To me it seems to highlight the division between the mind and the will. He seems to say that you can control your mind, but you can not control the way your mind makes you control your mind.
To me it seems to highlight the division between the mind and the will. He seems to say that you can control your mind, but you can not control the way your mind makes you control your mind.
Silas,
I see what you're saying, but I don't think I have a moral obligation to take every available opportunity to make money. I'm reminded of an event when I was about 10 years old: I took some small change and threw it in the trash. I don't remember why I did it, but I do remember that my dad was really offended. But, hey, it was my money. Betting is fine but I don't see why it should be privileged over other means of expression.
This seems a little bossy to me. Beyond the issue of transaction costs ("the vig") and the effort of gathering the information to try to beat the market (this would an intellectual hobby, like blogging, doing crosswords, or following the horses, that would make sense to do if enjoyable in itself), maybe some people don't want to bet. I have no problem with betting--I enjoy it--but I'm a little puzzled by the statement that people should be betting, or that they have some sort of moral obligation to put their money where their mouth is. Maybe you personally don't "really believe" things unless you put money on them, but not everybody feels that way.
Eliezer,
OK, one more try. First, you're picking 3^^^^3 out of the air, so I don't see why you can't pick 1/3^^^^3 out of the air also. You're saying that your priors have to come from some rigorous procedure but your utility comes from simply transcribing what some dude says to you. Second, even if for some reason you really want to work with the utility of 3^^^^3, there's no good reason for you not to consider the possibility that it's really -3^^^^3, and so you should be doing the opposite. The issue is not that two huge numbers will exactly cancel out; the point is that you're making up all the numbers here but are artificially constraining the expected utility differential to be positive.
If I really wanted to consider this example realistically, I'd say that this guy has no magic powers, so I wouldn't worry about him killing 3^^^^3 people or whatever. A slightly more realistic scenario would be something like a guy with a bomb in a school, in which case I'd defer to the experts (presumably whoever in the police force deals with people like that) on their judgment of how best to calm him down. There I could see an (approximate) probability calculation being relevant, but, again, they key thing would be whether giving him $5 (or whatever) would make him more or less likely to set the fuse. It wouldn't be appropriate to say a priori that it could only help.
OK, let's try this one more time:
To put it another way, conditional on this nonexistent person having these nonexistent powers, why should you be so sure that he's telling the truth? Perhaps you'll only get what you want by not giving him the $5. To put it mathematically, you're computing pX, where p is the probability and X is the outcome, and you're saying that if X is huge, then just about any nonzero p will make pX be large. But you're forgetting two things: first, if you have the imagination to imagine X to be super-huge, you should be able to have the imagination to imagine p to be super-small. (I.e., if you can talk about 3^^^^3, you can talk about 1/3^^^^3.) Second, once you allow these hypothetical super-large X's, you have to acknowledge the possibility that you got the sign wrong.
When I do this demo in class (see here for details or here for the brief version), I phrase it as "the percentage of countries in the United Nations that are in Africa." This seems less ambiguous than Kahneman and Tversky's phrasing (although, I admit, I haven't done any experiment to check). It indeed works in the classroom setting, although with smaller effects than reported by Kahneman and Tversky (see page 89 of the linked article above).
Eliezer,
You write: "I'm sure they had some minor warnings of an al Qaeda plot, but they probably also had minor warnings of mafia activity, nuclear material for sale, and an invasion from Mars." I doubt they had credible warnings about an invasion from Mars. But, yeah, I'd like the FBI etc. to do their best to stop Al Quaeda plots, Mafia activity, and nuclear material for sale. I wonder if you're succumbing to a "bias-correction bias" where, because something could be explainable by a bias, you assume it is. Groups of people do make mistakes, some of which could have been anticipated with better organization and planning. I have essentially no knowledge of the U.S. intelligence system, but I wouldn't let them off the hook just because a criticism could be simply hindsight bias. Sometimes hindsight is valid, right?
Eliezer,
I agree with what you're saying. But there is something to this "everything is connected" idea. Almost every statistical problem I work on is connected to other statistical problems I've worked on, and realizing these connections has been helpful to me.
To me it seems to highlight the division between the mind and the will. He seems to say that you can control your mind, but you can not control the way your mind makes you control your mind.