A typical situation is that there’s a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.
You have three ways to respond:
You can under-update your belief in the hypothesis, ignoring the anecdotes completely
You can update by precisely the measure warranted by the existence of these anecdotes and the fact that they reached you.
You can over-update by adding too much credence to the hypothesis.
In almost every situation you’re likely to encounter, the real danger is 3. Well-known biases are at work pulling you towards 3. These biases are often known to work even when you’re aware of them and trying to counteract them. Moreover, the harm from reaching 3 is typically far greater than the harm from reaching 1. This is because the correct added amount of credence in 2 is very tiny, particularly because you’re already likely to know that the competing hypotheses for this issue are all likely to have anecdotes going for them. In real-life situations, you don’t usually hear anecdotes supporting an incredibly unlikely-seeming hypothesis which you’d otherwise be inclined to think as capable of nurturing no anecdotes at all. So forgoing that tiny amount of credence is not nearly as bad as choosing 3 and updating, typically, by a large amount.
The saying “The plural of anecdotes is not data” exists to steer you away from 3. It works to counteract the very strong biases pulling you towards 3. Its danger, you are saying, is that it pulls you towards 1 rather than the correct 2. That may be pedantically correct, but is a very poor reason to criticize the saying. Even with its help, you’re almost always very likely to over-update—all it’s doing is lessening the blow.
Perhaps this as an example of “things Bayesianism has taught you” that are harming your epistemic rationality?
A similar thing I noticed is disdain towards “correlation does not imply causation” from enlightened Bayesians. It is counter-productive.
These biases are often known to work even when you’re aware of them and trying to counteract them.
This is the problem. I know, as an epistemic matter of fact, that anecdotes are evidence. I could try to ignore this knowledge, with the goal of counteracting the biases to which you refer. That is, I could try to suppress the Bayesian update or to undo it after it has happened. I could try to push my credence back to where it was “manually”. However, as you point out, counteracting biases in this way doesn’t work.
Far better, it seems to me, to habituate myself to the fact that updates can by miniscule. Credence is quantitative, not qualitative, and so can change by arbitrarily small amounts. “Update Yourself Incrementally”. Granting that someone has evidence for their claims can be an arbitrarily small concession. Updating on the evidence doesn’t need to move my credences by even a subjectively discernible amount. Nonetheless, I am obliged to acknowledge that the anecdote would move the credences of an ideal Bayesian agent by some nonzero amount.
...updates can by miniscule … Updating on the evidence doesn’t need to move my credences by even a subjectively discernible amount. Nonetheless, I am obliged to acknowledge that the anecdote would move the credences of an ideal Bayesian agent by some nonzero amount.
So, let’s talk about measurement and detection.
Presumably you don’t calculate your believed probabilities to the n-th significant digit, so I don’t understand the idea of a “miniscule” update. If it has no discernible consequences then as far as I am concerned it did not happen.
Let’s take an example. I believe that my probability of being struck by lightning is very low to the extent that I don’t worry about it and don’t take any special precautions during thunderstorms. Here is an anecdote which relates how a guy was stuck by lightning while sitting in his office inside a building. You’re saying I should update my beliefs, but what does it mean?
I have no numeric estimate of P(me being struck by lightning) so there’s no number I can adjust by 0.0000001. I am not going to do anything differently. My estimate of my chances to be electrocuted by Zeus’ bolt is still “very very low”. So where is that “miniscule update” that you think I should make and how do I detect it?
P.S. If you want to update on each piece of evidence, surely by now you must fully believe that product X is certain to enlarge your penis?
A typical situation is that there’s a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.
It is interesting that you think of this as typical, or at least typical enough to be exclusionary of non-contentious issues. I avoid discussions about politics and possibly other contentious issues, and when I think of people providing anecdotes I usually think of them in support of neutral issues, like the efficacy of understudied nutritional supplements. If someone tells you, “I ate dinner at Joe’s Crab Shack and I had intense gastrointestinal distress,” I wouldn’t think it’s necessarily justified to ignore it on the basis that it’s anecdotal. If you have 3 more friends who all report the same thing to you, you should rightly become very suspicious of the sanitation at Joe’s Crab Shack. I think the fact that you are talking about contentious issues specifically is an important and interesting point of clarification.
Thanks for that comment! Eliezer often says people should be more sensitive to evidence, but an awful lot of real-life evidence is in fact much weaker, noisier, and easier to misinterpret than it seems. And it’s not enough to just keep in mind a bunch of Bayesian mantras—you need to be aware of survivor bias, publication bias, Simpson’s paradox and many other non-obvious traps, otherwise you silently go wrong and don’t even know it. In a world where most published medical results fail to replicate, how much should we trust our own conclusions?
Would it be more honest to recommend people to just never update at all? But then everyone will stick to their favorite theories forever… Maybe an even better recommendation would be to watch out for “motivated cognition”, try to be more skeptical of all theories including your favorites.
A typical situation is that there’s a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.
You have three ways to respond:
You can under-update your belief in the hypothesis, ignoring the anecdotes completely
You can update by precisely the measure warranted by the existence of these anecdotes and the fact that they reached you.
You can over-update by adding too much credence to the hypothesis.
In almost every situation you’re likely to encounter, the real danger is 3. Well-known biases are at work pulling you towards 3. These biases are often known to work even when you’re aware of them and trying to counteract them. Moreover, the harm from reaching 3 is typically far greater than the harm from reaching 1. This is because the correct added amount of credence in 2 is very tiny, particularly because you’re already likely to know that the competing hypotheses for this issue are all likely to have anecdotes going for them. In real-life situations, you don’t usually hear anecdotes supporting an incredibly unlikely-seeming hypothesis which you’d otherwise be inclined to think as capable of nurturing no anecdotes at all. So forgoing that tiny amount of credence is not nearly as bad as choosing 3 and updating, typically, by a large amount.
The saying “The plural of anecdotes is not data” exists to steer you away from 3. It works to counteract the very strong biases pulling you towards 3. Its danger, you are saying, is that it pulls you towards 1 rather than the correct 2. That may be pedantically correct, but is a very poor reason to criticize the saying. Even with its help, you’re almost always very likely to over-update—all it’s doing is lessening the blow.
Perhaps this as an example of “things Bayesianism has taught you” that are harming your epistemic rationality?
A similar thing I noticed is disdain towards “correlation does not imply causation” from enlightened Bayesians. It is counter-productive.
This is the problem. I know, as an epistemic matter of fact, that anecdotes are evidence. I could try to ignore this knowledge, with the goal of counteracting the biases to which you refer. That is, I could try to suppress the Bayesian update or to undo it after it has happened. I could try to push my credence back to where it was “manually”. However, as you point out, counteracting biases in this way doesn’t work.
Far better, it seems to me, to habituate myself to the fact that updates can by miniscule. Credence is quantitative, not qualitative, and so can change by arbitrarily small amounts. “Update Yourself Incrementally”. Granting that someone has evidence for their claims can be an arbitrarily small concession. Updating on the evidence doesn’t need to move my credences by even a subjectively discernible amount. Nonetheless, I am obliged to acknowledge that the anecdote would move the credences of an ideal Bayesian agent by some nonzero amount.
So, let’s talk about measurement and detection.
Presumably you don’t calculate your believed probabilities to the n-th significant digit, so I don’t understand the idea of a “miniscule” update. If it has no discernible consequences then as far as I am concerned it did not happen.
Let’s take an example. I believe that my probability of being struck by lightning is very low to the extent that I don’t worry about it and don’t take any special precautions during thunderstorms. Here is an anecdote which relates how a guy was stuck by lightning while sitting in his office inside a building. You’re saying I should update my beliefs, but what does it mean?
I have no numeric estimate of P(me being struck by lightning) so there’s no number I can adjust by 0.0000001. I am not going to do anything differently. My estimate of my chances to be electrocuted by Zeus’ bolt is still “very very low”. So where is that “miniscule update” that you think I should make and how do I detect it?
P.S. If you want to update on each piece of evidence, surely by now you must fully believe that product X is certain to enlarge your penis?
It is interesting that you think of this as typical, or at least typical enough to be exclusionary of non-contentious issues. I avoid discussions about politics and possibly other contentious issues, and when I think of people providing anecdotes I usually think of them in support of neutral issues, like the efficacy of understudied nutritional supplements. If someone tells you, “I ate dinner at Joe’s Crab Shack and I had intense gastrointestinal distress,” I wouldn’t think it’s necessarily justified to ignore it on the basis that it’s anecdotal. If you have 3 more friends who all report the same thing to you, you should rightly become very suspicious of the sanitation at Joe’s Crab Shack. I think the fact that you are talking about contentious issues specifically is an important and interesting point of clarification.
Thanks for that comment! Eliezer often says people should be more sensitive to evidence, but an awful lot of real-life evidence is in fact much weaker, noisier, and easier to misinterpret than it seems. And it’s not enough to just keep in mind a bunch of Bayesian mantras—you need to be aware of survivor bias, publication bias, Simpson’s paradox and many other non-obvious traps, otherwise you silently go wrong and don’t even know it. In a world where most published medical results fail to replicate, how much should we trust our own conclusions?
Would it be more honest to recommend people to just never update at all? But then everyone will stick to their favorite theories forever… Maybe an even better recommendation would be to watch out for “motivated cognition”, try to be more skeptical of all theories including your favorites.