{"id":23320,"date":"2013-06-13T11:02:53","date_gmt":"2013-06-13T15:02:53","guid":{"rendered":"http:\/\/blogs.ams.org\/mathgradblog\/?p=23320"},"modified":"2015-02-20T14:50:43","modified_gmt":"2015-02-20T19:50:43","slug":"newcombs-paradox","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/mathgradblog\/2013\/06\/13\/newcombs-paradox\/","title":{"rendered":"Newcomb’s Paradox"},"content":{"rendered":"

\"Unknown-1\"<\/a>In the realm of mathematical puzzles and thought experiments one can find a stock pile of paradoxes.\u00a0\u00a0 The Mariam-Webster Dictionary<\/i> defines a paradox as \u201can argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises.\u201d\u00a0 One short example of such oddities is the Liar\u2019s Paradox.\u00a0 It is the deceptively simple declaration, \u201cThis sentence is false.\u201d\u00a0\u00a0\u00a0After\u00a0some evaluation, one concludes that, if the sentence is false, it is also true.\u00a0 Likewise, if it is true it must be false, providing a self-contradiction that does not permit\u00a0the assignment of a single truth value.<\/p>\n

<\/p>\n

Another mind-bending conundrum is Newcomb\u2019s Paradox.\u00a0 \u00a0\u00a0The paradox was first created by William Newcomb at the University of California Lawrence Livermore Laboratory and later first published as a philosophy paper by Robert Nozick in 1969.\u00a0 In a review by Olle H\u00e4ggstr\u00f6m of William Eckhardt\u2019s book Paradoxes in Probability Theory<\/i> in the March 2013 edition of Notices <\/i>(a publication of the American Mathematical Society), H\u00e4ggstr\u00f6m describes Newcomb\u2019s Paradox as follows:<\/p>\n

Newcomb\u2019s Paradox<\/strong><\/p>\n

An incredibly intelligent donor, perhaps from outer space, has prepared two boxes for you: a big one<\/em> and a small one. The small one (which might as well be transparent) contains $1,000. The big one<\/em> contains either $1,000,000 or nothing. You have a choice between accepting both boxes or just the<\/em> big box. It seems obvious that you should accept both boxes (because that gives you an extra $1,000<\/em> irrespective of the content of the big box), but here\u2019s the catch: The donor has tried to predict<\/em> whether you will pick one box or two boxes. If the prediction is that you pick just the big box, then it<\/em> contains $1,000,000, whereas if the prediction is that you pick both boxes, then the big box is empty.<\/em> The donor has exposed a large number of people before you to the same experiment and predicted<\/em> correctly 90 percent of the time, regardless of whether subjects chose one box or two. What<\/em> should you do?<\/em><\/p>\n

The interesting thing about this paradox is that picking the bigger box alone does not guarantee a payoff; since there is still a 10 percent chance not in one\u2019s favor based on past experiments that the intelligent donor is wrong.\u00a0\u00a0 In the same vein, there will always be the payoff of $1000 by picking the smaller box, either alone or with the bigger box.\u00a0 However, in the case of picking both boxes, there is a 10 percent\u00a0 chance in one\u2019s favor based on past experiments\u00a0 that the intelligent donor is wrong.\u00a0\u00a0\u00a0So, with this in mind, what would be your optimal choice?<\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

In the realm of mathematical puzzles and thought experiments one can find a stock pile of paradoxes.\u00a0\u00a0 The Mariam-Webster Dictionary defines a paradox as \u201can argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises.\u201d\u00a0 One short example … Continue reading →<\/span><\/a><\/p>\n

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