The other day before Trump closed the borders, I was at the store buying a bit of extra food. My area has yet to be hit by the spread of the corona virus. It is however right on our doorstep. So I was being a bit safe just in case we can’t leave our homes for a little bit in the coming weeks. The situation got worse the following day as people reacted to the border closings. Then they closed down the local schools. As this is going on, the grocery store becomes packed with people buying up supplies. Soon there is a shortage of various important items, such as toilet paper.
If people would just buy a normal or slightly increased quantity of supplies, then the shortage would not exist. However the anticipation of a shortage, leads people to hoard supplies, which causes the shortage. This is one of the emergent behaviors where apparently irrational outcomes can creep into even rational actions. To understand how this happens we need to look at beauty contests.
The great economist Keynes, a pioneer of macro-economic thought, wanted us to think about voting in a beauty contest. People will look at the contestants and cast a vote based on whom they think is the most beautiful. This is pretty straight forward and we can get a good idea of the consensus choice.
Now, I want to introduce a new rule here. Suppose that there is now a prize for voting for the most popular choice. This has radical implications on how the voting will go. People will now try to guess how others will vote. This has a kind of recursive logic on the research. I will propose an example beauty contest to help us think here.
Here are a few contestants: Natalie, Aydin, and Kaitlin. Suppose we ask people who they think is the most beautiful, without a reward:
Now, the issue is that Natalie’s fans are much more rabid. Many people wrongly perceive that Natalie would win the contest. Often people at large can make incorrect guesses about the outcome of some event. There is often a distortion of the available information or ignoring of crucial bits of information. If people were asked who they think would win the most votes:
The crucial thing to note here is that when we incentivize correct guessing, this perception becomes relevant. If people think that Natalie will win and thus make money, they will change their vote to Natalie. Now, let us look at the people who correctly guess Kaitlyn would win. They are now losing as public perception was initially incorrect. This however has a recursive effect. It is not merely the perception of who is most beautiful. It is the perception of who is perceived to be most beautiful. And so on. The best guess will be an infinite chain of perceptions on perception.
Knowing that people think Natalie would win even if she wouldn’t win will lead even the rational and informed to vote for her. Irrational and ignorant beliefs can alter the rational choice. This is how Keynes attempts to present how perception alters outcomes. Economics is about trying to isolate and model human action. Sometimes human action is hard to explain by purely rational factors. People are often misinformed and act in contradiction to evidence. One way to explain this is to assume people like ignorance and irrationality.
Buying and hoarding toilet paper is a fun activity. You can take a lot of cool selfies to post on social media. You see yourself feeling like a genius when your friends are out searching in vain for toilet paper and you have a closet full of the stuff. Maybe that woman you fantasize about will message you on facebook and ask you for some of your toilet paper stash. Then something might happen? There are all sorts of cool fantasies you can spin up which will make you feel great.
When Keynes developed this thought experiment, he imagined this as helping explain why stock market bubbles occurred despite evidence that they were overvalued. It doesn’t matter if they are overvalued necessarily. As long as people think they are correctly or undervalued. This probably can’t continue on forever. I mean even the most ignorant and irrational people at some point might start to wake up if the stakes are raised. This is the difference between saying you can fly and actually jumping off a building to prove it. When the stakes are too high and people stop acting irrational, then we can get a crash.
One way to look at this while preserving a more classical view of rationality; There is an asymmetry in the choices. I would like to present a controversial anecdote, Jeffery Epstein. Now some people argue, in my opinion correctly, that Epstein probably killed himself. It is a good possibility he was murdered, but not definitive. The reason that you should focus on the idea that Epstein was murdered is because of the magnitude of impact. So what if he killed himself, it is likely, but it does not have wide socio-political implications. However there is a decent chance he was murdered and there is so much potential there for a deep conspiracy. 😉
Bringing it back to toilet paper. If you think there is a small percentage chance of running out of toilet paper, then you might want to stock up. Running out of toilet paper is a really regrettable outcome. This then leads people to rationally stocking up on extra toilet paper. As people realize it is rational to stock up on more toilet paper, it makes the possibility of running out of toilet paper more possible. Thus the recursive thinking takes place and people all run to the store to buy as much toilet paper as possible.
In order to explain this variant of panics, people invented something called a p-beauty contest. It is a variant of the Keynesian beauty contest. Basically you choose a number p between 0 and 1. You ask people to pick a number between 0 and 100. The closest you can get to the average multiplied by p, the more money you get.
For example, we assume p = ⅔; Then we ask a group of people to pick a number between 0 and 100; Remember you get more money the closer you get to two thirds of the average. You are rewarded for guessing much lower than everyone else. If everyone realizes this and acts on it, then it will drag the average down to the lowest possible value. If everyone acted rationally, they would drag the average down to zero.
This may or may not be good. This is just an abstract model. However, in many cases zero can be the collapse of society. In the panic, you are always incentivized in beating out the crowd. This however allows the crowd to emerge immediately and rapidly overwhelm the situation. Run on the banks, shortages, market bubbles; Also the object of discussion, hoarding toilet paper.