- Another Round Of The Ultimatum Game. Adnotated.

Tuesday, 23 July, Year 11 d.Tr. | Author: Mircea Popescu

Let's see if it's fair this time.

My issue is simply that the Ultimatum Game, which supposedly shows a sense of fairness, and is evidence that this fairness is an evolutionary trait that was selected, doesn't necessarily show any of these things.

The premise is that when people play a round of the UG, they generally do not offer a 99/1 split but something more "fair" (e.g. 60/40) and people repeatedly refuse to accept deals that aren't "fair."

Ergo, it is fairness that this game tests, and fairness is what has evolved.

Even if we grant that 60/40 is the ordinary split, why does this mean it is fairness that has been selected for?

An easy counterexample is to rewrite the discussion in terms of envy: in the UG, people rarely offer 99/1 because they know it will be refused -- because they know the other person would just as soon shoot his own foot to spite his hand. And Player 2 would refuse anything less than 70/30 not because it's not fair, but because he is a jealous, deeply spiteful person who hates when other people have more, even if it is fair. Flat tax, anyone? No? Thought not.i

I rewrite this all as envy not to show that it is actually envy that the Game tests; or that envy is not evolved, or that even fairness is not evolved; but merelyii to demonstrate that the outcome of the UG can not be taken to be an example of any specific idea or behavior. People may choose the same results for entirely different reasons. Sales of guns are probably a good example of this.

The best we can say -- and even this isn't completely accurate -- is that the common choices of 60/40 have been selected for; that they multiply disparate and unconnected causes, yet by virtue of their overdetermination, this choice becomes the one humans pick. In other words, what has been selected for is the propensity to choose 60/40. Period. No cause can be inferred.iii


Let's look at whether the Ultimatum Game and Prisoner's Dilemma actually measure fairness.

A. If it were indeed fairness that was being displayed, then fairness should be immune to the payoff. Whether the pot were a billion dollars, or 6 silver coins, the outcome should be the same. Within cultures, this is generally true. What matters is that the pot consist of something valued, that does not have a self-imposed maximum (e.g. chocolates wouldn't work because there's a point when you actually don't want any more chocolates.)iv

B. Fairness presupposes an ability to value something. You can't use a pot of dirt, not because it doesn't have any value, but because it is impossible to value consistently (e.g. it may have personal value to one or the other but not a general value.)v Also, you expect the representation of that value to be irrelevant, so long as we all know the value. The game can be played with pesos or dollars if I know the conversion

C. The value of something must be economic. Not monetary, necessarily, but in the simplest possible sense, more has to be more and less has to be less.vii

But, sadly for the evolution of humanity and the hopes of millions who believe they are greater than their history, this is not the case.


pd-payoffImagine games with a pot of 3 cents, $3, 300 cents, or $300. Look at those carefully. If fairness was at issue, game outcomes should not vary substantially based on the pot. And, if they did, you'd at least expect very similar results for the 300 cents and the $3 pots; they are, after all, the same, and the players are likely not retarded.

This is the Prisoner's Dilemma, a slightly different game, but the difference is not important here.

Take a look at the results of "mutual cooperation." Not only are they very much dependent on the size of the pot, but they are dependent in a way which makes no sense at allviii: not based on the amount of money, but the size of the number. 300 (cents) was "bigger" than 3 (dollars.)

Note that the results of 300 cents were in every case more similar to the results of $300 then of $3. Their brains saw 300 cents and 300 dollars as more similar than 3 dollars. (1) I'll save you the trouble of looking it up: none of the players had had strokes.

The interpretation of nearly every UG and PD paper depends on assuming that the players are judging the value of the pot based on monetary value or its conversion, but it is quite apparent that they are (at least also) judging it using some deeper cognitive construct of "amount" or "size -- that here overruled monetary value.

A quick correlate from the stock market: people perceive Google ($300/share) as more expensive than Bank of America ($9) -- that $1000 buys you "more" BoA, even though it's the same $1000 invested either way, and, by most metrics, Google is cheaper.ix

Given that these cognitive distortions -- and who knows if they're distortions, or don't have some positive value after all? -- exist, how can we believe that a 60/40 split using a $10 pot is an example of "fairness?" Is our sense of fairness so weak (despite millennia of selection) that it can't withstand the presence of a few non-significant zeros?

How do you know these games aren't actually showing you the effect of a single cognitive constraint, and that constraint -- not fairness or cooperation -- is what has been selected for?


Even if these games did test fairness, why would we think they were defining fairness using Western standards -- which have existed only for a fraction of humanity's history, in only a small part of the world? People have had slaves longer then they have not had slaves, and had no moral problem with it.x Is that fair? If the ancient Romans played the Ultimatum Game, would the split be the same? Or, if it was, would it have the same meaning?xi

To assume the common outcome of 60/40 from a few studies applies to the general population independent of cultural effects; to assume the results are independent of the cognitive distortions of size, number, and value; and to extrapolate these results across different times in history -- is such madness as to border on religion. To then believe this all as the outcome of the natural selection of a single complex behavioral trait is religion.

And to be so mad as to believe we know the nature of this single trait -- to know the the character of the god Fairness -- brings us back to madness again.xii

1 Not only that, but there is a trend towards overestimating 300 cents -- why? Go ahead and imagine 300 cents. That's bigger than $300 -- bigger in terms of weight, volume, height, etc.

2 Consider a number line, with numbers labeled one through ten. Now extend the line, place the number 100. Now place the number 1000. Then 10000. Etc. The distance from 1 to 100 is more accurate than your distance from 100 to 1000, and 1000 to 10000. The larger the number, the more difficult it is to [mark] accurately.xiii

Similarly, consider getting punched in the face. The perception of the pain is related to [your] starting level of pain. A punch that is ten times as hard isn't felt to be exactly ten times as painful.xiv

Not only is the error greater with each successive increse; it turns out that in specific cases, the error follows a mathematically demonstrable progression, namely, that our perception of is proportional to the logarithm of of the stimulus difference.xv

P=k ln S/So, where So is the lowest possible perceived stimulus (Weber-Fechner law).

I'll let the awesomeness of that sink in for a moment. (3).

Turns out this law may only be applicable in certain cases. For example, the perception of stimulus is also related to other variables like distraction, temperature of the body, etc. And maybe a power function rather than logarithmic function is more applicable. All this is for another day.

3. But here's a perplexing little conundrum. Fechner's law shows that the perception of a physical stimulus is proportional to the logarithm of the magnitude of the physical stimulus. But our perception of magnitude itself -- our perception of numbers -- also follows such a logarithmic function. So choosing a number ("on a scale from one to ten") to describe our perception, that number itself is related to the stimulus by a power function. In other words, the mere act of attempting to quantify a perception adds an additional level of complexity to the problem.

  1. He has a point, in that what the ultimatum game actually "measures", after a fashion (it doesn't really measure anything) is the same thing "Gini indexes" and the assorted social pseudosciences wank measures : how implicitly equal do the goats feel, not to the other goats, but to the goat ideal. I said before,

    You believe man to be the measure of all things. This is a purely religious belief, exactly identical, and directly reducible, to the notion that there's a magical teapot spinning in the sky.

    You believe that you are man, in the strict and strictly laughable sense that everything is equal to everything else and thus therefore you see yourself as not merely a uniquely bent spoon, vaguely related to various other better implementations of an ideal spoon and thus twice removed from that ideal but instead fully and completely, in and by yourself, equal and idempotent to everything man is, ever was or ever could be. This is also a religious belief, I suppose, although more indicative of psychopathology than what usually is called religion - on the continuum between the buddhist chanting and the fanatic beheading this sort of nonsense is certainly past the fanatic, hapilly floating in a schizoid sea towards waxy flexibility.

    When some schmuck, presented to another randomly chosen schmuck, decides the other schmuck can at the absolute outside most be 7/3 = 2.333333333 times better than him, what has happened is that he has capped an outcome. As actual specialists in the field (of risk assessment and risk management, which is all daytrading ever is) will readily say, "this isn't even wrong", as a distinct category from being wrong -- but it comes with some advantages! It is a lot easier not to mention immensely cheaper to move about in a world with capped outcomes. So what if it doesn't exist ?

    Would you rather eat a cookie now or a bag of cookies later ? So what if the cookie doesn't exist ? In the now, the bag of cookies from later doesn't exist either. And yes, "waxy flexibility" is an oblique reference to schizophrenia. Because it has to be, derealization doesn't really go any other way.

    PS. The reason first players display a wider spread than second players, which is to say the reason why first players will offer deals the second players will not accept has entirely nothing to do with "fairness" : both first players and second players use the same exact mental thresholds, 70/30 or whatever they are, but the first player figures he's got the drop on the other one. That's why he sometimes goes outside the bounds, he adds 15% or whatever he adds, accidentally widening the scope outside of social acceptability. Thus the experiment doesn't prove "fairness is an evolved trait in humans", it proves that humans, in common with cheetahs and all other savannah meat-eating predators, are hard-wired to try and exploit a perceived tactical advantage.

    Wait, what... why are you crying ? Sorry, did I accidentally disexist your complicated theoretical facades for your hopes and dreams as to "society" and bla bla bla SkyMom ? Looky here -- women do not matter socially ; in the affairs of mankind women are objects, not agents, nor subjects. It's all, through&through, a story of men. Okay ? []

  2. ... "to assuage my own terrors on the topic. Hey, guise, wanna hear how I fixed some holes in the blablabla SkyMom theory that none of you even perceive ? No ? Why not ?!"

    Just as long as you believe "fairness" is a thing as opposed to it being some nonsense invented by dagos mid 1800s (hey check it out, just as "nigger" became a thing!) like "altruism" or "acid rain" he's perfectly happy.

    Are you still getting those acid rains where you live, by the way ? No ? How come ? Don't fucking tell me it's because "the world got together and followed the pantsuit indications" -- their own press at the time was claiming the exact contrary ; and then they stopped mentioning it, and then... guess what ? It got fixed! All by itself! As if it had never existed in the first place! Fancy that.

    Who knows, maybe it was the hole in the ozone layer that fixed acid rain. That was totally real, right ? Hey, remember when the pantsuit press saved those whales ? Oh, wait, you were just using that "save the whales" expression, no idea where it came from ? Aww! See, you don't know your own history, and thereby you're missing out on such historic imperial glories! The journalists that saved the whales, fixed the acid hole, knitted back the rain layer, retconned "fairness" and "no means no" oh sorry, I mean "metoo" and "global warming" into five million years of exactly contrary record and so on. Isn't insanity a wonderful thing ? []

  3. He'd be saying "Schelling point", if he were familiar with game theory enough to namedrop ; but he isn't. However, the Ultimatum Game stability is not related to Schelling points -- specifically because there is a reason for it.

    Most people trying to fuck your daughter will attempt sticking their penis between her legs, not into her armpit. This isn't a Schelling point, this is like the Ultimatum Game. Meanwhile most kids in school trying to fuck your daughter will drop a pen. There's no objective reason to drop it, they could throw it in the air just as well. Dropping's just what they do -- back when your grandmother was still a virgin, after your granddaughter'd have had the clingwrap removed for her... that's a Schelling point.

    PS. If you're curious, when there's reason not to do it then it becomes stotting. []

  4. Wait, wait. There isn't a point where you wouldn't actually want more money ? You actually believe this ?

    Do you know why you believe it ?

    You believe it because you're poor, that's why. Not even "a little" poor, "kinda" poor, "arguably" poor. You're absolutely poor, you're so fucking poor your poverty's your only experience of the world, to the exclusion of all else. Do you know who, similarily, wouldn't think there's a point where you don't want any more chocolate ? Ever heard of Biafra ?

    Funny thing, too -- because people in the past, such as for instance the famously poor Alfred P. Doolittle, nevertheless weren't quite as poor as you (nor, apparently, quite as illiterate -- you even ever heard "With A Little Bit Of Luck" before ?) Do you know what the (also eminently poor) father of the sold daugther says, in
    Il corpo della ragassa
    ? That two hundred thousand is too much money. He wants the hundred thousand he asked for, no more. For him, two hundred thousand is a capital, he has to hassle with it, whereas a hundred thousand he can just spend, it doesn't matter. Do you understand yet ?!

    And no, she didn't mind being sold. Not one bit. Meanwhile you... you're so fucking poor, yo momma only had you for lack of perceiving any better ways to occupy her spare time. You're not even worth selling, had she liked cats more you wouldn't even be here, poveraccio 'sgraziato. You're the poorest generation of poor fucks that ever lived. []

  5. Yet if you take my pot of dirt Ima fairly shoot you right between the eyes (just, probably, from the back, so it'll be the exit wound). What's the value of a peppercorn ? []
  6. Amusing enough, seeing how the dollar is absolutely worthless, both in theory as in practice ; as well as per the declarations of the scammers issuing it.

    Why does Ballas want to believe the dubaloo is the only value ? Note that his idea isn't to make the dubaloo "the principal value" or "the best value" or anything like that -- nothing short of it being the only value suffices for his needs. Could it be specifically because he is so poor he has absolutely nothing else ? Is this belief in any way relatable to his belief that marriage is the only way, not the principal or even the best, but the only, absolutely must be only way ? And then what, having children, right ? And being poor, yes ?

    African poverty is self-reproducting because of exactly the above completeness -- once the moron's found a cycle, the moron's also trapped, and permanently as far as he's concerned. One way to look at Columbian history is to say that the redskins were such fucking imbeciles, they spent millenia trapped in a little cycle until someone undertook all the expense of sending a technician over to knock them out of it. I mean... the Mexicans didn't go back to worshipping Montezuma once the Spanish left, did they ? So it was a case of their being trapped in a cycle, yes ? []

  7. Somebody would benefit immensely from studying some basic set theory. Just sayin'. []
  8. Makes plenty of sense : at small values (and yes, all life has an intrinsic notion of value, because calories) the signalling function exceeds the feeding function. There's a fucking reason the busker asks for 'spare change' rather than 'spare bills' : you don't associate coins with food and therefore are much more likely to cooperate.

    Ever wondered why extremely poor people, such as for instance the sad fucks inhabiting our colonies in America, seem so invested in signalling above all else ? Doh. If they weren't so poor they'd find other shit to do ; but they're poor beyond measure, literally the poorest generation of poorfucks the world's ever seen. Numbers don't lie. []

  9. For the curious - BoA is now 29.57 ; Google is now 1138. Before you get too excited with "it's the same thing god damned it!", Google also split once since 2009. In a decade, BoA would have tripled your money, while Google would have 7'd it. How's your portofolio been doing ? []
  10. In no small part because there isn't any moral problem with it.

    Moreover, "the time where people have not had slaves" is entirely imaginary, or in any case it absolutely hasn't started yet. I've had slaves for a while. []

  11. Except the ancient Romans'd never have played that -- or any other game -- with anyone they did not know. []
  12. Quite exactly right : the pantsuit cycle from madness to faith to madness again, I couldn't have said it better myself.

    How many people do you know who carry this badge, by the way ? []

  13. Wouldn't this then propose there should be a trend towards... underestimating 300 cents ? Ie, it's never "difficult" just like that, in general, it's always biased towards dekulakizing the larger numbers. The person asked to mark 1 to 10 will use half the paper for it, and then another half of the remainder for 1000 and then half of the remainder again for 10k, meaning 10k's worth about the same amount of paper as two and a half. []
  14. This is nonsense ; a punch that is ten times as hard as a base punch will kill you. Experimentally, young women in reasonable shape will punch about 30 on their first innocent tries, and as high as 50 once taught the basic mechanics of how to punch. This is, definitionally, girl punches, meaning you might not feel them ; yet if someone hits you for anything above 70 you will definitely feel it ; and at 90 or so you're just about guaranteed to pass out.

    Now go try and hit a 300, to say nothing of a 500... we're talking "being hit by a motorcycle" fare by now. []

  15. Rather, that old arithmetic-geometric stimulus-perception thing. Check it out, I was aware of it in the notes above, even! Good thing this "science" hasn't made so much progress since decades ago, back when I was reading Romanian translations of Russian originals on the same topic -- it saves me having to do all that much work. []
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