another example: before the invention of the microscope, there was no evidence supporting the existence of bacteria because there were no means to observe them. Should've this fact alone been interpreted as evidence of absence of bacteria (even though bacteria did exist before microscopes were invented)?

Comment author: 24 February 2011 01:43:10PM 0 points [-]

Proof means "extremely strong evidence". Absence of proof and absence of evidence are both evidence of absence. Their strength is determined by the probability with which we'd expect to see them, conditional on the thing existing and not existing.

Comment author: 24 February 2011 01:56:06PM 6 points [-]

Hi DevilMaster, welcome to LessWrong!

Generally, the answer to your question is Bayes' Theorem. This theorem is essentially the mathematical formulation of how evidence ought to be weighed when testing ideas. If the wikipedia article doesn't help you much, Eliezer has written an in-depth explanation of what it is and why it works.

The specific answer to your question can be revealed by plugging into this equation, and defining "proof". We say that nothing is ever "proven" to 100% certainty, because if it were (again, according to Bayes' Theorem), no amount of new evidence against it could ever refute it. So "proof" should be interpreted as "really, really likely". You can pick a number like "99.9% certain" if you like. But your best bet is to scrap the notion of absolute "proof" and start thinking in likelihoods.

You'll notice that an integral part of Bayes' Theorem is the idea of how strongly we would expect to see a certain piece of evidence. If the Hypothesis A is true, how likely is it that we'll see Evidence B? And additionally, how likely would it be to see Evidence B regardless of Hypothesis A?

For a piece of evidence to be strong, it has to be something that we would expect to see with much greater probability if a hypothesis is true than if it is false. Otherwise there's a good chance it's a fluke. Furthermore, if that evidence is something that we wouldn't expect to see much either way, than it's not very informative when we don't see it.

So you see how this bears on your examples. I'm not especially familiar with astronomy, so I don't know whether it's true that we haven't seen other galaxies with planets, or how powerful our telescopes are. But let's assume that what you've said is all true.

If we know our telescopes aren't powerful enough to see other planets, then the fact that they don't see any is virtually zero evidence. The probability of us seeing other planets is basically the same whether they're out there or not (because we won't see them either way), so our inability to see them doesn't count as evidence at all. This test doesn't actually tell us anything because we already know that it will tell us the same thing either way. It's like counting how many fingers you have to determine if the stock market will go up or down. You're gonna get "ten" no matter what, and this tells you nothing about the market.

The same reasoning applies to the bacteria example. If we're not more likely to see them given that they're real than we are given that they're not real, then our inability to see them is not evidence in either direction. The test is a bad one because it fails to distinguish one possibility from the other.

But all this isn't to say that it would be valid to reject these notions based on the absence of these evidences alone. There may be other tests we can run that would be more likely to come out one way or the other based on whether the hypothesis is true. So no, it wouldn't make sense to reject the existence of planets or bacteria, because in both of your examples people are using tests that are known to be useless.

Comment author: 24 February 2011 02:57:05PM *  1 point [-]

For a sense of scale: the most distant extrasolar planet is 21,500 ± 3,300 light years away, and rather hypothetical-- look at the size of the error bar on that distance.

The nearest dwarf satellite galaxy is 25,000 light years away, so I suppose we've got a chance of seeing planets there.

The nearest actual galaxy is Andromeda, at 2.5 million light years.

Comment author: 24 February 2011 06:50:51PM 3 points [-]

If we're not more likely to see them given that they're real than we are given that they're not real, then our inability to see them is not evidence in either direction. The test is a bad one because it fails to distinguish one possibility from the other

Thank you. That's what I did not understand.

Comment author: 10 May 2011 04:39:27PM 0 points [-]

The simple answer is that absence of proof towards a possibility is not proof that that the possibility cannot exist, merely that there is no actual proof either way. However, in this specific case, the absence of evidence pointing towards the existence of a fifth column that is engaging in sabotage is evidence that indicates that the fifth column does not exist. I agree that the specific terminology is a bit confusing, but that is the simple explanation as to your question.

Comment author: 10 May 2011 04:50:50PM *  1 point [-]

If absence of proof is not proof of absence, but absence of evidence is evidence of absence, what makes proof different from evidence?

Proof is absolute, evidence is probabilistic.

Example: we currently have no evidence supporting the existence of planets orbiting stars in other galaxies, because our telescopes are not powerful enough to observe them. Should we take this as evidence that no galaxy except ours has planets around its stars?

No, absence of evidence is not evidence of absence if evidence is impossible, but it is evidence of absence if evidence is possible but absent.

(try saying that quickly 3 times :)

Comment author: 10 May 2011 05:04:47PM *  0 points [-]

Benelliot and others have explained this well, but note that we do have direct evidence for planets in other galaxies. We've had it for about two years.

Comment author: 10 May 2011 06:28:32PM *  3 points [-]

we currently have no evidence supporting the existence of planets orbiting stars in other galaxies, because our telescopes are not powerful enough to observe them. Should we take this as evidence that no galaxy except ours has planets around its stars?

Yes we do. We have evidence about how physics (ie. gravity) works and about the formation phases of the universe. That earth and the other planets here exists is evidence. We just didn't happen to have one particular kind of evidence (seeing them). And no, until we developed (recently) the ability to see evidence of them ourselves you would not have been entitled to that piece of evidence either. Because we should not have expected to see them. Seeing planets with tech that should not see them would have been evidence that something else was wrong.

Comment author: 17 July 2011 04:09:31AM 0 points [-]

There is more discussion of this post here as part of the Rerunning the Sequences series.

Comment author: 06 October 2011 03:36:22PM 1 point [-]
Comment author: 12 October 2011 12:15:40AM 1 point [-]

Another proof & discussion: http://kim.oyhus.no/AbsenceOfEvidence.html

Comment author: 01 April 2012 06:39:11PM 1 point [-]

I'm pretty sure you just used this as an rhetoric tool, but by bayesian theory, isn't it impossible to construct a hypothesis which allocates a probability of zero to an event? But don't you say exactly that in your text?

even if the alternative hypothesis does not allow it at all

I mean allocating a probability of zero to an event implies that it doesn't matter what evidence is presented to you, the probability of that particular event will never become anything else than zero. And as it is impossible to disprove something in the same way it is impossible to prove something, a hypothesis which allocates a probability of zero to an event can not be true and is therefore not of use as a hypothesis in bayesian math. Someone please correct me if I'm wrong...

Comment author: 30 September 2012 10:14:21PM *  3 points [-]

A simple counter example (hopefully shorter and more clear than the other more in depth criticism by michael sullivan) is the scenario where warren had exactly equal priors for organized fifth column, unorganized fifth column, and no fifth column.

p(organized) = .33

p(unorganized) = .33

p(none) = .33

If he was practically certain that an organized fifth column would wait to make a large attack, and a unorganized fifth column would make small attacks then seeing no small attacks his new probabilities would approximately be:

p(organized) = .5

p(none) = .5

So he would be correct in his statement of concern (assuming an organized fifth column would be very bad), even though the probability of no fifth column was also increased.

Comment author: 11 August 2013 07:23:20PM 0 points [-]

The video game Star Ocean: Til The End Of Time has a model of interstellar society that tries to solve Fermi's conundrum. Planets capable of interstellar travel form an accord that treats less advanced civilizations as nature preserves and agree not to contact or help them. This model does have several problems, such as communication wavelengths would still be visible to us (they have some undiscovered form of communication?) and sufficiently advanced societies should have an ethical dilemma with allowing intelligent species to go through dark ages and protracted suffering for the sake of "not interfering in the development of their unique culture." Most rationalists will likely agree that we would trade slightly more homogenized art and culture for cures to disease and death. an absence of evidence is still stronger evidence of absence, with the only alternative being a series of suspiciously convenient excuses.

Comment author: 25 August 2013 05:07:25PM 1 point [-]

Planets capable of interstellar travel form an accord that treats less advanced civilizations as nature preserves and agree not to contact or help them.

Sounds similar to the Federation's Prime Directive in Star Trek.

Most rationalists will likely agree that we would trade slightly more homogenized art and culture for cures to disease and death

I'm uncomfortable with the resemblance of this to an argument by definition. It also ignores the more reasonable view that "slightly more homogenized art and culture" isn't usually the worst consequence of more a powerful (I won't say "advanced") society trying to "help" a less powerful one. (Not that that increases the prior probability of space aliens.)

Comment author: 01 September 2013 11:07:34AM 1 point [-]

Glad you called me out. There are much worse possible outcomes for encountering advanced intelligence, or at least more varied possibilities, and I note that I need to work on adjusting my expectations down. Still, I suppose what I should have stated is, if there are benevolent aliens out there that are aware of us I'd sure like them to make with the "we come in peace" already and just cross my fingers that their first contact doesn't play out like The Day The Earth Stood Still. But then I have to follow my own advice from the beginning of this comment and be more pessimistic, so it would be exactly like TDTESS, except that Gort would just follow through and blow us up. Hmm... Okay, the Prime Directive (or Underdeveloped Planet Preservation Pact as in my original example) makes much more sense to me now. Thank you for helping me notice my confusion, Document!

Comment author: 16 May 2014 04:14:05PM *  0 points [-]

I disagree with the article for the following reason: if I have two hypotheses that both explain an "absence of evidence" occurrence equally well, then that occurrence does not give me reason to favor either hypothesis and is not "evidence of absence."

Example: Vibrams are a brand of toe-shoes that recently settled a big suit because they couldn't justify their claims of health benefits. We have two hypotheses (1) Vibrams work, (2) Vibrams don't work. Now, if a well-executed experiment had been done and failed to show an effect, that would be evidence against a significant benefit from Vibrams. However, if the effect were small or nobody had completed a well-executed experiment, I see no reason that (2) would fit the evidence better than (1), so we are justified in saying this absence of evidence is not evidence of absence.

Although the original saying, I think, was meant in the absolute sense (evidence meaning proof), it is still fitting in the probabilistic sense. Absence of evidence is only evidence of absence when combined with one hypothesis explaining an occurrence better than the other, so the saying holds.

Comment author: 16 May 2014 06:23:59PM 1 point [-]

In the situation you describe, the settlement is weak evidence for the product not working. Weak evidence is still evidence. The flaw in "Absence of evidence is evidence of absence," is that the saying omits the detailed description of how to correctly weight the evidence, but this omission does not make the simple statement untrue.

Comment author: 16 May 2014 08:59:06PM *  1 point [-]

if I have two hypotheses that both explain an "absence of evidence" occurrence equally well, then that occurrence does not give me reason to favor either hypothesis and is not "evidence of absence."

This statement is technically true, but not in the way you're using it.

Suppose Vibrams had been around for a thousand years. For a thousand years, people had been challenging their claims to health benefits in court. For a thousand years, time and again, Vibrams had been unable to credibly defend their claims. Would that make you any more skeptical of the claims in question, at least a little bit? If the answer is "yes", you are agreeing that some very large number of such events constitutes evidence against Vibrams. I don't see any way around concluding, from there, that at least one individual instance provides some nonzero amount of evidence - perhaps very small, but not zero.

"Vibrams work, but the effect is small and/or the experiment was shoddy" and "Vibrams don't work" explain the outcome nearly equally well. They cannot explain it precisely equally well: the first hypothesis would assign a higher P(claims defended) than the second, because even small effects are sometimes correctly detected, and even shoddy experiments sometimes aren't fatally flawed. So the second necessarily has a higher P(~claims defended) than the first. This difference is precisely the thing that makes (~claims defended) evidence for the second hypothesis.

Evidence is not proof. Depending on the ratios involved, it may constitute very weak evidence, sometimes weak enough that it's not even worth tracking for mere humans: a .0001% shift is lost in the noise when people aren't even calibrated to the nearest 10%.

If you have two hypotheses that both explain an "absence of evidence" precisely equally well, then you're looking at something completely uncorrelated: trying to deduce the existence of a Fifth Column from the result of a coin flip. And if they explain it only nearly, but not exactly equally well, then you have evidence of absence - although maybe not very much, and maybe not enough to actually push you into the other camp.

Comment author: 16 May 2014 10:28:23PM 1 point [-]

Alternately, you might have alternative hypothesis that explain the absence equally well, but with a much higher complexity cost.

Comment author: 19 February 2016 03:07:55AM 0 points [-]

Warren's full speech is available at archive.org: "Unfortunately, however, many of our people and some of our authorities and, I am afraid, many of our people in other parts of the country are of the opinion that because we have had no sabotage and no fifth column activities in this State since the beginning of the war, that means that none have been planned for us. But I take the view that that is the most ominous sign in our whole situation. It convinces me more than perhaps any other factor that the sabotage that we are to get, the fifth column activities that we are to get, are timed just like Pearl Harbor was timed and just like the invasion of France, and of Denmark, and of Norway, and all those other countries." Hon. Earl Warren, pg 11011-11012, San Francisco Hearings, February 21 and 23, 1942, part 29, National Defense Migration https://archive.org/details/nationaldefensem29unit

Comment author: 03 June 2016 06:18:14PM 0 points [-]

So is there ever a time where you can use absence of evidence alone to disprove a theory, or do you always need other evidence as well? Because is some cases absence of evidence clearly does not disprove a theory, such as when quantum physics was first being discovered, there was not a lot of evidence for it, but can the inverse ever be true will lack of evidence alone proves the theory is false?

Comment author: 03 June 2016 07:02:46PM 1 point [-]

The idea of Bayesianism is that you think in terms of probability instead of true and false.

Comment author: 03 June 2016 09:20:02PM 0 points [-]

From the OP:

The absence of an observation may be strong evidence of absence or very weak evidence of absence, depending on how likely the cause is to produce the observation.

So, yes, absence of evidence can convincingly disprove a theory in some cases (although, as ChristianKI points out, Bayesians typically do not assign probabilities of 0 or 1 to any theory).

Comment author: 20 September 2016 02:29:38PM 1 point [-]

Let E stand for the observation of sabotage

Didn't you mean "the observation of no sabotage"?