קאווע שטיבל

שאלתיאל האט געשריבן:@מי אני איז בהעוויערעל עקאנאמיקס פעלד א סתירה צו געים טעאריע?
געים טעאריע גייט ארויס בהנחה אז דער מענטש איז נעטא-ראצינאליסט און ארבעט אך ורק נאר פאר די ריינע בענעפיטס אבער למעשה איז עס דאך נישט פונקט אזוי אין מציאות וכדמצינו במחקריהם פון כהאנמאן און טווערסקי.

The archetypal co‑operation game is the Prisoner’s Dilemma. Imagine that two prisoners, each held in isolation, are given a chance to rat on the other. If only one takes the bait, he gets a reduced prison sentence while the other gets a longer one. But if both take it, neither gets a reduction. In other words, mutual co‑operation (saying nothing) provides a higher reward than mutual defection (ratting on your partner), but the best reward comes from defecting while your partner tries to co‑operate with you, while the lowest pay‑off comes from trying to co‑operate with your partner while he stabs you in the back

The most obvious evolutionarily stable strategy in this game is simple: always defect. If your partner co‑operates, you exploit his naïveté, and if he defects, you will still do better than if you had co‑operated. So there is no possible strategy that can defeat the principle ‘always act like an untrusting jerk’

At this point, you could be forgiven for thinking that game theory is both appalling and ridiculous. Co‑operation clearly pays off. Indeed, if you make normal people (i.e. people who are not economics students) play the Prisoner’s Dilemma, they almost never defect. And not just people. Rats will go out of their way to free a trapped cage-mate; rhesus monkeys will starve for days rather than shock a companion. Even bacteria are capable of supreme acts of altruism

This trend toward biological niceness has been something of an embarrassment for biology. In fact, the task of finding ways around the more dismal conclusions of game theory has become a sub-disciplinary cottage industry. In the Prisoner’s Dilemma, for example, it turns out that when players are allowed to form relationships, co‑operators can beat defectors simply by avoiding them. That’s fine in small societies, but it leaves us with the problem of co‑operation in large groups, where interactions among strangers are inevitable

Game theory (as well as common sense) tells us that policing can help. Just grant some individuals the power and inclination to punish defectors and the attractions of cheating immediately look less compelling. This is a good first pass at a solution: not for nothing do we find police-like entities among ants, bees, wasps, and within our own bodies. But that just leads us back to the problem of corruption. What happens if the police themselves become criminals, using their unusual powers for private profit? Who watches the watchers?

In 2010, two researchers at the University of Tennessee built a game-theoretical model to examine just this problem. The results, published by Francisco Úbeda and Edgar Duéñez-Guzmán in a paper called ‘Power and Corruption’, were, frankly, depressing. Nothing, they concluded, would stop corruption from dominating an evolving police system. Once it arose, it would remain stable under almost any circumstances. The only silver lining was that the bad police could still suppress defection in the rest of society. The result was a mixed population of gullible sheep and hypocritical overlords. Net wellbeing does end up somewhat higher than it would be if everyone acted entirely selfishly, but all in all you end up with a society rather like that of the tree wasps where the police themselves cheat

דביתהו דאביי הוה לה ההיא ברתא הוא אמר לקריבאי היא אמרה לקריבה אמר לה תיתסרא הנאתי עלך אי עברת אדעתאי ומינסבת לה לקריבך אזלת ועברת על דעתיה ואינסבא לקריבה אתא לקמיה דרב יוסף אמר ליה אילו הוה ידעת דעברת על דעתך ומנסבא לה לקריבה מי אדרתה אמר לא ושרייה רב יוסף ומי שרי כי האי גוונא אין והתניא מעשה באדם אחד שהדיר את אשתו מלעלות לרגל ועברה על דעתו ועלתה לרגל ובא לפני רבי יוסי אמר לו ואילו היית יודע שעוברת על דעתך ועולה לרגל כלום הדרתה אמר לו לא והתירו רבי יוסי

The most important requirement for [the western model of] choice [in Love] is not the availability of multiple options. It is the existence of a savvy, sovereign chooser who is well aware of his needs and who acts on the basis of self-interest. Unlike all previous lovers who ran amok and acted like lost children, the new romantic hero approaches his emotions in a methodical, rational way. He sees an analyst, reads self-help literature and participates in couples counselling. Moreover, he might learn ‘love languages’, read into neuro-linguistic programming, or quantify his feelings by marking them on a scale from 1 to 10. The American philosopher Philip Rieff called this type ‘the psychological man’. In Freud: The Mind of a Moralist (1959), Rieff describes him as ‘anti-heroic, shrewd, carefully counting his satisfactions and dissatisfactions, studying unprofitable commitments as the sins most to be avoided’. The psychological man is a romantic technocrat who believes that the application of the right tools at the right time can straighten out the tangled nature of our emotions

מי אני האט געשריבן:מ׳האט דאס אויסגעברייטערט צו ווען מ׳בעהט פון מענטשן צו וועהלן א נומער פון 1 ביז 100. מ׳זאגט צו זיי אז דער וואס האט געוועלט די נומער וואס איז די נענסטע צו 2/3 פון די עוורידזש פון די נומערן וואס אלע צוזאמען האבן געוועלט, וועט באלוינט ווערן. עס קומט אויס אז ווען די וועליוּ וואס מ׳גיבט פאר די מאל די עוורידזש איז ווייניגער ווי 1 [אזוי ווי 2/3 אין אונזער משל], דעמאלטס טוהט די נעשׁ עקוויליבּריאום קאנווערדזשען צו 0, און דאס זאל מען וועהלן. דאס איז ווייל, אזוי ווי פריער ביים שיינקייט פארמעסט, איינער וואס טראכט פשוט [לעוועל 0] וועהלט א רענדאם נומער. איינער וואס טראכט שוין מער אויף וואס אנדערע טראכטן, והיינו ער איז לעוועל 1 אבער אנדערע זענען לעוועל 0, חשבונ׳ט שוין אן עוורידזש פון 50 [פון 100] און 2/3 דערפון איז 33. די וואס טראכטן נאך טיפער, לעוועל 2 אבער אנדערע זענען לעוועל 1, טראכט שוין אז ס׳גייט טאקע דעריבער מעיקרא אנקומען צו 33 און נעמט 2/3 דערפון. וכן הלאה והלאה ביז עס קומט אן צו 0.

אין 1997 האט א דייטשע סייענטיפישע מאגאזין אפ געהאלטן אזא סארט קאנטעסט, וואו מ׳דארף בוחר זיין פון 1 ביז 100 און דער וואס איז די נענסטע צו 2/3 פונעם עוורידזש געוואונט. עס האט זיך אויסגעשטעלט אז די עוורידזש פון 2,728 געוועלטע נומערן איז 22.08 געווען די עוורידזש וואס 2/3 איז געווען 14.72. עס זענען געווען וואס האבן געוועלט 14.7. דאס האט געוואוזן אויף א ריִזעניִנג פון לעוועל 2 און 3.

In the study of rationality, there’s a well-known party game: the one where everyone throws a number from 0 to 100 into a hat, and that player wins whose number was closest to two-thirds of the average of everyone’s numbers. It’s easy to see that the only Nash equilibrium of this game — that is, the only possible outcome if everyone is rational, knows that everyone is rational, knows everyone knows everyone is rational, etc. — is for everyone to throw in 0. Why? For simplicity, consider the case of two people: one can show that I should throw in 1/2 of what I think your number will be, which is 1/2 of what you think my number will be, and so on ad infinitum until we reason ourselves down to 0

On the other hand, how should you play if you actually want to win this game? The answer, apparently, is that you should throw in about 20. Most people, when faced with a long chain of logical inferences, will follow the chain for one or two steps and then stop. And, here as elsewhere in life, “being rational” is just a question of adjusting yourself to everyone else’s irrationalities. “Two-thirds of 50 is 33, and two-thirds of that is 22, and … OK, good enough for me!”

I’ve heard it said that the creationists are actually perfectly rational Bayesians; they just have prior probabilities that the scientifically-minded see as perverse. Inspired by conversations with Kurt and others, I hereby wish to propose a different theory of fundamentalist psychology. My theory is this: fundamentalists use a system of logical inference wherein you only have to apply the inference rules two or three times before you stop. (The exact number of inferences can vary, depending on how much you like the conclusion.) Furthermore, this system of “bounded inference” is actually the natural one from an evolutionary standpoint. It’s we — the scientists, mathematicians, and other nerdly folk — who insist on a bizzarre, unnatural system of inference, one where you have to keep turning the modus ponens crank whether you like where it’s taking you or not

Kurt, who looked only slightly older than I am, is already married with two kids, and presumably more on the way. In strict Darwinian terms, he’s clearly been more successful than I’ve been. Are those of us who can live with A→B or B→C or C→not(A) but not all of them at once simply evolutionary oddities, like people who have twelve fingers or can’t stand sunlight?