Tuesday 5 May 2020

Judging a bookcase by its politician

Michael Gove’s bookcase has gained attention recently due to some controversial books which appeared on its shelves. Inevitably some people expressed concern that he would own these books as they inferred he may share their views. In response to this, some people suggested that just because he owns these books, doesn’t mean he agrees with them.
Even though it seems like a disagreement, both of these statements are compatible with each other. But to explain this, I am going to talk about a concept in economics called “signalling”. 

Signalling is when your action indicates to others some information about you. Let’s think of a situation where an employer has two candidates, one that went to university and one that didn’t. The candidate that didn’t go to university may actually be smarter (and hence more employable) than the one that did, but just decided not to go. However, the employer has no way of knowing this, and so must choose a candidate that they believe is most likely going to be smarter than the other. 

To do this, the employer reasons using conditional probability, sometimes referred to as Bayesian probability after the mathematician. Personally, I prefer to call it conditional probability as it helps people remember what it is: conditional on x happening, what are the chances of y. So the question the employer must ask is “given the condition that the person did or did not go to university, what is the probably that they are smart?”

The way to think about this is to look at the two different types of groups. Those what went to university have to be at least smart enough to meet the entry requirements. Those that did not go, however, include people who are not smart enough to meet the entry requirements. 

Therefore even though it is possible that the person who didn’t go to university is smarter than the person who did, it is still more likely that the person we pick at random, who went to university, is smarter. Therefore, one* reason why people may be tempted to go to university is because that it acts as a signal to future employers that they are smart.

Personally, I am really not a fan of how economics uses signalling a lot of the time. It is not that I do not think people should use Bayesian reasoning, it is that economists generally use signalling to find negatives in people. Telling some academic economist about a hobby is tricky as in their minds you should always be working on your research. Saying that I enjoy pottery acts as a signal to them that I am not spending every waking moment on a new paper. However, I have in fact started to tell economists about my hobbies. This is so that if they start saying anything about my research I have a signal that they are, most likely, assholes.

So what has all this got to do with Michael Gove’s bookshelf? Is a bookshelf a signal or is it just a place to store books. I can buy that some politicians may be sitting in front of their bookcases to appear smart, even going so far as to choose the books that are on view. But even if they were not consciously trying to signal something, we could still perform the same sort of Bayesian reasoning on them.

To say that we cannot learn anything about a person by their bookshelf is just silly. It either indicates they have read or are going to read a book. You should be able to work out from my bookshelf that I have at least studied economics given the amount of economic textbooks on my shelf. At the same time, it is also true that just because you own a book does not mean you agree with its views.

For example, owning a copy of Mein Kampf does not mean you are a Nazi. In fact, I am pretty sure most people who own a copy of Mein Kampf are not Nazis. However, if you do happen to be a Nazi, I think it is also quite likely you would own a copy of Mein Kampf. So if we were to pick a person at random who owns Mein Kampf, then we may be more likely to pick a Nazi then someone who does not own Mein Kampf.** But importantly here, even though we are more likely to pick a Nazi, it still pretty unlikely. This is because the overall number of Nazis is quite low. For example, let us say the probability of finding a Nazi, given that they own Mein Kampf, is 0.01%, whereas the probability of finding a Nazi, given that they do not own Mein Kampf is 0.001%.

So yes, I think it is more likely that Michael Gove holds these controversial views than people who do not own these books, but overall pretty unlikely that he does hold these views. Whatever my views are on Michael Gove as a politician, I tend not to think the worst in people in these sorts of situation. This is because as I was told never to judge a book by its cover (unless it’s a book about Beysian inference).

*I say ONE reason to go to university here, as I think it is important (especially as an economist) to say there are many reasons to go to university then just employability.
**It could be the case the owning a copy of Mein Kampf makes a random person less likely to be a Nazi if we believe many Nazi’s don’t actually read that many books.

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