January 15, 2009

Another Round Of The Ultimatum Game

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

Go ahead and read Part 1, The Ultimatum Game Is A Trap.

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 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 merely 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.


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.)

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.)  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 rate.

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.

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.


Imagine 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.

pd payoff.jpg

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 all: 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. 

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.  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?

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.


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.

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 accurately.

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

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.

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.

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.


We assume games which simul... (Below threshold)

January 16, 2009 2:17 AM | Posted by ITW: | Reply

We assume games which simulate bartering or cooperation as testing fairness for the same reason we assume analgesic drug trials are testing efficacy to control pain. The whole point of this behavior, in theory, is mutual gratification. Cheating is incidental, beneficial if you benefit, but not intended as the expected outcome. If cheating were intended no one would ever cooperate or attempt to barter and our brains would not have evolved to be that of a social animal (because who would play a game where the outcome is cheating, and fairness is incidental?? Ya have to be bonkers!)

Therefore, common sense says fairness is the goal outcome of any social interaction. Real life isn't like that (now or back then) but that's not the point. THe point is that fairness is the default. It is the whole point of the thing. Well, actually, self interest is the point of the thing (from a gene perspective) but since we are social animals fairness is almost always the vehicle that we reach self interest through (fairness: defined as mutual self interest).

Saying these games show envy is like saying percocet was invented for withdrawals. Withdrawals are part of percocet use but it's not the intention of using it. Envy is part of social competition/bartering but it's not the goal. The goal is fairness : mutual self interest.

Saying the games show nothing at all is like saying drugs do random things and any of the effects are incidental. That's obviously not true. Drugs are designed and selected for and become popular because of specific and reliable effects that they have on more people than not. This is true of human behaviors in situations that were common during evolution.

Like a refined modern medical therapy, the way human brains respond to certain situations is not random or meaningless, it is based in a sort of crude logic that worked at the time of human brain gene selection.

Since it is only logical that the goal outcome of social interaction is fairness (mutual self interest) it must therefore be logical that simulated social bargaining must be testing fairness.

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I'm genuinely delighted to ... (Below threshold)

January 16, 2009 8:18 AM | Posted by Je: | Reply

I'm genuinely delighted to see someone from the psych side of science posting critically about evolutionary psychology. There seem to be a lot of untested assumptions in evolutionary psych, and no plans to test them anytime soon.

The game does seem to be great at revealing the attitudes of the commentators. I reckon the comments explaining the results are much more interesting than the game itself.

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Subjective value fullfillme... (Below threshold)

January 16, 2009 8:50 AM | Posted by Philip: | Reply

Subjective value fullfillment.

Doc, have you ready any Mises?

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I'm not saying the games... (Below threshold)

January 16, 2009 10:15 AM | Posted, in reply to ITW's comment, by Alone: | Reply

I'm not saying the games show nothing; the obviously do show something. I'm saying that the something can't be generalized across time, culture, and value. To say the UG is useful to generalize how Americans in 2000s might feel about cooperation seems plausible; but not because cooperation is plausible, but because other explanations (envy, spite, cognitive distortion about value, etc) do not conflict with the cooperation explanation.

Did oil prices fall because of decreased demand, or because speculation decreased? Both answers are plausible, both may be operational, and they don't conflict with each other. But to get on the air and announce, "it is absolutely decreased demand" and to create a logical thesis why that is doesn't really prove anything, because I can construct an equally plausible thesis why it's speculation; or stronger dollar. Or hedge funds dumping large positions. Etc. See? oil prices are also overdetermined. To pick one and proclaim it loudly is, well, religion.

I certainly am not against religion, but if you're going to have a religion, at least have the humility to acknowledge you can't fully know your god.

I'm also going to disagree with your premise about fairness being the default, though I admit it's a good one. First, why should mutual self interest be the default, and not conquest or victory? Second, why is fairness the same as mutual self interest? I might agree that UG shows mutual self interest, but not that this is the same thing as fairness. Why would mutual self interest be for the same reasons? Two people have a one night stand. There is mutual self interest, but who knows if it is even close to fairness? Maybe it's the stereotype of the guy is just looking to get off, and the woman feels lonely. So you can't claim the outcome of "sex" is related to fairness. The woman in this example is valuing her sex differently during a lonely period than she might at a happier time. Etc.

Unfortunately (for me), debates about evolutionary psychology really come down to who has the best sounding story.

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The first UG analysis was a... (Below threshold)

January 16, 2009 5:04 PM | Posted by Nadia: | Reply

The first UG analysis was a bit more accessible, but this one proved your point beyond a doubt.

Evolutionary psychology is interesting in the way any new theory is interesting: maybe we can explain why we do what we do and even predict it. An alarm goes off when a group tries to explain every human behavior with their theory, and I'll admit that I want to believe some biological of the basis. While a few explanations seem plausible, others are an obvious stretch from behavior to because, without any evidence in between. Not even all basic animal behavior is explained, and humans have entirely different planes of reality added to the equation.

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i'm a pedant.you kic... (Below threshold)

January 18, 2009 8:06 PM | Posted by www: | Reply

i'm a pedant.
you kick ass.
i'll proof your stuff for free.

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"and the players are likely... (Below threshold)

January 21, 2009 1:55 AM | Posted by Farkov: | Reply

"and the players are likely not retarded."

Using Occam's razor this is a big assumption. I propose that the numbers given simply reflect the ratio of retarded people in a given sample. Surely someone who differentiates between 300 cents and 3 dollars is retarded, however functional they may prove to be.

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"To then believe this all a... (Below threshold)

January 22, 2009 10:47 AM | Posted by Roger: | Reply

"To then believe this all as the outcome of the natural selection of a single complex behavioral trait is religion"

I love this quote, it has had me thinking for days. This article also hits a lot on why any field that studies complex systems(global climate, the human brain, human sociology, etc) seems to act more like religion than science. When you have a complex system, you can end up with multiple explainations for a phenomenon that are all equally factual. At that point which way to go is a matter of preference and faith(Hey I trust this guy more than that guy, etc). Once start taking scientific theories of faith, and stop trying to disprove them, you are only a small step away from religion.

As for the article, if the UG were really about testing scientific hypothesis, then follow up experiements would be divised to try an disprove it. It isn't hard, Try running the game in a setting where player A believes that player B doesn't know how much money is at stake, then record 3 results. 1. How many players disclose the amount of money at stake? 2. How many players lie about the amount of money at stake(either outright lie or lie by omission)? 3. What split to the players offer? In this experiment player B is irrelevant. The question is does player A still follow the fairness ideal when they believe they have a hidden advantage or do they use the edge to try and get an upper hand.

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It's not too surprising tha... (Below threshold)

January 23, 2009 7:16 AM | Posted by Syllopsium: | Reply

It's not too surprising that people treat larger numbers differently - most people aren't good at evaluating orders of magnitude.

I don't think anyone is suggesting that 'fairness' is the only factor here. When the point is reached whereby refusing the deal would create a large opportunity cost that outweighs the possible social cost (being scammed or embarassed) people will probably change their tactics.

You're not offering sensible economic arguments, either. A flat tax isn't fair, and it isn't equal. 30% tax on someone who earns 10 quid is different than 30% tax on someone that earns 1000 quid.

Your stock market example is also flawed, and I am neither in finance or using the stock market. More shares provides more granularity on the deals you do. Given two stocks with equal outlooks it makes perfect sense to buy the same economic quantity of the cheaper one.

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Tangentially, regarding log... (Below threshold)

January 23, 2009 9:27 AM | Posted by DGlenn: | Reply

Tangentially, regarding logarithmic perception of physical stimuli ... as both a chronic pain patient and a math geek, I've always had difficulty with the standard question, "On a scale of one to ten, how bad is your pain?", because where my mind immediately goes is the responding question, "Is that scale linear or logarithmic?" I'm inclined to answer logarithmically, so that when I say "nine" I mean a hell of a lot more than "eight" but when I say "four" I mean only moderately worse than "three", but I never know whether that's the same way that the practitioner asking the question will interpret my answer, and, disturbingly, I've not yet found a formula for asking them which they mean, that any of them have understood enough to be able to answer.

I'd be tempted to answer them in decibels, but given that they're usually confused when I say "one gram" instead of "one thousand milligrams", that'd probably be asking for trouble.

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And then there's this:... (Below threshold)

January 24, 2009 6:57 AM | Posted by SusanC: | Reply

And then there's this:

Monoamine oxidase A gene (MAOA) predicts behavioral aggression following provocation.

I think it was Richard Rorty who said it was a feature of postmodernism that the same thing can be made to seem either good or bad by being differently described.

"Fairness" sounds good, "envy" not so much, and as for "behavioral aggression"...

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P.S. The Rorty reference is... (Below threshold)

January 24, 2009 7:14 AM | Posted by SusanC: | Reply

P.S. The Rorty reference is "Ironists and Metaphysicians".

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Fair is a division of X mor... (Below threshold)

February 7, 2009 6:00 PM | Posted by Valerie: | Reply

Fair is a division of X more equal than all or nothing. It's not intrinsically moral. It's amoral and is not interchangeable with 'mutually beneficial'-even though that is often a moral descriptive of fair transactions and has subsequently morphed the popular lexicon. I think you can agree that despite whatever intangibles the individuals came to the deal possessing, the tangible result was for the most part fair. As a culture we've decided to value a fair divide more often than not, but that's a pattern of preference. It doesn't mean that as a culture we have decided to change the definition of fair to include a positive moral judgment. I should know. I just paid my taxes.

But maybe it's the word 'fair' that is throwing us off. What does this game measure? I guess what I'm supposed to walk away with is: We naturally divide fairly. (Fair is good.) Therefore we are good.

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It is surely important that... (Below threshold)

February 1, 2013 10:54 AM | Posted by Eddie Edwards: | Reply

It is surely important that there are only 4 ways to divide $3 or 3c while there are 301 ways to divide $300 and 300c. With $3, if you don't pick 66:33 to you, you either pick a combination where you get less than the other guy, or you offer him nothing. With 300c you have a bigger decision. The $3 / 3c game seems incomparable to the $300/300c game for this reason - one is an exercise in highly discrete choices; the other offers a continuum of options.

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It IS fair, because it's th... (Below threshold)

January 8, 2015 5:53 PM | Posted, in reply to Syllopsium's comment, by Atarii: | Reply

It IS fair, because it's the same proportion of your money going to tax. You make more, you pay more, but you pay the exact same fraction.

A person who makes one-hundred dollars a check at 10% taxes will pay ten dollars (not a ton; he still has ninety dollars) whereas a person who makes a thousand dollars a check will still only pay a paltry 100 dollars, and still have 900 dollars remaining. That seems fair to me. How is it not?

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