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.
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.
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.
I found this article because someone linked it to the all roads load to Rome (ARLR) fallacy [https://www.reddit.com/r/Destiny/comments/1dyuxtm/the_all_road_lead_to_rome_fallacy_is_better/], where there's no evidence that would reduce someone's confidence but there is evidence that would increase it. This commonly occurs with conspiracy theorists where an absence of evidence is evidence of a cover up. I think the article was a good pointer even if the point is kind of trivial. I still had to sit down and formally prove some of the authors conclusions, however. For example, P(H|E) > P(E) --> P(H|~E) < P(E) which more directly shows that a Bayesian reasoner can't fall for the ARLR fallacy. So I think the author could have said more with less. As a matter of fact, the quote you gave actually clarified some points for me.
I'd like to add that this article isn't clear about its normative commitments such as strong Bayesianism [that all valid inferences are Bayesian ones]. Given this article's place in The Sequences, it could prime readers to think strong Bayesianism is uncontroversial among other things. On a personal note, I'm in the camp that we have limited control over our beliefs [they are largely determined by the information we consume] and this supports my applied position that we should deliberately expose ourselves to confirmatory information until our credence's are at a prescribed level. This is to make the point that the author offers a certain theory of mind when they say "this realization can take quite a load off your mind". So you definitely aren't getting the same amount of neutrality as you would get from, say, SEP. However, I don't think this is as bad as quote guy makes it out to be if it's even bad?
All that being said, I think quote guy is kind of missing the point. I don't think any blog about the basics of reasoning is going to introduce anything new and that wouldn't be covered in class [that's just beyond its scope]. So I think that criticism isn't entirely fair since I see way more value in stating the obvious. However, the front page vibe of The Sequences feels like it's supposed to be "deep" and it seems to support an epistemology that I'm heavily opposed to [I'll affectionately call it optimistic rationalism]. And because I'm one to think the truth tends to be boring, that kind of marketing is always going to give me pause.
Really, this article is better for its pure philosophy and I don't think there's any unique applications for this. After all, witch hunters aren't Bayesian reasoners.
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.
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.
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.