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# NNN Blog

## Monte Hall and the Job Market

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?

## Advertise Your QR

Over the weekend I saw an effective example of QR in advertising: H&R Block's Get Your Billion Back, America campaign. The premise of the campaign is hardly new: American's fail to claim all of the tax refunds available to them by about \$1B each year. What was new (to me, at least) was H&R Block's attempt to make that number meaningful:

"That's \$500 on every single seat–not just in this stadium, but in every professional football stadium in America [with visual of an NFL stadium]."

We can certainly discuss whether this is the 'right' way to think about this problem:

• How big is \$1B? \$1B is 1/1000th of the approximately \$1T paid in income taxes. Is 99.9% a bad success rate?
• We already spend 31.5 billion dollars to pay tax professionals and buy tax software. How much more will we have to pay to squeeze out that last \$1B?
• Do we know that the \$1B is really "lost?" I know that when I do my own taxes I am conservative at times, intentionally leaving some deductions off my taxes to reduce the odds of an audit. Of course, my hypothetical tax preparer doesn't have to worry about feeling the full brunt of that audit since she isn't on the hook if I say I did something that I actually didn't. So, her incentives are to push me to claim the biggest refund possible.

But, all of that stated, I think it is great to see advertisers who are QR-literate and use "compared to what" to make their pitches as clear as possible.

## How Cold Is It?

Those who regularly exercise their QR state of mind routinely find themselves asking, "Compared to what?" So, as I look out my window at daytime temps of -20o F (we're headed to a high of -15o F from a low below -20o F) I thought I would take on this important question.

All in all, I feel better about my lot when it is put in perspective. Another advantage of QR literacy!

## QR and Football

Colleague Christopher Tassava pointed me to this interesting short film on the use of QR in high school football. A successful high school coach shares the reasoning behind his decisions to never punt (even on his own 5 yard line!) and always onside kick. Watching the video made me think three things:

• This is a great example of taking QR seriously. In the context it's being used, the consideration of trade-offs seems pretty sound.
• Given that the research on the under-use of 4th down has been around a while and we still don't see many coaches following this strategy, there must be some other component to coaches decision-making. For example, could it be that to lose unconventionally poses a greater risk to job security than losing the same way everyone else loses? Or could it be that winning isn't the only thing (pace Mr. Lombardi)–that coaches are trying to give students a "football experience" even if that doesn't mean maximizing the probability of wins.
• Recent concerns surrounding head injuries have led some to question the danger of kickoffs and punt returns. This video suggests the game wouldn't necessarily be radically different at the high school level if rules were adopted to eliminate these risky plays. (For example, rule could heavily penalize any kickoff that traveled more than 20 yards and outlaw punts.) Presumably receiving teams would get better at handling "on side" kicks and, as the video points out, the change in starting field position wouldn't necessarily be that great.

Overall, I share Christopher's recommendation of the video as an interesting application of QR to sport.

## Numerous Neurons

The current (Nov 7, 2014) issue of Nature is all about recent science surrounding the human brain. One interesting tidbit I picked up is that our current best guess is that the human brain includes 86 billion neurons.

Now, that's a pretty big number. But just how big is it? I poked around Nature's website and found this interesting blog that gave me an answer. Author Bradley Voytek notes that the most common comparison is that "there are as many neurons in the human brain as there are stars in the Milky Way." But Voytek tells us that this isn't quite right–our best guess for stars in the Milky Way is between 200 and 400 billion.

He also shares some details about how we estimate the number of neurons. (Turns out counting one by one isn't a good strategy–who knew?!) Problems abound. The brain isn't uniformly dense with neurons, so sampling matters. And the neurons are so intertwined that the current best estimate comes from a strategy of disolving brain samples and introducing a dye that sticks to the nuclei of neurons. All in all, a pretty interesting example for teaching ideas of representative sampling and estimation techniques. An interesting problem to which your students can apply a few of those neurons!

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