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diff --git a/scratch/newcomb-paradox.page b/scratch/newcomb-paradox.page new file mode 100644 index 0000000..58ace89 --- /dev/null +++ b/scratch/newcomb-paradox.page @@ -0,0 +1,69 @@ +--- +format: rst +toc: no +... +================== +Newcomb's Dialemma +================== + +Newcomb's paradox was thought up by a researcher named Newcomb; it was first +explored and written up by Robert Nozick in the 1969 paper +"Newcomb's Problem and Two principles of Choice". + +The Situation +------------- +As narrated by an all knowing "predictor":: + + I am going to give you a choice. It is important to know that I really + pretty much know what you are going to do. I have been watching their whole + life and am additionally an immortal being; i've been doing this a long + time and always guess correctly. It's also important to know that I am + unbiased and don't care which decision you make, I have nothing to gain + either way. + + Here are two boxes: a large and a small. The small has a 10 shekel coin + in it (show everybody). The large one may or may not have a thousand + shekels in it; you don't know. Your choice is to either take only the + large box or to take both the large and small boxes. The twist is that + I already knew which decision you will make and decided whether or not + to put the $1000 in the large box or not based on that knowledge. + If I knew you would "two box", then I left the large box empty. If I knew + you would "one box" then I filled it. + +Dominance Mindset +----------------- +Regardless of what decision was made previously, and whether or not there +is anything in the large box, the person is better off taking both boxes; +either they will get just $10 (better than none) or $1010 (better +than $1000). So two-box. + +Trusting Mindset +---------------- +The predictor is pretty much always right so we can just ignore the +possibility that they are wrong. In this case, choosing to one-box +implies that the Predictor knew you would and you get $1000; +choosing to two-box implies that the predictor knew you would and you +only get $10. + +The predictor doesn't even have to be perfectly accurate; say they are +90%: +If you one-box, your expected value is $900. +If you two-box, your expected value is $110. + +Discussion +---------- +It's disputed whether this is a paradox, and there are many deeper arguments +that I don't have time to go into here. Ultimately, I am a one-boxer +though this is something of a minority position. + +Afterword +--------- +The person who taught me this paradox, Professor Augustin Rayo, a +two-boxer, then had this to add. He was talking with his one-boxing friend +and accused her of letting irrationality undermine her logic: she is so +optimistic that if a statement S is unprovable, but it would be nicer if S +was true than false, then she pretens that S is proven. So basically, even +though there is no rationalization, she will accept a statement "just +because it would be nice", and this isn't how logic works. To which she +replied "but wouldn't it be nice if it was?". + |