Is homo economicus rational?

Nicolás Bernoulli

In 1713, Nicolás Bernoulli formulated the St. Petersburg paradox, which can be summarized as follows:

Let us consider the following game: a coin is tossed. If it comes up heads, you receive $2. If it comes up tails, it is tossed again. If it comes up heads, you receive $4. If it comes up tails, it is tossed again. And so on. With each toss, the prize is multiplied by 2. How much would you be willing to pay to participate in the game?

The probability of winning $2 is 0.5; the probability of winning $4 is 0.25; the probability of winning $2^k is 2^-k. The expected value is obtained by multiplying each value by its probability and adding them all together. So the expected value of the profit that could be obtained by playing that game is:

The Chinese and artificial intelligence

Wolfgang von Goethe

The media has been reporting on a recent breakthrough in LLMs (large language models), the hottest applications in the field of artificial intelligence, which in the last two years have given rise to great hype, suspicions of stagnation and accusations of excessive energy and water costs.

This latest breakthrough has been achieved by a Chinese company, DeepSeek, which has jumped to the front line because it successfully competes with the big companies in the field, OpenAI (which built ChatGPT and GPT4) and Google (with GEMINI), but at a lower cost.

There are now many tools of this type, but the two mentioned in the previous paragraph (GEMINI and GPT4) provided the best performance, although they were the most expensive. Their code is secret, owned by the two companies (Google and OpenAI) and users cannot modify it. Alongside them, now there are others with open source, which can be adapted to each user, but with lesser performance.

Anything can be assigned a probability?

In the previous post I mentioned the book Radical Uncertainty: Decision Making Beyond the Numbers by Mervyn King and John Kay. The book, written by two prestigious British economists, attacks the bad use of statistics and probability calculus in fields where they are not always applicable, such as history, economics and the law. Let’s look at a few examples:

• What do we mean when we say that Liverpool F.C. has a 90% chance of winning the next match? One possible interpretation is that if the match were to be played a hundred times, with the same players and the same weather conditions and the same referee, Liverpool would win 90 times, and draw or lose the other ten. But the match will be played just once. Does it make sense to talk about probabilities? No, because there are no supporting data on frequency. What is meant is that the person speaking believes that Liverpool will win. Nothing more. It is a subjective probability. Milton Friedman wrote: We can treat people as if they assigned numerical probabilities to every conceivable event. (Price Theory, 1962).

Risk versus Uncertainty

I have read the book Radical Uncertainty: Decision Making Beyond the Numbers by Mervyn King & John Kay. As the title suggests, it talks about radical uncertainty. What is uncertainty? Its definition is simple: any uncertain knowledge. But there are two types of uncertainty:

·         Risk: Measurable or resolvable uncertainty. Probability calculations can be applied. Example: the outcome of a roulette or lottery game. Problems of this type can be called puzzles. Phenomena of this type are stationary (their properties do not change over time).

·         Radical uncertainty: Uncertainty that is not measurable. It arises when there is obscurity, ignorance, vagueness, ambiguity, ill-defined problems, lack of information. It cannot be described by probability calculations. Problems of this type can be called mysteries. Phenomena of this type are usually not stationary.