shkrobius ([info]shkrobius) wrote,

Why is life unfair?

Fairness is one of these enigmatic concepts stubbornly defying definition. It is easy to see why. Suppose A and B are playing a coin-tossing game: when it comes up a tail, A is given a dollar, otherwise B is given a dollar. There were ten tosses and A got $10 while B got zilch. How could it be fair that A has everything while B has nothing? Now, suppose there is an elimination tournament starting with equal stakes and winner-takes-all coin tossups; in the end, there will a single winner taking everyone’s money. The game can be fair, but the outcome is unfair.

In reality, people would always argue that not only the outcome of the game but the game itself was unfair. Fair games are expected to produce fair results. Perhaps unnaturally lucky A was a cheater who skillfully replaced the coin. The rich winner of the tournament had the advantages of being lucky and/or having otherworldly intuition. Perhaps he should be given more money, as he must be good at this game. Such rationalizing logic accurately describes the success of our financial gurus.

But that’s just the beginning. Ever tighter scrutiny will always detect hidden agendas and advantages. The two players are never the same – imagine that... I’ve heard countless times how unfair it is that children of the rich have more opportunity open to them than children of the poor. One would think that the solution of this problem is self-obvious: newborn children should be randomized at birth, so biological children of the poor would have equal opportunity to be raised in the families of the rich. Logically, this should solve the problem once and for all, but good luck selling it to the public. They want equal opportunity AND raising their own children, while it is obvious that the two things are mutually incompatible. For all this talk about the equality of opportunity, you will be told that this (equally) randomized opportunity is still unequal. Well, let me open a secret: it cannot be made equal no matter what you do. No matter how you level the field in one respect there will always be striking inequality of the outcomes. Having higher IQ is as unfair as having been born rich. If people are poor, they can be given money; if they are stupid, that is much harder to fix. The most idiotic thing one can require, in this respect, is material equality. First, it simply cannot last, even if the “game” is absolutely fair; second, it means that unfairness will find a subtler outlet, be it access to status, power, knowledge, privilege, respect, happiness, etc. By far, unequal distribution of colored pieces of paper is the most benign type of unfairness imaginable, but people are still unhappy and bitterly complaining about it.

As people themselves have no clue as to what they mean by fairness, weird rumors about this elusive condition abound. Some say that fairness is giving by desert. Some say that it is giving by need. All of that sounds great until you realize that a human being is a pit of wants. You cannot give according to one’s need, because this need is bottomless and the appetite only grows as more is given. You cannot give according to one’s desert, because everyone is deserving in his own eyes.

Perhaps for this reason people do not like to define fairness; that would obviously stand in the way of extortion in the name of fairness. However, one can define fairness so imaginatively that the latter is always possible. Hart and Rawls defined the principle of fairness

... when a number of persons engage in a just, mutually advantageous, cooperative venture according to rules and thus restrain their liberty in ways necessary to yield advantages for all, those who have submitted to these restrictions have a right to similar acquiescence on the part of those who have benefited from their submission.

Observe that their notion of fairness is conditioned on voluntary admission of mutual advantage and restraint of liberties. Naturally, most of our ventures are neither mutually advantageous nor entirely voluntary, so the principle applies to an abstraction; the sleight of hand is to identify this abstraction with ourselves. Would these imaginary persons try to get “similar acquiescence” they would learn that some people are in greater need and are more deserving than themselves. Besides, this equity may apply to anything from time spent to level of skill used to personal commitment to personal sacrifice and loyalty, and significant differences of opinion will immediately emerge. If they surpass these hurdles, there is still the question of equal division. Even in this most abstract form the problem cannot be solved. The procedure for envy-free division (=each person thinks that he receives at least a tied for largest piece) of goods for just four parties was solved only in 1997, and even this laborious procedure is not equitable (=each person’s subjective valuation of the piece that he or she receives is the same as the other person’s subjective valuation.)
http://www.ams.org/notices/200611/fea-brams.pdf
Generally, envy-free and efficient (no other allocation that is better for one person and at least as good for the other person) divisions are not equitable and vice versa. If complete fairness cannot be achieved even in this hypothetical cake-cutting division, how can it be achieved in real life? We are content with using various approximated methods (such as sealed bids or designated divider) that provide a degree of “fairness,” which is ALWAYS questionable, as our own intuitions about fairness are inherently contradictory. To get our “equal” piece of divided cake we are always ready to sacrifice fairness, which makes perfect sense as the alternative is to die of starvation.

Sometimes one is brutally reminded of this fact. Today I’ve spent an hour explaining to my son, why a Russian roulette duel is unfair to one of the players, as they exchange a single loaded gun when they miss. It is not hard to work out the probability of killing the first shooter (6/11), but the interesting thing is that intuitively the “game” does not feel unfair, perhaps because the bias is only 0.045. So we examined a modification, when A spins the cylinder and shoots at B, and B gets two shots at A and passes it to A, who gets three shots at B, etc. The probability changes to 0.524, but it is not something that one can calculate in one’s head. It is even less clear with the coin, because of dynamic instability (giving it 0.008 advantage) and unequal mass distribution. Yet such biased wagers are routinely taken in full understanding that they are unfair. The question is why.

I believe that deep down we are well aware that the pursuit of fairness is futile. Had people really wanted fairness and fairness were meaningful, we would have it long time ago. Fairness is not something we can afford. When things are unfair one can always blame one’s faults on the others. Would things be fair, who is going to be blamed for the sorry outcome?

Exactly. So it is much better to have fuzzy notions of fairness that leave plenty of room to complain about unfairness of life, and that is what we do.

Why is life unfair?
Tags: whys

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  • 34 comments

[info]saccovanzetti

December 29 2011, 03:15:57 UTC 4 months ago

Intuitively the first shooter is at a disadvantage in a game of Russian roulette.

Is "desert" a proper use of the word meaning "deserving"? It never occured to me that "dessert" may have the same origin.

We are talking about bridging the gap (moderating the dynamics of inequality) not fairness in equality, which is harder to attain or define. When far from being equal, things are a little more obvious than you describe: instead of 1-2-3-4.. sequence, life is more like 1-5-1-5-...

[info]shkrobius

December 29 2011, 06:06:20 UTC 4 months ago

Correct, but it is not clear that this disadvantage is of such magnitude that it is not easy to even it up; the second scheme of shooting (presumably, improving chances of the sonsequent shots) illustrates that.

I wonder how is it possible to "bridge the gap" in a way that can be subjectively felt fair. I often hear about "social lifts" and such like. Somehow no one tells that those wonderful places up there have been occupied, so the social lift carrying someone to the top means another person carried down. It can't be ALL upward mobility. So "closing the gap" means people going up AND down. The descendants of today's rich will become tomorrow's poor and the descendants of today's poor will become tomorrow's rich. I think that this is all bridging that one needs, but it is happening anyway, without anyone's engineering efforts. Very few of the rich can stay at the top for more than 2-3 generations. It is much closer to beating random odds than most people are willing to admit. If you are patient, you will see "fairness" in action despite the fact that its every snapshot is the display of unfairness.

[info]saccovanzetti

December 29 2011, 09:45:42 UTC 4 months ago

you are right that life is a universal equalizer and "жизнь прожить - не поле перейти". however what you are missing in your argument is that the number of places in what we call "the top" should be expanding. people just fill the shape that society offers them; if an architect designed it to be a pyramid - they will fill a pyramid, but if it is designed as a prism or truncated pyramid - they will fill that shape too.

Besides, "bridging the gap" does not have to feel fair to everyone. It just has to feel "less unfair, compared to the old system" for the overwhelming majority of participants. All I would argue for is a system where merit of a young person would be a determing factor of his success, not wealth or race or origins of his parents.

[info]shkrobius

December 29 2011, 18:11:39 UTC 4 months ago

I guestion whether that is possible. The top is called the top in relation to something, and if this imaginary shape is not tapered, how woul you even know that it's the top? "Topness" is measured exactly in proportion to how fewer people are there, so it is still about rarification. A crowded "top" would not feel like the top, providing no satisfaction of achievement or purpose for climbing. There is another, related problem. You say, let's stop our pyramid in some truncated state so there are more people on its upper tier. But this pyramid is in people's imagination, it has no physical reality. You cannot turn their imaginations off; it will continue the lines and finish the truncated structure. The same force that pushed people to reach the upper floors will force them to complete the pyramid.

The problem with your last argument is that merit is different from wealth, race, or parents only in being even more pure form of inequity. Perhaps you believe that people have full control over it. But this is not so. I think that meritocracy is the most unfair arrangement of all, as there is no compensation and no consolation to those without merit. Furhtermore, I have my doubts that success even depends on merit.

[info]gineer

December 29 2011, 11:22:50 UTC 4 months ago

\\ It can't be ALL upward mobility

If it was the case, we all still been living in the caves. :)


\\ So "closing the gap" means people going up AND down

There is NO crime in it.
It's just a distant consequence of the fact that humans are mortal.

[info]shkrobius

December 29 2011, 18:30:44 UTC 4 months ago

The joke of it all is that there is no evidence whatsoever that people ever lived in caves rather than using them as occasional shelters, fortifications, or art galleries. Caves are nasty, cold, wet, unlivable places. There is evidence of dwellings located near cave mouths, but of course no one lived there. So the promotion you mention is mostly imaginary: a natural cave was traded for an artificial one (subway).

And this reflects the general problem with the "social lift". The concept is contradictory in its most basic notion: verticality. The elevation is always relative, so one cannot have a "social lift" without stratification. The supposed means of bestowing fairness on the masses is conditional on the existence amd maintainance of inequity. The most amazing thing is that people can talk about such things without any discomfort, in all seriousness and with utter conviction. The engines of social lifts are greased with inequality; such devices can not ameliorate inequality, on principle. All they do is stirring the pot more vigorously.

[info]gineer

4 months ago

[info]vdinets

December 29 2011, 03:24:16 UTC 4 months ago

"It is even less clear with the coin, because of dynamic instability (giving it 0.008 advantage) and unequal mass distribution." Could you elaborate, please? Do you mean that for all coins the chances of falling on two sides are not equal?

[info]shkrobius

December 29 2011, 06:19:23 UTC 4 months ago

Yes, I do mean that. It's a famous result by Persi Diaconis, see
http://comptop.stanford.edu/u/preprints/heads.pdf
there is a bias of 0.8% for the coin to come up as started if you flip it at random. So you can always argue that coin tossing was unfair. But even if the coin is in the dynamic regime when the wedges in the phase space get very thin, there is still a chance that the two sides are unequal in mass. Suppose it is a small bias of 0.1%. Well, after a billion tosses you can be pretty sure that it is there and then using this knowledge you can make money on the subsequent bets. Some physical systems (a roulette) are examples of true dynamic chaos, but coin tossing is not. All "randomness" comes from your inability to control your muscles, and this is not good enough to even the chance.

[info]vdinets

December 29 2011, 15:35:55 UTC 4 months ago

But you don't know in advance which side is heavier. It would take at least thousands of trials to find out.
Roulette, BTW, is not a true dynamic chaos. Experienced croupiers can manipulate it quite well.

[info]shkrobius

December 29 2011, 17:52:27 UTC 4 months ago

There is a theorem of Poincare stating that the probability of stopping on red and black sectors in an equally divided roulette infinitely closely approaches 1/2 as the number of sectors goes to infinity for any distribution function with a bound derivative. That means it is true dynamic chaos. Had the physical roulette been divided in 10,000 sectors even the most experienced cheaters would find it nearly impossible to cheat.

[info]vdinets

4 months ago

[info]shkrobius

4 months ago

[info]vdinets

4 months ago

[info]solomon2

December 29 2011, 04:33:18 UTC 4 months ago

Fairness is reversion to the mean.

[info]shkrobius

December 29 2011, 06:46:51 UTC 4 months ago

Do you mean Galton's regression towards mediocrity? You can say that, but then one needs explaining why life does not want to regress to the mean (=unfair). Galton, for example, believed that this regression occurs because a child inherits not only from his parents but from all of his ancestors; numerically, the latter prevail. As you go further in time, the larger is the sampling pool, and these ancestors begin to sample population on average. His "fairness" was hereditary: any exceptional qualities would even up over a few generations. But he was not quite right on that: exceptional traits are poorly retained because (typically) they are recessive. However, this does not have to be the case, and then genetics provides no guarantee of fairness. Had it been fair, there would not be humans and amoebas. (Biological) life is a fundamentally unfair winner-inherits-the-future affair. It is hard to imagine that any culture can nullify this built-in unfairness. I suspect it is like trying to even the odds of the Russian roulette using a clever scheme. Not only it is not working, the game itself is of questionable value. Regression to the mean has a deeper layer of reality explaining it. Fairness, in my opinion, does not. It is pure wishful thinking; it cannot be achieved on principle, nor that anyone ever seriously tried achieving it. The way I see it, it is more an instrument of change than a desired state.

[info]gineer

December 29 2011, 11:32:40 UTC 4 months ago

\\The way I see it, it is more an instrument of change than a desired state.

Yeah. It's an ideal.
And it is instrumental.

Its interesting question -- why so?
But answer is too obvious.

[info]shkrobius

December 29 2011, 17:55:09 UTC 4 months ago

As no state of affairs is fair it provides universal and truthful rationale for taking from A and giving it to B.

[info]gineer

4 months ago

[info]gineer

December 29 2011, 11:06:13 UTC 4 months ago Edited:  December 29 2011, 11:07:03 UTC

\\The most idiotic thing one can require, in this respect, is material equality. First, it simply cannot last, even if the “game” is absolutely fair

Heh!
It was. Its a Soviet Union.
At least in the minds of current youngsters. :))

[info]kobak

December 29 2011, 12:35:14 UTC 4 months ago

I have never thought about Russian roulette being unfair, thanks for mentioning this!

[info]shkrobius

December 30 2011, 03:10:48 UTC 4 months ago

Amazing, isn't it? One would think that people would check and double check when it comes to a duel, but its unfairness does not even register.

BTW, I enjoyed reading your recent posts on Russian elections. I even learned something scientific from the ensuing discussion: people frequently suggested sand grains as the typical example of normal distribution (of size). I've checked it up, and it turns out that log p is hyperbolic rather than parabolic. There is a simple explanation for that, http://www.math.ku.dk/~michael/size.pdf
but no math is really needed: it is intuitively clear that the wings should be exponential because of self-similarity of the problem. It is the same with the roulette: once you think about it, it is obvious it can't be fair.

[info]kobak

December 30 2011, 22:17:32 UTC 4 months ago

Thank you! This sand grain size distribution issue does look interesting, but I fail to see the "intuitive" explanation, could you elaborate on it?

In any case, best wishes for the new year! BTW, I was recently amused and amazed to find out that two of my favourite blogs are written by a brother and a sister (one of them being you). Happy New Year!

[info]shkrobius

December 30 2011, 22:35:19 UTC 4 months ago

Imagine the far tail of this distribution. Whatever physical process is responsible for sorting grains around the median would not matter in this tail; the distribution in this tail should not depend on the graining of this distribution, as it will mainly depend on the availability of grains to this process, i.e. it should be scale invariant. Only exponential distribution would be scale invariant.

Thank you for your kind words; I'll pass this to Masha - and a happy New Year!

[info]michaellogin

December 30 2011, 20:43:54 UTC 4 months ago

Честная русская рулетка???
Поскольку один из участников игры начинает первым, второй получает существенное преимущество — он не должен испытывать судьбу в случае неудачи первого. Для выравнивания риска второй участник НЕ должен вращать барабан после успешного хода первого. В этом случае вероятность гибели первого участника равна 1/6, а второго равна (вероятность получения хода) * (вероятность выпадения патрона)= 5/6 *1/5=1/6. То есть, рулетка без дополнительных вращений барабана является честной игрой в математическом смысле. ВИКИ
Т.е. вводим два правила - а) второй участник не должен вращать барабан, а первый - всегда должен вращать, б) второй участник должен в случае смерти первого, вложить новый патрон, вращать барабан и стрелять. Будет ли такой вариант 100% справедлив???

[info]shkrobius

December 30 2011, 22:47:29 UTC 4 months ago

You can do even better:

(22 March 1999, Phnom Penh) Decades of armed strife have littered Cambodia with unexploded munitions and ordnance. Three friends recently spent an evening sharing drinks and exchanging insults at a local cafe in the southeastern province of Svay Rieng. Their companionable arguing continued for hours, until one man pulled out a 25-year-old unexploded anti-tank mine found in his backyard.

He tossed it under the table, and the three men began playing Russian roulette, each tossing down a drink and then stamping on the mine. The other villagers fled in terror. Minutes later, the explosive detonated with a tremendous boom, killing the three men in the bar. "Their wives could not even find their flesh because the blast destroyed everything," the Rasmei Kampuchea newspaper reported. http://darwinawards.com/darwin/darwin1999-07.html

[info]fe_b

January 6 2012, 22:53:46 UTC 4 months ago

Стремление к справедливости столь же иррационально, как и инстинкт продолжения рода.

И столь же полезно для общества как целого.

Я не понимаю, почему Вам не нравится справедливость.
Возможно, потому, что всякая социальная уравниловка кажется Вам несправедливой.

Конечно же всякие рассуждения о справедливости полны самообмана и нарушений логики.
Но это же касается и многих других рассуждений.

Нас же не возмущает, что большинство людей не умеют складывать дроби.

[info]shkrobius

January 7 2012, 21:06:28 UTC 4 months ago

Неужели Вам безразлично, что Вас могут убить за то, что кто-то себя обманывает?

[info]fe_b

January 7 2012, 21:53:23 UTC 4 months ago

Это натяжка.
Стремление к справедливости и уровень насилия это разные вещи.

Логика хромает у всех, но стремление к убийству есть не у всех.

[info]shkrobius

January 7 2012, 22:20:11 UTC 4 months ago

Разве стремление к справедливости в материальном мире и насилие разны по природе?

[info]fe_b

4 months ago

[info]shkrobius

4 months ago

[info]fe_b

4 months ago

[info]shkrobius

4 months ago

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