# Probability, Information and Economics

These days I was busy reading the biography of John Maynard Keynes, the most famous economist in the past century. One point mentioned in that book attracted my attention -- that is about his ideas on probability.

Every one who has studied macroeconomics must know a word "rational expectations". That is a great issue if talked. Simply, as the wikipedia says,

To assume rational expectations is to assume that agents' expectations are wrong at every one instance, but correct on average over long time periods. In other words, although the future is not fully predictable, agents' expectations are assumed not to be systematically biased and use all relevant information in forming expectations of economic variables.

HereĀ  I do not want to say much about it. I'd like to mention another area, Information Economics. Typically, information economics deals with the situation that there is asymmetric information between principal and agent. Then as we all know, there is moral hazard and adverse selection. With the application of game theory, the common issues can be solved. However, seldom do I read paper discussing about the role of information in economic activities in other approaches. Therefore, followed Keynes' idea, I wonder what will happen if the spread of information is introduced into the economic activities.

Simply, probability reflects the situation that we do not know enough about how the real world functions. Therefore, we use probability to describe the combination every possible result. There is an interesting question: the normal distribution. I'll talk about it later on.

As the aim of science, we are pursuing the ability to predict. I know many people will have different ideas, but it does not matter much. At least, we want to know the mechanisms in every particular field. That is, we are pursuing "certainty" instead of "uncertainty". From uncertainty to probability, then to certainty, in this way we know much better about the real world. It is an old philosophic issue: is there a fixed point?

Then what will happen if the knowledge spreads? I have not got a clear understanding yet. The disappearance of probability is too hard to imagine. We can use "normal distribution" to describe some phenomenons, such as people's height, weight. The result is a description of a group, but not that accurate for a particular person. To predict a person's height, for example, we should get enough information, if applicable, his gene, his nutrition, and what he did in the past... Maybe it is too hard to define what is "enough". Anyway, the probability can be replaced under a special circumstance.

In the first step, I want to talk about how the spread of information influences the social activities. I think we have underestimated the importance of information in economics, or we have no applicable models to explain. I do not know whether more modern mathematical tools are needed in the explanations. As least, I need to read more about the history of probability, including the famous debate between frequency school and Bayesian. And maybe more knowledge about psychology and communication are essential. I want to talk about it later after learning measure theory.