On the whole, it seems clear that the Russian dictator has fallen into a rut of constant losses. Now he is inevitably forced to become a tyrant, because to maintain at least a short-term perspective, he has to intensively tighten political decisions both against the population and against “unfriendly” states. Otherwise, the end will come not “tomorrow,” but “today. The “day after tomorrow” is out of the question.

The rational behavior of a dictator becoming a tyrant, under conditions of sharply increased risks for him and the virtual absence of a good scenario, is to create maximum uncertainty for everyone: to hypertrophy threats and make extreme decisions. With each new round of escalating tension and with each new failure, the dictator needs to escalate even further, hoping to realize the decreasing probability of success and the increasing importance of that success for him.

In fact, this is quite simply explained by different models of rational and boundedly rational behavior: the dynamics of the benefit-cost ratio under the influence of the relevant factors.

The Martingale strategy is very appropriate, in this case, to describe the incentives and decisions of a losing dictator. In essence and very simplified, it consists of the following: with each new loss, the player must increase the bet by the cumulative value of all losses. The option is to add to such a bet the value of the desired winnings.

The Martingale strategy has some very important nuances that are important for a player. First, losses and weight of the next bet are doubled with each new iteration. That is, losses grow almost exponentially. This means that if the stakes are large at once, the player has a limited number of iterations relative to his bank. Secondly, the number of iterations can be limited from the outside, for example casinos often limit the maximum bet size, which means the player cannot endlessly search for a winning probability realization. Thirdly, the player’s bank is limited, and as losses increase and bets increase, the player’s desires may override common sense and distort the rationality of the next betting decision. And fourth, an extremely important cumulative factor in decisions is a variety of real-life conditions, circumstances, and player motivations not directly related to the game, but ultimately significantly affecting its outcome.

Expected utility theory, when applied to explanations of the losing dictator’s actions, can also be a quite solid basis for explaining the dictator’s decisions, actual and potential. Expected utility theory explains decisions based on the risk/reward ratio, depending on the various conditions and factors that determine probabilities. Such explanations are based on the simple mathematical expectation of a potential choice, which is the sum of the products of probability-outcome pairs.

For example, a player has $100. He can bet $50 at odds of 1 and have a 50% probability of winning. If he wins, the player will win $50 and his pot will end up equal to $150: $50 bet, $50 left in his hands and $50 won. That is, the player’s capital increases by a third. If the player loses, the player will lose $50 and the pot will be equal to $50. Then the player’s capital will be halved

The mathematical expectation in this case is obviously as follows:

(50 * 0,5) + (-50 * 0,5) = 0.

Then what will be the expected utility? Expected utility is a subjective assessment of possible outcomes – obviously will be different. However, this subjective assessment has several objective determinants. First, it is the rule of diminishing marginal utility: with each new unit, total utility – the availability of something – increases, while marginal utility – value – decreases. Second, people value more what they already own than what may be greater or more valuable, but does not yet belong to them. Third, people generally tend to take less risk and less benefit as opposed to more risk and more benefit. That is, they are willing to prefer a lower expectation if it carries less risk. In other words, for most people, the maximum benefit is the one that carries the minimum risk, rather than the maximum expectation.

This is the main difference between expectancy-a linear utility that maximizes with increasing expectation-and expected utility-a subjective value that increases with decreasing risk.

In the mathematical representation, unlike the expectation formula, the outcome is quantified not in absolute terms, such as money, but in relative units, comparable between all options involved and having value depending on subjective value.

In the above example, the feeling of losing will be stronger than the feeling of winning.

Then mathematically, taking into account the evaluations of capital increase or decrease, as well as the mentioned determinants and possible non-systemic factors, the expected utility can be presented as

(1 * 0,5 ) + (-2 * 0,5) = -1.

That is, the expected utility of the decision to bet $50 with odds of 1 and a probability of winning 50% for a normal person will be negative and he will most likely decide not to bet.

The question of probability, like the question of the expected utility of each choice, does not usually have an unambiguous linear solution. Probabilities can be objective and subjective. They can be presented more or less simply, for example, as the coefficient of the number of positive outcomes to the total number of outcomes, and can be seen as a subjective belief in the occurrence of one or another outcome.

In general, we can say that the expectation includes directly and quantitatively defined options of outcomes and objectively defined probabilities of occurrence of each of them. Expected utility quantifies each outcome as a subjective value, and probability – as the power of belief in the occurrence of each of them.

For example, you have an opportunity to win $1,000 in the lottery with a probability of 10% and, correspondingly, with a probability of 90% of not winning anything. And the probability and outcome in monetary terms are predetermined by the lottery system. Then the expectation is

(1000 * 0,1) + (0 * 0,9) = 100.

That is, if a lottery ticket costs $100, it makes rational sense to play, but if it costs $101, it doesn’t.

7. Given all of the above, the rule of rational behavior is evident, which can be represented as follows:

Risk = Reward * Probability

Accordingly, the lower the probability, the less risk you should take. If my probability of winning $1,000 is only 20 percent, then I cannot risk more than $200, because

1000 * 0,2=200

If my probability of winning is 75 percent, then it is rational to risk $750.

However, based on the rule of expected utility, individuals, under conditions of incomplete information, choose to take less risk in order to preserve the largest portion of their assets. If you ask the average individual to bet $750 to win $1,000 with a high probability of 75 percent, or to bet only $100 for the same win, but with a probability of only 10 percent, the individual will choose $100. This is the axiomatics of the Kahneman-Twersky Prospect Theory. I will not consider here additional factors affecting decisions, such as the effect of a pitch, etc., where the way the condition is posed determines the individual’s choice. My main focus is on the most important postulate – under conditions of uncertainty and incomplete information, the individual chooses less risk and less reward.

What did the Russian dictator do wrong and what was his mistake? He stopped estimating probabilities adequately. Accordingly, mispriced probabilities entail mispriced stakes, i.e., taking risks in the hope of a certain reward. Mispricing of probabilities is characteristic of tightening autocracies, since the absence of free channels of social communication, competition, and unbiased analysis makes it impossible to make decisions that aspire to objectivity.

In the above rule, it is important to understand that a wrongly estimated variable leads to a distortion of the entire outcome. By overestimating the probabilities, you naturally have to increase the risks, and if you subsequently lose, you need to increase the risks further, to compensate for the loss, according to Martingale.

By demanding a too large reward, you are forced to either convince yourself of the greater probability of its occurrence and increase the risks or simply increase the risks, so to speak, by praying. Thus, you are forced to choose the paradigm of Martingale action, because you have no more options to choose a lower risk with a lower reward – a lower reward can’t compensate for losses.

For the dictator becoming a tyrant, the reward is now always a compensation for losses, that is, you must do everything to maintain your own status quo, and this is only possible by increasing the stakes – that is, by tightening and escalating against everything and everyone. The expected utility – the subjective value – of each outcome for the tyrant now inevitably increases, and the risks increase accordingly, with obviously decreasing probabilities. Any reduction in the stakes, i.e., the risks, will mean a reduction in the reward, i.e., the prolongation of his life – literally and figuratively, politically.

A rut is a rigidly limited trajectory for maneuvering, where all the actions of the subject moving within it are mediated not by his will, but by the limitations and direction of the rut. All but one: one-step self-destruction. But to count on this is to overestimate the probabilities.

Let us not exaggerate the probabilities, let us not resemble dictators.