The reply that it “is impossible for A and ~A to both be evidence for B” is to ignore what Frank said in favor of insisting on the very overgeneralization I think he was trying to point out. It’s not impossible at all when we are being imprecise enough about the prior expectations involved, such as when we lump all moments in a sustained effort together.
Here’s an example to illustrate what I’m saying: Say you are a parent of a 10 year old boy who generally wants to stay up past his bedtime. His protests vary from occasional temper tantrums to the usual slumped-shoulders expression of disappointment that bedtime has finally arrived. Under normal circumstances, the expectation is that he would give at least some evidence of wanting to stay up later. We’ll call this resistance “A,” and A is evidence for “B”: his desire and motivation to stay up later. What shall we say when ~A happens? That is, what shall we say when the boy one day suddenly goes enthusiastically to bed? That he has given up his desire? That it is impossible for this to be evidence of his continued desire and motivation? Of course not. It is exactly what we would expect a motivated and reasonably intelligent person to do: try different and probably more effective strategies. If we generalize the ongoing experience of the little boy’s quest to say up later, A and ~A are both evidence of B. “It is impossible for A and ~A to both be evidence for B” is simply not narrow enough to be a true statement, and using it in that way can easily amount to a bad counterargument.
Rather, we need to be specific about each situation. What I think we should pay attention to here is the prior expectation of B. With a high enough prior, A and ~A could either (but not both) be evidence of B. But if we are not being specific to each precise situation, the generalization “it is impossible for A and ~A to both be evidence of B” can be a very subtle straw man, because the person being argued against may not be relying on the assumption that A and ~A are equal evidence for B at the same time and in the same situation.
Returning to the Japanese Fifth Column argument, unlike the little boy in my example the Japanese (and, in general, descendants from countries that go to war with their current country of citizenship) do not have a consistent track record of wartime sabotage. Also, there isn’t any reason to think they would not generally be more loyal to their country of citizenship than the country of their parents, grandparents, or even of their own childhood. So there is no particularly strong expectation that they would commit sabotage… and thus no such expectation that some mysterious lack of sabotage is itself a sign of a new strategic attempt as part of a sustained effort. The argument should come down to the prior expectation of Japanese sabotage. That seems to be the crux of it to me.
It seems to me the weakness in Frank’s argument also lies in the basic premise that we should expect the Japanese to commit sabotage. And I believe the governor would need to rely on that premise, or a similar one, in order to sustain his argument beyond what Eliezer presented.
But. The inside information premise seems nearly undefeatable to me. We can’t comment on information we don’t have. I think that is always a possibility with controversial official responses that most people would prefer to deny. If the person whose claims you are evaluating has secret but pertinent information you don’t have access to, then it can be very difficult to offer a fair analysis. For one, you will have very different yet subjectively valid prior expectations.
If we generalize the ongoing experience of the little boy’s quest to say up later, A and ~A are both evidence of B.
You seem to be using “evidence of X” to mean something along the lines of “consistent with X”. That’s not what it means in this context.
An event is evidence for or against a scenario insofar as it changes your subjective probability estimate for that scenario. Your example child going enthusiastically to bed is in fact evidence that he’s changed his mind about staying up past his bedtime: it makes that scenario subjectively more plausible, even though it’s still probably a long-shot option given what you know. It might simultaneously be evidence for some new bedtime-avoidance scheme, but that’s entirely consistent with it also pointing to a possible change of heart: the increased probability of both is made up for in the reduced probability of him continuing with his old behavior.
Subjective probabilities for either/or scenarios have to sum to unity, and so evidence for one such option has to be balanced out by evidence against one or more of the others. A and ~A cannot both be evidence for a given scenario; at best they can both leave it unaffected.
I think I understand that a little better now. So thank you for taking the time to explain that to me.
Even so, it seems all I must do is add to my counterexample a prior track record of the little boy changing strategies while pretending to go along with authority. Reconsidering my little boy example with that in mind, does that change your reply?
Also, I fail to see how your response ameliorates my objection to the claim “it is impossible for A and ~A to both be evidence for B.” By your own explanation, they are both evidence, albeit offering unequal relative probabilities (forgive me if I’m getting the password wrong there, but I think you can surmise what it is I’m getting at). Maybe if we say that “It is impossible for A and ~A to both offer the same relative probability for B at the same time and concerning the same situation and given the same subjective view of the facts, etc,” we have something that doesn’t lead us to claim things that are not true about someone else’s argument, as in the case above, that their argument depends on A and ~A at the same time and in the same way, when the precise claim in question is actually that A can be evidence for B in one situation; and based upon the expectation set upon the observance of subsequent facts, at some later date, ~A could also end up being evidence for B. I’m not sure if I’ve explained that clearly, but I’ll keep trying until either I get what I’m missing, or I manage to express clearly what may well be coming out as gibberish. Either way, I get a little slice of the self-improvement I’m looking for.
Thanks again, and I hope you can forgive my wet ears on this and bear with me. The benefits of our exchanges here will probably be pretty one sided; I have almost nothing to offer a more experienced rationalist here, and lots to gain… and I realize that, so bear with me, and please know I am grateful for the feedback.
based upon the expectation set upon the observance of subsequent facts, at some later date, ~A could also end up being evidence for B
Here’s a contradiction with A and ~A both being evidence for the same thing. You could tell your spouse “Go up and check if little Timmy went to bed”. Before ze comes back you already have an estimate of how likely Timmy is to go to bed on time (your prior belief). But then your spouse, who was too tired to climb the stairs, comes back and tells you “Little Timmy may or may not have gone to bed”. Now, if both of those possibilities would be evidence of Timmy’s staying up late then you should update your belief accordingly. But how can you do that without receiving any new information?
Yes. I get that. We cannot use A and ~A to update our estimates in the same way at the same time. That’s not the same as saying that it is impossible for A and ~A to be evidence of the same thing. One could work on Tuesday, and the other could work on Friday, depending on the situation. That was my only point: can’t generalize a timeline but need to operate at specific points on that timeline. That goes back to the justification for interning Japanese citizens. If we say ~A just can’t ever be evidence of B because at some previous time A was evidence for B, then we are making a mistake. At some later date, ~A could end up being better evidence, depending on the situation. My point was that a better counterargument to the governor’s justification is to point out that the prospect of naturalized citizens turning against their home country in favor of their country of ancestry presents a very low prior, because the Japanese (and other groups that polyglot nations have gone to war with) have not usually behaved that way in the past. I could be wrong, but it doesn’t have anything to do with updating estimates with a variable and its negation to reach the same probability at the same time. I pretty much agree with what you said, just not the implication that it conflicts in some way with what I said.
I think the brief answer to this point is that it is very important to define the hypothesis precisely, to avoid being confused in the way you describe.
Applying that lesson to Earl Warren, we can say that he failed to distinguish between motive for big-sabotage and motive for little-sabotage. Lack of little-sabotage events is evidence in favor of motive-for-big-sabotage (and for no-motive-to-sabotage: with the benefit of hindsight, we know this was the true state of the world). But unclear phrasing by Warren made it sound like he believed absence of little-sabotage was evidence of motive-to-little-sabotage, which is a nonsensical position.
Given the low probability of big-sabotage (even after incorporating the evidence Warren puts forth), it’s pretty clear that the argument for Warren’s suggested policy (Japanese-American internment) depended pretty heavily on the confused thinking created by this equivocation.
The reply that it “is impossible for A and ~A to both be evidence for B” is to ignore what Frank said in favor of insisting on the very overgeneralization I think he was trying to point out. It’s not impossible at all when we are being imprecise enough about the prior expectations involved, such as when we lump all moments in a sustained effort together.
Here’s an example to illustrate what I’m saying: Say you are a parent of a 10 year old boy who generally wants to stay up past his bedtime. His protests vary from occasional temper tantrums to the usual slumped-shoulders expression of disappointment that bedtime has finally arrived. Under normal circumstances, the expectation is that he would give at least some evidence of wanting to stay up later. We’ll call this resistance “A,” and A is evidence for “B”: his desire and motivation to stay up later. What shall we say when ~A happens? That is, what shall we say when the boy one day suddenly goes enthusiastically to bed? That he has given up his desire? That it is impossible for this to be evidence of his continued desire and motivation? Of course not. It is exactly what we would expect a motivated and reasonably intelligent person to do: try different and probably more effective strategies. If we generalize the ongoing experience of the little boy’s quest to say up later, A and ~A are both evidence of B. “It is impossible for A and ~A to both be evidence for B” is simply not narrow enough to be a true statement, and using it in that way can easily amount to a bad counterargument.
Rather, we need to be specific about each situation. What I think we should pay attention to here is the prior expectation of B. With a high enough prior, A and ~A could either (but not both) be evidence of B. But if we are not being specific to each precise situation, the generalization “it is impossible for A and ~A to both be evidence of B” can be a very subtle straw man, because the person being argued against may not be relying on the assumption that A and ~A are equal evidence for B at the same time and in the same situation.
Returning to the Japanese Fifth Column argument, unlike the little boy in my example the Japanese (and, in general, descendants from countries that go to war with their current country of citizenship) do not have a consistent track record of wartime sabotage. Also, there isn’t any reason to think they would not generally be more loyal to their country of citizenship than the country of their parents, grandparents, or even of their own childhood. So there is no particularly strong expectation that they would commit sabotage… and thus no such expectation that some mysterious lack of sabotage is itself a sign of a new strategic attempt as part of a sustained effort. The argument should come down to the prior expectation of Japanese sabotage. That seems to be the crux of it to me.
It seems to me the weakness in Frank’s argument also lies in the basic premise that we should expect the Japanese to commit sabotage. And I believe the governor would need to rely on that premise, or a similar one, in order to sustain his argument beyond what Eliezer presented.
But. The inside information premise seems nearly undefeatable to me. We can’t comment on information we don’t have. I think that is always a possibility with controversial official responses that most people would prefer to deny. If the person whose claims you are evaluating has secret but pertinent information you don’t have access to, then it can be very difficult to offer a fair analysis. For one, you will have very different yet subjectively valid prior expectations.
You seem to be using “evidence of X” to mean something along the lines of “consistent with X”. That’s not what it means in this context.
An event is evidence for or against a scenario insofar as it changes your subjective probability estimate for that scenario. Your example child going enthusiastically to bed is in fact evidence that he’s changed his mind about staying up past his bedtime: it makes that scenario subjectively more plausible, even though it’s still probably a long-shot option given what you know. It might simultaneously be evidence for some new bedtime-avoidance scheme, but that’s entirely consistent with it also pointing to a possible change of heart: the increased probability of both is made up for in the reduced probability of him continuing with his old behavior.
Subjective probabilities for either/or scenarios have to sum to unity, and so evidence for one such option has to be balanced out by evidence against one or more of the others. A and ~A cannot both be evidence for a given scenario; at best they can both leave it unaffected.
I think I understand that a little better now. So thank you for taking the time to explain that to me.
Even so, it seems all I must do is add to my counterexample a prior track record of the little boy changing strategies while pretending to go along with authority. Reconsidering my little boy example with that in mind, does that change your reply?
Also, I fail to see how your response ameliorates my objection to the claim “it is impossible for A and ~A to both be evidence for B.” By your own explanation, they are both evidence, albeit offering unequal relative probabilities (forgive me if I’m getting the password wrong there, but I think you can surmise what it is I’m getting at). Maybe if we say that “It is impossible for A and ~A to both offer the same relative probability for B at the same time and concerning the same situation and given the same subjective view of the facts, etc,” we have something that doesn’t lead us to claim things that are not true about someone else’s argument, as in the case above, that their argument depends on A and ~A at the same time and in the same way, when the precise claim in question is actually that A can be evidence for B in one situation; and based upon the expectation set upon the observance of subsequent facts, at some later date, ~A could also end up being evidence for B. I’m not sure if I’ve explained that clearly, but I’ll keep trying until either I get what I’m missing, or I manage to express clearly what may well be coming out as gibberish. Either way, I get a little slice of the self-improvement I’m looking for.
Thanks again, and I hope you can forgive my wet ears on this and bear with me. The benefits of our exchanges here will probably be pretty one sided; I have almost nothing to offer a more experienced rationalist here, and lots to gain… and I realize that, so bear with me, and please know I am grateful for the feedback.
Here’s a contradiction with A and ~A both being evidence for the same thing. You could tell your spouse “Go up and check if little Timmy went to bed”. Before ze comes back you already have an estimate of how likely Timmy is to go to bed on time (your prior belief). But then your spouse, who was too tired to climb the stairs, comes back and tells you “Little Timmy may or may not have gone to bed”. Now, if both of those possibilities would be evidence of Timmy’s staying up late then you should update your belief accordingly. But how can you do that without receiving any new information?
Yes. I get that. We cannot use A and ~A to update our estimates in the same way at the same time. That’s not the same as saying that it is impossible for A and ~A to be evidence of the same thing. One could work on Tuesday, and the other could work on Friday, depending on the situation. That was my only point: can’t generalize a timeline but need to operate at specific points on that timeline. That goes back to the justification for interning Japanese citizens. If we say ~A just can’t ever be evidence of B because at some previous time A was evidence for B, then we are making a mistake. At some later date, ~A could end up being better evidence, depending on the situation. My point was that a better counterargument to the governor’s justification is to point out that the prospect of naturalized citizens turning against their home country in favor of their country of ancestry presents a very low prior, because the Japanese (and other groups that polyglot nations have gone to war with) have not usually behaved that way in the past. I could be wrong, but it doesn’t have anything to do with updating estimates with a variable and its negation to reach the same probability at the same time. I pretty much agree with what you said, just not the implication that it conflicts in some way with what I said.
I think the brief answer to this point is that it is very important to define the hypothesis precisely, to avoid being confused in the way you describe.
Applying that lesson to Earl Warren, we can say that he failed to distinguish between motive for big-sabotage and motive for little-sabotage. Lack of little-sabotage events is evidence in favor of motive-for-big-sabotage (and for no-motive-to-sabotage: with the benefit of hindsight, we know this was the true state of the world). But unclear phrasing by Warren made it sound like he believed absence of little-sabotage was evidence of motive-to-little-sabotage, which is a nonsensical position.
Given the low probability of big-sabotage (even after incorporating the evidence Warren puts forth), it’s pretty clear that the argument for Warren’s suggested policy (Japanese-American internment) depended pretty heavily on the confused thinking created by this equivocation.