And mostly favorably, too. You might need a subscription to read the review, alas. The reviewer is Donald Granberg, a sociologist (now retired) at the University of Missouri. He published several papers on the MHP during the nineties.
I liked this part of the review:
The author does a masterful job of tracing the problem back to its origin.
And this part:
One difficulty with word problems is their ambiguity. Rosenhouse does a superb job of reducing, if not eliminating, this source of endless argumentation with his canonical version.
Not to mention this part:
The Monty Hall Problem is much more comprehensive and wide-ranging than the many articles on the subject that have dribbled out. Those, of necessity, are more sharply focused. Rosenhouse offers readers much to think about concerning the perplexing question of whether to stick or switch.
I also got a kick out of this:
The nonmathematician deserves to be warned that The Monty Hall Problem‘s contents are highly mathematical. What would one expect from a math whiz?
Math whiz? Goodness! Haven’t been called that since high school.
It’s interesting the difference in perspective between a mathematician and a sociologist on this issue. I tend to view the problem as an exercise in probability, whereas someone like Granberg views it as a problem in human decision making. I think that distinction makes itself felt in a number of places. Here’s one:
Of greatest relevance is the “three prisoners” problem first published by Martin Gardner in 1959. Three convicts, A, B, and C, are scheduled to be executed. The governor decides that one of them is to be pardoned and tells the warden his identity but asks the warden to keep it a secret. However, A prevails upon the warden to tell A the name of one of the other two who will be executed. The warden tells A that B is to be executed. A is encouraged, thinking that his chance of being pardoned has increased from 1/3 to 1/2. Is he justified in thinking that his chance of being pardoned had actually increased?
Rosenhouse claims that this “is the Monty Hall problem in all but name…. or at least of something formally equivalent to it.” This raises the question of what constitutes the essence of the dilemma. I contend that lies in Monty’s offering the contestant the opportunity to change a choice in light of new information. It is the second-stage decision to switch or stick that is so excruciating, engaging, and entertaining. If I’m right about this, primary credit for introducing the Monty Hall dilemma to academia goes to Steve Selvin and his two brief letters in The American Statistician
I’m not sure if that’s the sort of thing about which one can be right or wrong. The Three Prisoners Problem (TPP) and the MHP are mathematically identical. That the TPP is typically presented as a problem in probability while the MHP is typically presented as a problem in decision making is not relevant from a mathematical standpoint. But I can understand why a sociologist would have a different emphasis.
I would like to clarify one point:
And, in her initial response to her critics, she showed confusion over the concepts of odds and probability, writing, “The winning odds of 1/3 can’t go up to 1/2” where (judging from what she wrote elsewhere) she intended to say “odds of 1:2 can’t go up to 1:1.” For some reason, when Rosenhouse presents this section from her second column he corrects “odds” to “chances” and makes other small changes in the wording without marking them. Elsewhere he repeats part of the same section without altering the original wording. In her 1996 book (4), vos Savant corrected the errors herself.
I did not “correct” anything. I simply made a transcription error in one of the places I mentioned the vos Savant quote, and that is how “odds” got changed to “chances.” I would point out, though, that this small change had absolutely no relevance at all to any argument I was making.
A more serious error I made was in relying on vos Savant’s 1996 book for my quotes, rather than the original Parade magazine columns. It had not occurred to me that wordings would have been changed for the book from what was originally published. Live and learn. I would add, again, that absolutely nothing of relevance to the discussion was riding on these minor issues of phrasing.
At any rate, I’m glad Professor Granberg wrote such a generally positive review. I have already received one e-mail from a person telilng me he was going to buy the book based on the review. The first of many I hope!