I think ‘The Moral Landscape’ is brilliant, but there is an error in that book on page 86: the Monty Hall Problem. The error is not to see that the assessment of probability of an event depends upon the current information that the observer has.

For instance, seeing the three doors shut, the observer clearly assigns (all else being equal) one-third probability to each door. However, if he chooses door #1, and before it is opened then door #2 is opened to reveal the goat, then at that point his information changes, and he should then, on his then current information, assign one-half probability to each remaining closed door.

To say that before door #2 was opened he chose door #1 with 1/3 probability, therefore it must stay fixed at 1/3 even after door #2 is open, and so the balance if you like of 2/3 must all go to door #3, is to fail to appreciate that assignment of probability depends on the information held by the observer. And in that example, that information changes on the opening of door #2, so the observer’s probability of door #1 should also then change.

In a footnote this effect is exaggerated to 1000 doors. The claim is that the probability that he assigned originally and correctly to door #1 was 1/1000, which must therefore stay fixed even after 998 doors have been opened, so that all that extra information must then go to the other remaining closed door alone. This is clearly faulty.

In itself this does not greatly impact the book, except that this example is used to make strong comments about those naive people who fail to reason correctly and think that the probability should be 1/2 for each door after door #2 is opened. Unfortunately, they are actually correct, which rather spoils the force of the argument.

However, as I say, the book as a whole is a tour de force, and this small blip should not diminish it at all.

—Mike