that seems like an unnecessarily vague characterization of a precise description
I deny that we have a precise description. If you listed out a specific trillion trillion observations that I allegedly made, then we could talk about whether those particular observations justify thinking that we’re in the game with the bomb. (If those trillion trillion observations were all from me waking up in a strange room and interacting with it, with no other context, then as noted above, I would have no reason to believe I’m in this game as opposed to any variety of other games consistent with those observations.) The scenario vaguely alleges that we think we’re facing an accurate predictor, and then alleges that their observed failure rate (on an unspecified history against unspecified players) is 1 per trillion-trillion. It does not say how or why we got into the epistemic state of thinking that there’s an accurate predictor there; we assume this by fiat.
(To be clear, I’m fine with assuming this by fiat. I’m simply arguing that your reluctance to analyze the problem by cases seems strange and likely erroneous to me.)
I am not familiar with this, no. If you have explanatory material / intuition pumps / etc. to illustrate this, I’d certainly appreciate it!
The canonical explanatory text is the FDT paper (PDF warning) (that the OP is responding to a critique of, iirc), and there’s a bunch of literature on LW (maybe start at the wiki page on UDT? Hopefully we have one of those) exploring various intuitions. If you’re not familiar with this style of logic, I recommend starting there (ah look we do have a UDT wiki page). I might write up some fresh intuition pumps later, to try to improve the exposition. (We’ve sure got a lot of exposition if you dig through the archives, but I think there are still a bunch of gaps.)
I am not asking how I could come to believe the “literally perfect predictor” thing with 100% certainty; I am asking how I could come to believe it at all (with, let’s say, > 50% certainty).
Uh, I mean, we could play a version of this game where the sums were positive (such that you’d want to play) and smaller (such that I could fund the prizes), and then I could say “yo Said Achmiz, I decided to act as a predictor of you in this game, I’m about to show you either a box with $10 and a box with $1, or an empty box and a box with $1, depending on how I predicted you’ll behave”. And then I think that at least the other readers on this post would predict that I have >50% probability of predicting your behavior correctly. You haven’t exactly been subtle about how you make decisions.
Predicting someone accurately with >50% likelihood isn’t all that hard. A coin predicts you “perfectly accurately” 50% of the time, you’ve only gotta do slightly better than that.
I suspect you’re confused here in putting “perfect prediction” on some big pedestal. the predictor is trying to reason about you, and they either reason basically-correctly, or their reasoning includes some mistake. And insofar as they reason validly to a conclusion about the right person, they’re going to get the answer right.
And again, note that you’re not exactly a tricky case yourself. You’re kinda broadcasting your decision-making procedure all over the internet. You don’t have to be a supermind studying a brainscan to figure out that Said Achmiz takes the extra $1.
My girlfriend often reasons accurately about whether I’m getting dinner tonight. Sometimes she reasons wrongly about it (eg, she neglects that I had a late lunch) but gets the right answer by chance anyway. Sometimes she reasons wrongly about it and gets the wrong answer by chance. But often she reasons correctly about it, and gets the right answer for the right reasons. And if I’m standing in the supermarket wondering whether she already ate or whether I should buy enough cheese to make her some food too, I have no trouble thinking “well, insofar as she got the right answer for the right reasons tonight, she knew I’d be hungry when I got home, and so she hasn’t eaten yet”. None of this case-analysis requires me to believe she’s a supermind who studied a scan of my brain for twelve thousand years. Believing that she was right about me for the right reasons is just not a very difficult epistemic state to enter. My reasons for doing most of what I do just aren’t all that complicated. It’s often not all that tricky to draw the right conclusions about what people do for the right reasons.
Furthermore, I note that in the high/low/extremeball game, I have no trouble answering questions about what I should do insofar as the game is highball, even though I have <50% (and in fact ~33%) probability on that being the case. In fact, I could analyze payouts insofar as the game is highball, even if the game was only 0.1% likely to be highball! In fact, the probability of me actually believing I face a given decision problem is almost irrelevant to my ability to analyze the payouts of different actions. As evidenced in part by the fact that I am prescribing actions in this incredibly implausible scenario with bombs and predictors.
And so in this wild hypothetical situation where we’ve somehow (by fiat) become convinced that there’s an ancient predictor predicting our actions (which is way weirder than my girlfriend predicting my action, tbh), presumably one of our hypotheses for what’s going on is that the predictor correctly deduced what we would do, for the correct reasons. Like, that’s one of many hypotheses that could explain our past observations. And so, assuming that hypothesis, for the purpose of analysis—and recalling that I can analyze which action is best assuming the game is highball, without making any claim about how easy or hard it is to figure out whether the game is highball—assuming that hypothesis, what action would you prescribe?
I deny that we have a precise description. If you listed out a specific trillion trillion observations that I allegedly made, then we could talk about whether those particular observations justify thinking that we’re in the game with the bomb. (If those trillion trillion observations were all from me waking up in a strange room and interacting with it, with no other context, then as noted above, I would have no reason to believe I’m in this game as opposed to any variety of other games consistent with those observations.) The scenario vaguely alleges that we think we’re facing an accurate predictor, and then alleges that their observed failure rate (on an unspecified history against unspecified players) is 1 per trillion-trillion. It does not say how or why we got into the epistemic state of thinking that there’s an accurate predictor there; we assume this by fiat.
(To be clear, I’m fine with assuming this by fiat. I’m simply arguing that your reluctance to analyze the problem by cases seems strange and likely erroneous to me.)
The canonical explanatory text is the FDT paper (PDF warning) (that the OP is responding to a critique of, iirc), and there’s a bunch of literature on LW (maybe start at the wiki page on UDT? Hopefully we have one of those) exploring various intuitions. If you’re not familiar with this style of logic, I recommend starting there (ah look we do have a UDT wiki page). I might write up some fresh intuition pumps later, to try to improve the exposition. (We’ve sure got a lot of exposition if you dig through the archives, but I think there are still a bunch of gaps.)
Uh, I mean, we could play a version of this game where the sums were positive (such that you’d want to play) and smaller (such that I could fund the prizes), and then I could say “yo Said Achmiz, I decided to act as a predictor of you in this game, I’m about to show you either a box with $10 and a box with $1, or an empty box and a box with $1, depending on how I predicted you’ll behave”. And then I think that at least the other readers on this post would predict that I have >50% probability of predicting your behavior correctly. You haven’t exactly been subtle about how you make decisions.
Predicting someone accurately with >50% likelihood isn’t all that hard. A coin predicts you “perfectly accurately” 50% of the time, you’ve only gotta do slightly better than that.
I suspect you’re confused here in putting “perfect prediction” on some big pedestal. the predictor is trying to reason about you, and they either reason basically-correctly, or their reasoning includes some mistake. And insofar as they reason validly to a conclusion about the right person, they’re going to get the answer right.
And again, note that you’re not exactly a tricky case yourself. You’re kinda broadcasting your decision-making procedure all over the internet. You don’t have to be a supermind studying a brainscan to figure out that Said Achmiz takes the extra $1.
My girlfriend often reasons accurately about whether I’m getting dinner tonight. Sometimes she reasons wrongly about it (eg, she neglects that I had a late lunch) but gets the right answer by chance anyway. Sometimes she reasons wrongly about it and gets the wrong answer by chance. But often she reasons correctly about it, and gets the right answer for the right reasons. And if I’m standing in the supermarket wondering whether she already ate or whether I should buy enough cheese to make her some food too, I have no trouble thinking “well, insofar as she got the right answer for the right reasons tonight, she knew I’d be hungry when I got home, and so she hasn’t eaten yet”. None of this case-analysis requires me to believe she’s a supermind who studied a scan of my brain for twelve thousand years. Believing that she was right about me for the right reasons is just not a very difficult epistemic state to enter. My reasons for doing most of what I do just aren’t all that complicated. It’s often not all that tricky to draw the right conclusions about what people do for the right reasons.
Furthermore, I note that in the high/low/extremeball game, I have no trouble answering questions about what I should do insofar as the game is highball, even though I have <50% (and in fact ~33%) probability on that being the case. In fact, I could analyze payouts insofar as the game is highball, even if the game was only 0.1% likely to be highball! In fact, the probability of me actually believing I face a given decision problem is almost irrelevant to my ability to analyze the payouts of different actions. As evidenced in part by the fact that I am prescribing actions in this incredibly implausible scenario with bombs and predictors.
And so in this wild hypothetical situation where we’ve somehow (by fiat) become convinced that there’s an ancient predictor predicting our actions (which is way weirder than my girlfriend predicting my action, tbh), presumably one of our hypotheses for what’s going on is that the predictor correctly deduced what we would do, for the correct reasons. Like, that’s one of many hypotheses that could explain our past observations. And so, assuming that hypothesis, for the purpose of analysis—and recalling that I can analyze which action is best assuming the game is highball, without making any claim about how easy or hard it is to figure out whether the game is highball—assuming that hypothesis, what action would you prescribe?