National Numeracy Network > NNN Blog > Monte Hall and the Job Market

# Monte Hall and the Job Market

published Feb 5, 2014

At last fall's NNN meetings, Esther Wilder and Elin Waring included a discussion of teaching the Monte Hall problem. For those of you not familiar with the problem, the reference is to the Monte Hall program in which a contestant is told a big prize sits behind one of three doors. The other two doors each contain something worthless like a goat. The contestant chooses one of the three doors. Then, before revealing what is behind the contestant's chosen door, Monte Hall would reveal a goat behind one of the other two doors and give the contestant the option of switching to the other remaining closed door.

The statistics of this problem suggest you are better off switching. The contestant owns a door with a 1/3 probability of containing the prize. The other two doors collectively hold the remaining 2/3 probability. Monte Hall's offer boils down to this: Would you like to hold the option on one, randomly chosen door or the other two? (Because he will reveal one of the remaining two to be a loser, the contestant gets the prize if is was behind either of the two non-chosen doors to begin with.)

Esther and Elin gave a nice demonstration about how the counter-intuitive nature of this result can be overcome by having students play the game repeatedly with playing cards. But what I am writing about today is a question they asked at the end: Can anyone give an example of the Monte Hall problem in real life. One of the session attendees threw out the academic job search. We typically bring in 3 candidates. We get a sense of who we like. Then one of the other two bows out due to exogenous reasons. Do we switch preferred candidates?

I'm in the middle of hiring and so have been thinking about this. My first thought has been that my process isn't really like the Monte Hall problem. I don't have a choice between one car and two goats. I have three goods of varying quality. And I am not randomly picking. I am assessing them and then sorting out an expected value. So, when one job candidate bows out, it is nothing like the choice: Two random doors or one?

However, suppose my objective function was simply that I had to get the best candidate. Perhaps I have a strong sense of regret and just can't stand to learn that I didn't pick the best colleague when I had the chance. My guess is that even though I do my best to assess candidates, many times I really can't rule out the possibility that any of the three would be the best of the bunch. So long as none of the candidates is so clearly dominant that s/he has a probability of more than 50% of being the best, I'm back in Monte's world. So, if we assume someone with this kind of objective, the Monte Hall problem does apply.

Curious what others think. Is your hiring practice similar to the Monte Hall problem? Either way, do you know of other "real" examples of the problem in everyday life?

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