I’ve had a similar nagging feeling about the smoker’s lesion paradox for a long time, but have never actually taken the time to research it. I’m going to use the the language of the chewing gum version though.
A common way (I’ve heard) of describing EDT is that you make the decision that will make your cousin the happiest (assuming your cousin has no particular stake in the matter, other than your own well being). Well, if I am your cousin, and I learn that chewing gum corresponds to a gene, which corresponds to higher rates of throat cancers, I will revise my probability that you will get cancer up. However, if I learn that you have never chewed gum before, and started chewing gum after you read the same study I did, I will revise my probability of cancer down, suggesting that maybe you should chew gum after all. The same argument holds for if you did chew gum before. So it’s always seemed to me that EDT gives the wrong answer on the smoker’s lesion problem only if you don’t take into account the observation that you previously did (or did not) chew gum.
I’ve had a related doubt about the olympic medalist issue. The probability that someone is a very fast runner, given that they are wearing an olympic gold medalist (for a running event, presumably), is very high. But the probability that someone is a very fast runner, given that they are wearing a gold medal and that they are wearing this medal because they believe it will make them a faster runner is not.
Now, I assume that both of the previous paragraphs are wrong. It seems unlikely to me that very intelligent people would spend entire careers thinking about issues like this, and fail to see flaws that I spotted almost immediately, despite having no training in the field. That’s just probably not true. My guess is that I’m getting these errors because my own brain is drawing “obvious” conclusions that weak, simplistic decision theories don’t have the intelligence to handle. The only reason it seems obvious to me that chewing gum will decrease the probability that I get cancer is because I don’t have introspective access to my brain’s decision making. It would be really nice if I could get that confirmed by somebody.
I’ve had a similar nagging feeling about the smoker’s lesion paradox for a long time, but have never actually taken the time to research it. I’m going to use the the language of the chewing gum version though.
A common way (I’ve heard) of describing EDT is that you make the decision that will make your cousin the happiest (assuming your cousin has no particular stake in the matter, other than your own well being). Well, if I am your cousin, and I learn that chewing gum corresponds to a gene, which corresponds to higher rates of throat cancers, I will revise my probability that you will get cancer up. However, if I learn that you have never chewed gum before, and started chewing gum after you read the same study I did, I will revise my probability of cancer down, suggesting that maybe you should chew gum after all. The same argument holds for if you did chew gum before. So it’s always seemed to me that EDT gives the wrong answer on the smoker’s lesion problem only if you don’t take into account the observation that you previously did (or did not) chew gum.
I’ve had a related doubt about the olympic medalist issue. The probability that someone is a very fast runner, given that they are wearing an olympic gold medalist (for a running event, presumably), is very high. But the probability that someone is a very fast runner, given that they are wearing a gold medal and that they are wearing this medal because they believe it will make them a faster runner is not.
Now, I assume that both of the previous paragraphs are wrong. It seems unlikely to me that very intelligent people would spend entire careers thinking about issues like this, and fail to see flaws that I spotted almost immediately, despite having no training in the field. That’s just probably not true. My guess is that I’m getting these errors because my own brain is drawing “obvious” conclusions that weak, simplistic decision theories don’t have the intelligence to handle. The only reason it seems obvious to me that chewing gum will decrease the probability that I get cancer is because I don’t have introspective access to my brain’s decision making. It would be really nice if I could get that confirmed by somebody.