Do neurotypes ever want to be psychopaths
Kelly Criterion, which is followed by psychopaths?
I don't know whether or not psychopaths adhere to the Kelly Criterion. From a technical point of view, the Kelly criterion for a perfectly informed agent who wants to take advantage of an objectified, winning yet risky position again sets the maximum stake that would make bets irrational. In the sense that betting more than the Kelly Criterion would put a strain on your finances by exposing yourself to too high a risk.
Imagine knowing that a tossed coin lands on its head 49% of the time and its tail 51% of the time. For $ 1 you wager, you will earn $ 0 or $ 2, depending on the outcome of the coin toss.
Betting on heads is irrational. So you bet on tails. The question is: "What percentage of your total assets would you like to wager?" If you wager 0% of your wealth, you will never earn anything. If you wager 100% of your fortune, you have a 49% chance of going broke in the next round and not wagering anything, which is kind of stupid as you have a rational structural advantage over the bookmaker.
So the question is, "What part of my wealth should I use to maximize return in terms of risk?" The answer depends on what is called your "utility function". In the case where every dollar won increases your utility linearly (i.e. you are just as eager to win a dollar whether you are broke or a billionaire, to put it simply ... a dollar is a dollar no matter what ), the Kelly criterion applies:
You set the fraction that maximizes the probability expectation of the logarithm of the ratio of assets after the bet to assets before the bet. When I remember well things that fell on my head.
Betting less than Kelly is not greedy enough. Betting more than Kelly is self-defeating. That's the theory.
The Kelly criterion has been used in the financial stockbroking business in the past ... almost. They divided the Kelly criterion by 2 to be on the safe side. The reason is simple: no matter how rational Kelly is, under perfect circumstances plot the typical fluctuations in your wealth using the Kelly criterion (even correcting your utility function). Take a close look at it. Then you will find that there is such a bumpy ride for your fortune that the Russian mountains will feel like zen meditation on cocaine. Technically, betting with Kelly is right on the verge of self-destruction ...
Nobody would ever "reasonably" wager their fortune with Kelly. Unless you have a number theorist's self-denial about ketamine. No joke.
Not even a psychopath.
The closer you can get to the question, the better: (1) Psychopaths are rational machines by nature. (2) Psychopaths are extremely greedy that a buck is a buck, whether they are broke or a billionaire, and (3) they are able to endure the cognitive dissonance by being (1) and (2) assertive and aggressive be reconciled without any fear.
I doubt it will. While they can score higher than the neurotypists, it is quite difficult to imagine that a psychopath would spontaneously follow the Kelly Criterion if the greediest stockbrokers didn't dare. According to your study, they can score higher on points (2) and (3).
Kelly does not apply in this study and does not set a stop-loss criterion. It simply shows that psychopaths are either less emotional or have a more linear utility than neurotypes. An anxious neurotype can stop playing if they have had repeated bad luck. A rational and fearful neurotype would have set his stop losses in advance based on what round he is in and played all rounds to the point where he would definitely have stopped playing: he knows it doesn't make any sense to postpone his luck. And he must be quite anxious about choosing to stop gambling, which means that his utility function must be very concave near ruin to trigger a stop loss and very insensitive to wealth if he chooses to trigger a stop loss at the beginning of the game. In short, rationality in the game is defined by playing all the rounds in the game to a point where you stop playing. If the player plays, then stops, and then keeps playing, he is irrational. But the more he plays, the less worried he is. From what I read about the article, psychopaths are not more rational, they are less fearful. Kelly has little to do here.
Another question you might ask is whether neurotypists and psychopaths end up behaving the same way cohorts do the longer they play the game. How insensitive to the irrationality of human conditioning towards play become, the more and at what speed they are exposed to play. For me, maybe that's the real question.
Furthermore, ruin theory as developed in actuarial science is NOT a Kelly criterion. It is a standard stochastic calculus with ruins constraints. Kelly criterion is the naive implementation of the stochastic calculus by the poor man. Much like mysticism is the poor man's naive first attempt at science.
Incidentally, the Kelly strategy cannot ruin, not because it is Kelly, but because it is a self-funded strategy, which in itself is a broad class of strategies, including very, very stupid ones.
I hope that clears the scope of the question.
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