An Allegory of Folly: Quentin Matsys (16th century).

On Cipolla’s Laws of Stupidity
(Rodrigo Peñaloza, May 1st, 2017)

Carlo Cipolla, professor of economic history at the University of California, Berkeley, published in 1976 an interesting essay outlining the “fundamental laws of a force he perceived as humanity’s greatest existential threat: Stupidity”. The laws he drew are:

LAW 1: Always and inevitably everyone underestimates the number of stupid individuals in circulation.
LAW 2: The probability that a certain person be stupid is independent of any other characteristic of that person.
LAW 3: A stupid person is a person who causes losses to another person or to a group of persons while himself deriving no gain and even possibly incurring losses.
LAW 4: Non-stupid people always underestimate the damaging power of stupid individuals. In particular non-stupid people constantly forget that at all times and places and under any circumstances to deal and/or associate with stupid people always turns out to be a costly mistake.
LAW 5: A stupid person is the most dangerous type of person.

Click here to read the original. I gave some thought to it and came to the following conclusions.

First of all, notice that laws 1 and 2 and the second part of law 4 are the only ones which really characterize stupidity in the probabilistic sense. I mean, they tell us about the probability of meeting stupidity. Laws 3 and 5 and the first part of law 4 characterize the effects of stupidity on humanity.

Secondly, let us consider an arbitrary person who is not stupid. For the sake of reference, let us call him Perspicax. I want to find out how Perspicax would act. If Perspicax is not stupid, then he knows the Laws of Stupidity. Suppose the world is made of 100 people. Assume that a percentage p% of the people is stupid, so a fraction (1-p)% is not, Perspicax among them. By Law 1, Perspicax underestimates the number of stupid individuals in circulation. If he knows Law 1, then he knows that the percentage of stupid people is greater than p%, whatever the percentage p% he has ever observed before. Therefore, p% must be 100%. Otherwise Law 1 is contradicted. What does it mean? It means that stupidity is uniformly distributed over all humanity. We are not allowed to say that only a fraction p% of Humanity is stupid, as if Humankind were divided into two distinct groups: stupid and non-stupid. All we can say is that any person, even Perspicax, can be stupid with a probability of p%. However, if Law 1 is true, then Perspicax does not apply to himself the reasoning he applied to others, as I wrote above. How is that possible? The only explanation is that Perspicax is unable to engage into interactive epistemic introspection, a game-theoretical concept that describes the fact that intelligent people like Perspicax accede that others are able to reason in the very same way they do. If Perspicax fails to accede to it, then he is not intelligent. He recognizes that everybody is stupid, including himself, but he does not recognize that he himself can eventually be stupid. This is not a contradiction in terms. It is only a contradiction insofar as we assume that Perspicax doesn’t reason epistemically as Game Theory prescribes. In any case, it contradicts the intelligence of Perspicax.

In the third place, Law 2 is nothing but a corroboration of what I concluded from Law 1. It says that the probability of being stupid is independent of any characteristic of the person, but stupidity itself. Indeed, it says that stupidity is an idiosyncratic random shock on any person, not on the whole population. In fact, it is not true that humankind is divided into two separate groups: stupid and non-stupid. The truth is, any person can be stupid with a probability p%.

Now we come to the second part of Law 4. It says that non-stupid people constantly forget that dealing and/or associating with stupid people is always a costly mistake. What is the meaning of this law? As I put it, it is a justification for Law 1, or equivalently for Law 2. It explains why Perspicax is not intelligent, that is, why he does not apply to himself the very same reasoning he applies to others: it is because he constantly forgets about it. By “constantly forgeting” I understand that whenever Perspicax acts stupid, he simply does not realize it. Law 4 says that this always happens. In other words, we are never stupid on purpose. If Perspicax knew he were acting stupid, then he would not act stupid. If he does act thus, then it was because he didn’t know about it.

Therefore, Laws 1, 2, and the second part of Law 4 say that non-stupidity is intermittent. Equivalently, stupidity is necessarily intermittent. In other words, we are all like Perspicax, but we are like him only part of the time. The other part we are stupid. When we are not stupid, we know we are not. But when we are, we don’t know we are. There is, however, a problem. When we know we are not stupid, this implies we are not intelligent, because while we know we are not acting stupid, we still doesn’t know we can eventually act stupid with probability p%!

Let us consider now the first part of Law 4, according to which “non-stupid people always underestimate the damaging power of stupid individuals”. How does Perspicax reason? Take any positive small number ε>0. Since Perspicax knows Law 4, he knows that he underestimates the damaging power of stupidity. In other words, he knows that there are acts that must be taken as stupid, but that were not thus taken for the estimation of stupidity, say the small probability ε, for any given ε. Therefore, he knows that the probability p% of acting stupid is greater than ε, for any ε. This will imply that the probability of acting stupid is 100%. However, it suffices, for our purposes, to recognize that p% is a constant positive number. Indeed, even if Perspicax knows Law 4, he is subject to Law 4 by his very knowing it. Since he is not intelligent, it maight happen that he cannot keep reasoning to come to the conclusion that the probability of stupidity is 100%. He has to stop somewhere in this chain of reasoning (bounded rationality). He might come to the 100% figure as well. It doesn’t matter for what follows from it. The problem is, Perspicax now knows that everybody else in the world acts stupid with a constant positive probability, while he himself acts only p% of the time, though unable to say more about p, because he cannot apply the same reasong to himself. This p% is 100% but it only matters that is is constant and positive. Remember Perspicax, by Law 1, is not intelligent. Since this applies to everybody in the world, then everybody thinks that everybody else is stupid with a constant positive probability.

In sum, stupidity as it accrues to any person, from the point of view of Perspicax, is a sequence of independent events with positive probability (actually probability 1, though it doesn’t matter). By the Second Borel-Cantelli Lemma, stupidity will always occur again in the future with probability one (this is given by the probability of the limsup of the sequence of independent random events). Therefore, Laws 1, 2, and the second part of law 4 imply that anybody in the world will be stupid again some time in the future. In addition, we all know this when we are not stupid, but this doesn’t help, because we WILL act stupid again.

The remaining laws are independent of the laws I analized above. Laws 3, 5, and the first part of Law 4 only say that the damages of stupidity are always bigger than we think. Stupidity has always an element of unexpectation, of surprise, something we haven’t thought of before, and about not-ever-having-thought-of-before we haven’t ever thought of before.

What are the consequences of Cipolla’s Laws of Stupidity on the laws themselves? If we agree to Cipolla’s laws, our agreement will be valid only when we are not stupid. Somehow they will not help us avoiding stupidity. What is their purpose then? You may find the Laws of Stupidity stupid. You may find me stupid for thinking about stupidity. If you don’t agree with it now, you will agree with it sooner or later, but then you will disagree afterwards again, as you disagree now. The fact is, the Laws of Stupidity are not new. They are as old as Humankind itself, a perennial warning about our essence. It certainly throws a hard truth on our faces: HOMO SUM, HUMANI NIHIL A ME ALIENUM PUTO, as Publius Terentius Afro, Roman writer (c. 190–159 a.C), once wrote in his Heauton Timorumenos (Ἐαυτον τιμωρούμενος).