This lets us see clearly the problem with using “The lady down the street is a witch; she did it” to explain the pattern in the sequence 0101010101. If you’re sending a message to a friend, trying to describe the sequence you observed, you would have to say: “The lady down the street is a witch; she made the sequence come out 0101010101.” Your accusation of witchcraft wouldn’t let you shorten the rest of the message; you would still have to describe, in full detail, the data which her witchery caused.
Witchcraft may fit our observations in the sense of qualitatively permitting them; but this is because witchcraft permits everything, like saying “Phlogiston!” So, even after you say “witch,” you still have to describe all the observed data in full detail. You have not compressed the total length of the message describing your observations by transmitting the message about witchcraft; you have simply added a useless prologue, increasing the total length.
The real sneakiness was concealed in the word “it” of “A witch did it.” A witch did what?
Of course, thanks to hindsight bias and anchoring and fake explanations and fake causality and positive bias and motivated cognition, it may seem all too obvious that if a woman is a witch, of course she would make the coin come up 0101010101. But I’ll get to that soon enough. . .
*
26
Your Strength as a Rationalist
The following happened to me in an IRC chatroom, long enough ago that I was still hanging around in IRC chatrooms. Time has fuzzed the memory and my report may be imprecise.
So there I was, in an IRC chatroom, when someone reports that a friend of his needs medical advice. His friend says that he’s been having sudden chest pains, so he called an ambulance, and the ambulance showed up, but the paramedics told him it was nothing, and left, and now the chest pains are getting worse. What should his friend do?
I was confused by this story. I remembered reading about homeless people in New York who would call ambulances just to be taken someplace warm, and how the paramedics always had to take them to the emergency room, even on the 27th iteration. Because if they didn’t, the ambulance company could be sued for lots and lots of money. Likewise, emergency rooms are legally obligated to treat anyone, regardless of ability to pay. (And the hospital absorbs the costs, which are enormous, so hospitals are closing their emergency rooms . . . It makes you wonder what’s the point of having economists if we’re just going to ignore them.) So I didn’t quite understand how the described events could have happened. Anyone reporting sudden chest pains should have been hauled off by an ambulance instantly.
And this is where I fell down as a rationalist. I remembered several occasions where my doctor would completely fail to panic at the report of symptoms that seemed, to me, very alarming. And the Medical Establishment was always right. Every single time. I had chest pains myself, at one point, and the doctor patiently explained to me that I was describing chest muscle pain, not a heart attack. So I said into the IRC channel, “Well, if the paramedics told your friend it was nothing, it must really be nothing—they’d have hauled him off if there was the tiniest chance of serious trouble.”
Thus I managed to explain the story within my existing model, though the fit still felt a little forced . . .
Later on, the fellow comes back into the IRC chatroom and says his friend made the whole thing up. Evidently this was not one of his more reliable friends.
I should have realized, perhaps, that an unknown acquaintance of an acquaintance in an IRC channel might be less reliable than a published journal article. Alas, belief is easier than disbelief; we believe instinctively, but disbelief requires a conscious effort.1
So instead, by dint of mighty straining, I forced my model of reality to explain an anomaly that never actually happened. And I knew how embarrassing this was. I knew that the usefulness of a model is not what it can explain, but what it can’t. A hypothesis that forbids nothing, permits everything, and thereby fails to constrain anticipation.
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.
We are all weak, from time to time; the sad part is that I could have been stronger. I had all the information I needed to arrive at the correct answer, I even noticed the problem, and then I ignored it. My feeling of confusion was a Clue, and I threw my Clue away.
I should have paid more attention to that sensation of still feels a little forced. It’s one of the most important feelings a truthseeker can have, a part of your strength as a rationalist. It is a design flaw in human cognition that this sensation manifests as a quiet strain in the back of your mind, instead of a wailing alarm siren and a glowing neon sign reading:
EITHER YOUR MODEL IS FALSE OR THIS STORY IS WRONG.
*
1. Daniel T. Gilbert, Romin W. Tafarodi, and Patrick S. Malone, “You Can’t Not Believe Everything You Read,” Journal of Personality and Social Psychology 65 (2 1993): 221–233, doi:10.1037/0022-3514.65.2.221.
27
Absence of Evidence Is Evidence of Absence
From Robyn Dawes’s Rational Choice in an Uncertain World:1
In fact, this 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, and ¬E for the observation of no sabotage. The symbol H1 stands for the hypothesis of a Japanese-American Fifth Column, and H2 for the hypothesis that no Fifth Column exists. The conditional probability P(E|H), or “E given H,” is how confidently we’d expect to see the evidence E if we assumed the hypothesis H were true.
Whatever the likelihood that a Fifth Column would do no sabotage, the probability P(¬E|H1), it won’t be as large as the likelihood that there’s no sabotage given that there’s no Fifth Column, 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), read “A implies B,” is not equivalent to (¬A ⇒ ¬B), read “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), i.e., seeing E increases the probability of H, then P(H|¬E) < P(H), i.e., failure to observe E decreases the probability of H. The probability 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 pro
duce 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.
*
1. Robyn M. Dawes, Rational Choice in An Uncertain World, 1st ed., ed. Jerome Kagan (San Diego, CA: Harcourt Brace Jovanovich, 1988), 250-251.
28
Conservation of Expected Evidence
Friedrich Spee von Langenfeld, a priest who heard the confessions of condemned witches, wrote in 1631 the Cautio Criminalis (“prudence in criminal cases”), in which he bitingly described the decision tree for condemning accused witches: If the witch had led an evil and improper life, she was guilty; if she had led a good and proper life, this too was a proof, for witches dissemble and try to appear especially virtuous. After the woman was put in prison: if she was afraid, this proved her guilt; if she was not afraid, this proved her guilt, for witches characteristically pretend innocence and wear a bold front. Or on hearing of a denunciation of witchcraft against her, she might seek flight or remain; if she ran, that proved her guilt; if she remained, the devil had detained her so she could not get away.
Spee acted as confessor to many witches; he was thus in a position to observe every branch of the accusation tree, that no matter what the accused witch said or did, it was held as proof against her. In any individual case, you would only hear one branch of the dilemma. It is for this reason that scientists write down their experimental predictions in advance.
But you can’t have it both ways—as a matter of probability theory, not mere fairness. The rule that “absence of evidence is evidence of absence” is a special case of a more general law, which I would name Conservation of Expected Evidence: The expectation of the posterior probability, after viewing the evidence, must equal the prior probability.
P(H) = P(H,E) + P(H,¬E)
P(H) = P(H|E) × P(E) + P(H,¬E) × P(¬E)
Therefore, for every expectation of evidence, there is an equal and opposite expectation of counterevidence.
If you expect a strong probability of seeing weak evidence in one direction, it must be balanced by a weak expectation of seeing strong evidence in the other direction. If you’re very confident in your theory, and therefore anticipate seeing an outcome that matches your hypothesis, this can only provide a very small increment to your belief (it is already close to 1); but the unexpected failure of your prediction would (and must) deal your confidence a huge blow. On average, you must expect to be exactly as confident as when you started out. Equivalently, the mere expectation of encountering evidence—before you’ve actually seen it—should not shift your prior beliefs. (Again, if this is not intuitively obvious, see An Intuitive Explanation of Bayesian Reasoning.)
So if you claim that “no sabotage” is evidence for the existence of a Japanese-American Fifth Column, you must conversely hold that seeing sabotage would argue against a Fifth Column. If you claim that “a good and proper life” is evidence that a woman is a witch, then an evil and improper life must be evidence that she is not a witch. If you argue that God, to test humanity’s faith, refuses to reveal His existence, then the miracles described in the Bible must argue against the existence of God.
Doesn’t quite sound right, does it? Pay attention to that feeling of this seems a little forced, that quiet strain in the back of your mind. It’s important.
For a true Bayesian, it is impossible to seek evidence that confirms a theory. There is no possible plan you can devise, no clever strategy, no cunning device, by which you can legitimately expect your confidence in a fixed proposition to be higher (on average) than before. You can only ever seek evidence to test a theory, not to confirm it.
This realization can take quite a load off your mind. You need not worry about how to interpret every possible experimental result to confirm your theory. You needn’t bother planning how to make any given iota of evidence confirm your theory, because you know that for every expectation of evidence, there is an equal and oppositive expectation of counterevidence. If you try to weaken the counterevidence of a possible “abnormal” observation, you can only do it by weakening the support of a “normal” observation, to a precisely equal and opposite degree. It is a zero-sum game. No matter how you connive, no matter how you argue, no matter how you strategize, you can’t possibly expect the resulting game plan to shift your beliefs (on average) in a particular direction.
You might as well sit back and relax while you wait for the evidence to come in.
. . . Human psychology is so screwed up.
*
29
Hindsight Devalues Science
This essay is closely based on an excerpt from Meyers’s Exploring Social Psychology;1 the excerpt is worth reading in its entirety.
Cullen Murphy, editor of The Atlantic, said that the social sciences turn up “no ideas or conclusions that can’t be found in [any] encyclopedia of quotations . . . Day after day social scientists go out into the world. Day after day they discover that people’s behavior is pretty much what you’d expect.”
Of course, the “expectation” is all hindsight. (Hindsight bias: Subjects who know the actual answer to a question assign much higher probabilities they “would have” guessed for that answer, compared to subjects who must guess without knowing the answer.)
The historian Arthur Schlesinger, Jr. dismissed scientific studies of World War II soldiers’ experiences as “ponderous demonstrations” of common sense. For example:
Better educated soldiers suffered more adjustment problems than less educated soldiers. (Intellectuals were less prepared for battle stresses than street-smart people.)
Southern soldiers coped better with the hot South Sea Island climate than Northern soldiers. (Southerners are more accustomed to hot weather.)
White privates were more eager to be promoted to noncommissioned officers than Black privates. (Years of oppression take a toll on achievement motivation.)
Southern Blacks preferred Southern to Northern White officers. (Southern officers were more experienced and skilled in interacting with Blacks.)
As long as the fighting continued, soldiers were more eager to return home than after the war ended. (During the fighting, soldiers knew they were in mortal danger.)
How many of these findings do you think you could have predicted in advance? Three out of five? Four out of five? Are there any cases where you would have predicted the opposite—where your model takes a hit? Take a moment to think before continuing . . .
. . .
In this demonstration (from Paul Lazarsfeld by way of Meyers), all of the findings above are the opposite of what was actually found.2 How many times did you think your model took a hit? How many times did you admit you would have been wrong? That’s how good your model really was. The measure of your strength as a rationalist is your ability to be more confused by fiction than by reality.
Unless, of course, I reversed the results again. What do you think?
Do your thought processes at this point, where you really don’t know the answer, feel diffe
rent from the thought processes you used to rationalize either side of the “known” answer?
Daphna Baratz exposed college students to pairs of supposed findings, one true (“In prosperous times people spend a larger portion of their income than during a recession”) and one the truth’s opposite.3 In both sides of the pair, students rated the supposed finding as what they “would have predicted.” Perfectly standard hindsight bias.
Which leads people to think they have no need for science, because they “could have predicted” that.
(Just as you would expect, right?)
Hindsight will lead us to systematically undervalue the surprisingness of scientific findings, especially the discoveries we understand—the ones that seem real to us, the ones we can retrofit into our models of the world. If you understand neurology or physics and read news in that topic, then you probably underestimate the surprisingness of findings in those fields too. This unfairly devalues the contribution of the researchers; and worse, will prevent you from noticing when you are seeing evidence that doesn’t fit what you really would have expected.
We need to make a conscious effort to be shocked enough.
*
1. David G. Meyers, Exploring Social Psychology (New York: McGraw-Hill, 1994), 15–19.
Rationality- From AI to Zombies Page 12
