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Subjective probability (like the opinion that the tomorrow rain is of 86%) is known for its "elusive" character defying formal mathematical consideration, unlike the "real" probability theory's probabilities. I however found a way to define them mathematically.

I definitely have found a way to formalize what is subjective probability. Contrary to academic pride, subjective probability can be defined by following a red-neckers' saying "it is how much you are ready to pay for it, bro". This, having fixed a formal market gives rise of two numbers: the maximum price one is going to pay in a bet of for this probability and the minimum price one would not agree to pay. Through these numbers we can define subjective probability. This has some complexities like dealing with too small sums for one to consider and the case when risk outweights even a big sum of money, but I am confident I have ideas of all math (of infinitesimals and of infinitely big amounts) needed for this, because I have formal training in mathematical analysis specialization.

I want to spend a month thinking (and, of course, writing my thoughts down for publication in peer review) about subjective probabilities. I will try to answer such questions, as how to unify two above subjective probabilities (one minimum and one maximum), do subjective probabilities match the definition of probability?, what may be an analogue(s) of Bayesian inference for subjective probabilities, why it is considered that the probability should be set to 1/2, if we know nothing about the outcome, etc.

Among subjective probabilities, I also consider other subjective quantities, such as subjective market value predictions. Also the entire market can be considered as one player, producing interesting results for such applications as legal theory (what is to blame the market?) and of course economy.

The goal is to describe most important properties of subjective probabilities. An additional goal is me to learn advanced game theory, while thinking how to apply it to subjective probabilities or apply subjective probabilities to game theory.

Following the John Nash's game theory, there were several random people's decisions that prevented nuclear war, not founded in any science. My theory aims to (partly) formalize such people's decisions to prevent nuclear war and it may lead to prevention of a nuclear war in the future.

My salary for a month.

Only me.

I wrote thick book Algebraic Theory of General Topology (+yet hundreds unpublished pages) consisting mainly of new mathematics. So, I have very strong experience in discovering new math.

The project may mostly fail if I will flow out of ideas. But writing down the ideas that I already have in mind definitely makes a positive (and in principle publishable in peer review) outcome of the project.

None.