mukashi

A very well known puzzle in probabilities says: Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys? There is much discussion about this puzzle because depending on how you find out that one of the kids is a boy, the probability changes. I understand this, but this is not what I wanted to discuss. If you want to know more about this, you can read this Wikipedia page. What I wanted to discuss is that for me to give the answer that I am expected, I need to be aware that the person posing the question is expecting me to write a tree with all the possible combinations etc. The tacit assumption about the problem is that it is a puzzle, i.e a problem of a small world with very clear rules. There are many puzzles such as this one that are used to illustrate things such as: humans behave irrationally, humans are very bad at judging probabilities, humans lack a basic understanding of the most fundamentals concepts in economics, etc. I feel that many of these puzzles rush too quickly into those conclusions and we should always treat them with a pinch of salt. The world is not a small world A small world is an artificial environment created with well-defined rules and probabilities. Usually, small worlds are inhabited by agents that are uniform (meaning that all of them behave the same under the same circumstances), have perfect knowledge, lack any feelings and are perfect reasoners; if the problem has a solution (in their small world environment) they will reach the solution. We don't live in a small world. We don't live in a world where most problems can be assigned a clear probability such as the ones you can compute when flipping a coin. Why is this relevant? In the last two hundred years, a large part of economic thinking, now considered to be the orthodoxy, has used simplified models of the world to understand the complex system of economics. In these models, every agent of the system has perfect infor