As this study shows, psychopaths are much more willing to take advantage of expected gains despite recent losses as opposed to normal people who frequently stop after a series of losses.

Has there been any follow up to this to observe whether psychopaths also take the Kelly Criterion into account? The participation rate was still only 84% for the psychopath group. I didn't see any data that shows whether those that stopped participating were ones whose amount of money in immediate control declined to nothing or near-nothing. If those who lost stopped at some point relative to the amount of money in their immediate control instead of a bad run regardless of money in immediate control, it might indicate that psychopaths are acting more rational than normal because they quit when the Kelly Criterion is being violated, that they quit positive expected values when their "risk of ruin" is greater than ~0%.

Do psychopaths care about the so-called "risk of ruin"?

Kelly Criterion

The math behind the Kelly Criterion was actually originally developed by John L. Kelly, Jr. to maximize data transfer rates relative to risk of data loss due to noisy (error prone) lines. Taking into account those two factors, the amount of data to transfer, the possible loss, and the possible success, choices of which lines to use at which times and amounts of data relative to noise can be quantitatively made to more or less maximize the total expected data transfer rate with an almost certain chance of no loss over time.

Later, Edward O. Thorpe, the first to prove that blackjack can be beat by counting cards, discovered that the Kelly Criterion can be employed to maximize returns from card counting with an almost certain chance of no loss over time (now called the "risk of ruin") when "bankroll" (total amount available for gambling), risk of a single or series of gambles, cost of the single/series of gambles, and payoff of the single/series of gambles are all taken into account.

A formula was also derived to give a risk of total loss, "risk of ruin", from a collection of potential investment choices. When the Kelly Criterion can be strictly adhered to, the risk of ruin is always ~0%.

  • $\begingroup$ it would be helpful to define the Kelly Criterion $\endgroup$ – Krysta Aug 22 '13 at 14:05
  • $\begingroup$ @Krysta plz note edit $\endgroup$ – user2475 Aug 22 '13 at 19:48

I do not know about psychopaths adhering to the Kelly criterion or not. Technically, for a perfectly informed agent seeking to take advantage reccuringly from an objectified winning yet risky position, the Kelly criterion sets the maximum bet amount over which betting would be irrational. In the sense that betting more than the Kelly criterion would deplete your finances by exposing yourself to too much risk.

Imagine that you know that a tossed coin ends up 49% of the time on heads and 51% of the time on tails. For 1 buck you bet, you earn 0 or 2 bucks depending on the outcome of the coin toss.

Betting on heads is irrational. So you bet on tails. The question is "what proportion of your total assets" are you willing to bet? If you bet 0% of your assets, you never earn anything. If you bet 100% of your assets, you've got 49% chances of being broke the next round and having nothing left to bet again, which is kind of stupid since you've got a rational structural advantage on the bookmaker.

The question therefore becomes "what fraction of my assets should I bet to maximise the gain with respect to the risk"? The answer depends on your so called "utility function". In the case where each buck gained increases your utility linearly, (i.e. you're as eager to gain a buck whether you're broke or a bilionaire, to put it simply... a buck is a buck no matter what), the Kelly criterion applies:

You bet the the fraction that maximises the probabilistic expectation of the logarithm of the ratio of assets after the bet to assets before the bet. If I recall things well off the top of my head.

Betting less than Kelly is not greedy enough. Betting more than Kelly is self-destructive. That's the theory.

In the financial stock broking business, the Kelly criterion has been used 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, draw up a chart of the typical fluctuation of your assets using the Kelly criterion under perfect circumstances (even correcting for your utility function). Take a close look at it. Then you'll realise that you'll be in for such a bumpy ride for your assets that russian mountains on cocaine will feel like zen meditation. Technically, betting using Kelly is exactly being on the verge of self-destructiveness...

No one, ever ever ever ever would "reasonably" bet their assets using Kelly. Unless you have the self-denegation of a number theorist on ketamine. Not joking.

Not even a psychopath.

The closer you can get to the question would be: (1) are psychopaths inherently rational machines (2) are psychopaths greedy to the extreme that a buck is a buck whether they're broke or a billionaire, and (3) are they able to endure the cognitive dissonance by reconciling (1) and (2) assertively and agressively without fear of any sort.

I doubt this to be the case. They may well score higher than neurotypics, but it's quite a stretch to imagine a psychopath would spontaneously follow Kelly criterion when the greediest stock brokers would not dare to. According to your study, they may well score higher on points (2) and (3).

In this study, Kelly does not apply and does not determine a stop loss criterion. It simply shows psychopaths are either less emotional or have a more linear utility function than neurotypics. A fearful neurotypic may stop playing if he has had repeated bad luck. A rational and fearful neurotypic would have laid out beforehand his stop losses depending on which turn he's in and would have played all turns up to the point where he would have stopped playing definitely: he knows there's no point in postponing his luck. And he must be rather fearful to decide to stop playing, meaning that his utility function must be very concave near ruin to trigger a stop loss and very insensitive to wealth if he decides to trigger a stop loss early in the game. In a nutshell, rationality in the game is defined by playing all turns in the game up to a point where you stop playing. If the player plays, then stops, then resumes playing, he's irrational. But the more he plays, the less he's anxious. From what I've read of the article, psychopaths are not more rational, they are less fearful. Kelly has little to do here.

Another question you may ask is whether or not neurotypics and psychopaths end up behaving the same way as cohorts the longer they play at the betting game. How desensitised to the irrationality of the human conditioning to the game do neurotypics and psychopaths become the more they're exposed to it, and at what pace. To me that's perhaps the real question.

Moreover ruin theory such as developped in actuarial science is NOT Kelly criterion. It's standard stochastic calculus with ruin constraints. Kelly criterion is the poor man's naive implementation of stochastic calculus. Very much the same way that mysticism is the poor man's naive first attempt at science.

By the way, Kelly strategy cannot go to ruin, not because it's Kelly, but because it's a self-funded strategy, which in itself is a broad class of strategies, that includes very very stupid ones.

I hope that clarifies the scope of the question.

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    $\begingroup$ Hi FDIA, thank you for the very extensive answer. I was wondering, however, do you have any references to back up some of your statements? For example about the comparison between Ruin en Kelly theory. $\endgroup$ – Robin Kramer May 12 '17 at 15:10
  • $\begingroup$ Ruin theory is mostly concerned about when does a strategy go to ruin in the face of probabilistic adverse events. Typical questions are: what insurance premiums will guarantee that the insurance will theoretically always face its liabilities. On the other hand, the Kelly criterion defines a fraction of your assets that you bet at each turn. So you've got remaining assets for the next bet which you'll fraction again using Kelly criterion. You may deplete your finances, but you're never technically broke. $\endgroup$ – FDIA May 12 '17 at 15:38

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