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August 13, 2008

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"Giving N people each 1/Nth is nonetheless a fair sort of thing to do"

How can we know this unless we actually define what "fair" is, or what its bedrock is? Or are we just assuming that roughly, "fair" means "equal proportions"?

I have a special interest in faireness. There's a technical definition in mechanism design: a mechanism (say for allocating goods) is Fair if all participants derive equal utility from participating. Compare to Efficiency: total utility is maximized (each good went to the person who wanted it most). You get both fairness and efficiency by having the winners pay the losers just enough so that the losers are as happy with the money as the winners are with the booty minus the money. A related mechanism property is envy-freeness: no one would prefer to trade places with anyone else.

It's fair when the participants all sincerely agree that it's fair.

If you think you're being unfair to somebody and he disagrees, who's right?

There isn't any guarantee that a fair solution is possible. If people can't agree, then we can't be fair. I say, fairness is a goal that we can sometimes achieve. There's no guarantee that we could always achieve all of our goals if only we did the right things. There's no guarantee that fairness is possible. Just, it's a good goal to try for sometimes, and sometimes we can actually be fair or mostly fair.

People often agree that equal shares is fair. Not always. It seems like a sort of default, and we might choose to start with the default and then argue why we should deviate from it. Like, the one who found the pie in the forest might deserve a finder's fee. The one who negotiated an agreement when it seemed unlikely might deserve a reward for that. If there's a danger that a bear might come take the pie, then one who guards the others while they eat might deserve a reward. If one person is carrying extra weight for things he shares with the others, he might deserve extra calories etc. There can be lots of reasons to deviate from equal shares once you accept equal shares as the default.

Approaching a fair solution is an art. It's an adventure that might not have any good ending possible, but when you don't know it can't be done then it's better to try than just accept failure from the beginning. Starting out with the assumption that there is a fair approach that everybody ought to accept, and that if it doesn't work you'll figure out who to blame, is both backward and counterproductive.

Daniel Reeves, I checked out your bio. Very impressive stuff, and best of success with your work and research!

I think the take-away from all this is that 'fairness' is ill-defined. In theory, we could all agree that fairness is having the pie split proportionally by desire, or split proportionally by the degree to which the actors qualify for moral consideration, or some combination thereof, or something else entirely. If we wanted to, we could be like the Inuits (who, as the story goes, have 37 different words for "snow"), and have 37 different words for slight variations of 'fairness'. It's a semantics argument.

When people get this deep into talking about fairness, they're usually _really_ talking about "what's the right thing to do here?" (which sometimes has little to do with what we would normally characterize as fair). But it sounds like that's what we're getting into tomorrow :)

Thanks for commenting, Reeves! Yes, there are fair division mechanisms more complicated than the object-level 1/Nth for everyone (as I noted in the post), though among humans, I think, only people of good will can do complicated things without incurring large overhead costs from politics as people argue and try to push the division their way. And most of the participants may all believe they got less than they deserved, if the fair division involves many decision points where people can all overestimate how much they deserve and underestimate how much others deserve.

How much should the winners compensate the losers? A dollar more, a dollar less and soon people are pulling out the handaxes again.

So I do admit that 1/Nth has a certain charm for me as a human solution to the given pie-in-the-forest problem - though I would laugh at the idea that AIs capable of perfectly introspecting on complex non-noisy inferences, would have to do the same thing.

An interesting question is whether we can view more complicated mechanisms as the equivalent of "1/Nth of the meta-pie for everyone", in the sense that the mechanism itself doesn't favor any particular party's interests over any other. (Obviously this is a more plausible assertion when the division mechanism has been worked out by outside game theorists, and adopted in advance of seeing the particular pie.) IMHO, one kind of fairness that's very clearly inspired by "1/Nth of the meta-pie for everyone" is Rawl's Veil of Ignorance.

In reality someone would have had to bake the pie, and it's fair that they get it since they put in the work. The problem is that the author, in creating the example, eliminated certain facts such as the baker in order to get to the essence of the problem. But the more facts you eliminate the more chance that something will appear arbitrary, due to fewer paths back to reality. It's the fallacy of the over-simplified model (no that's not a real fallacy :).

You cannot define fairness entirely in terms of "That which everyone agrees is 'fair'." This isn't just nonterminating. It isn't just ill-defined if Dennis doesn't believe that 'fair' is "that which everyone agrees is 'fair'". It's actually entirely empty, like the English sentence "This sentence is true."

I don't think the definition based on universal agreement is a particularly clever definition, nevertheless I don't see how it is empty. If there was something that everyone agreed was fair, then such definition would be meaningful and non-empty. It doesn't follow that the definition itself must be fair. It is your demand of fairness of the definition of fairness that makes it self-referential.

"Fair division" is 1/3 each, but if I were in Zaire's position - ie particularly hungry, or greedy, or more in need of food generally - I would ask the others to voluntarily give to me some of their "fair share" now, in return for specified (or unspecified) favours in the future.

I don't think the definition based on universal agreement is a particularly clever definition, nevertheless I don't see how it is empty. If there was something that everyone agreed was xyblz, then such definition would be meaningful and non-empty. It doesn't follow that the definition itself must be xyblz. It is your demand of xyblzness of the definition of xyblzness that makes it self-referential.

Fixed that for you.

If there was something that everyone agreed was fair, then such definition would be meaningful and non-empty.

ONLY if the agreement was based on identifiable principles. If the definition consists of nothing but the observation that people agree, then it provides information about people, not the ostensible subject.

Isn't it easier just to flip a coin and set the order of 1, 2, and 3?

then you can have each person choose the size of their slice. or to promote symmetric shares:

person 1 cuts the pie in 3
person 2 chooses a piece
person 3 chooses another piece
person 1 receives the rest

this way person one has the incentive to cut it as fair as she possibly could to ensure the overall outcome maximizes her piece (well this assumes that each person wants to maximize the pie share)

of course this is under the premise that all 3 already agree fairness at the minimal includes each person having at least a slice of the pie, and that chance is a fair way of solving this problem.

One very funny consecuence of defining "fair" as "that which everyone agrees to be "fair"" is that if you indeed could convince everyone of the correctness of that definition, nobody could ever know what IS "fair", since they would look at their definition of "fair", which is "that which everyone agrees to be "fair"", then they would look at what everyone does agree to be fair, and conclude that "that which everyone agrees to be "fair" is "that which everyone agrees to be "fair""", and so on!

However I think that in this post you are spilling too much ink over a trivial thing - you are too attached to the word "fair". One of my favourite rationalist's techniques is to not be attached to particular symbols at all, but only to referents. You could answer Zaire simply by saying, "Alright, I accept that your way is "fair", however I propose a better way that we can call "riaf"", and then explain your referent of the symbol "fair" and why it is better than Zaire's way.

Just a little nitpick.

Eliezer, I think you meant to say that "19 * 103 might not be 1957" instead of 1947. Either that or I'm misunderstanding that entire paragraph.

While it seems intuitively pretty clear that fairness involves an equal division of something - be it pie, meta-pie or whatever - there seems to be an embarrassment of plausible candidates for the quantity to be divided. Which is fairer: an equal distribution of goods, of opportunities or of utility? If I read him right, Eliezer would recommend deciding this question by first doling out an equal distribution of votes. But that just palms the dilemma off onto the voters.

While it seems intuitively pretty clear that fairness involves an equal division of something
I'd say that's wrong, and that humans believe fairness to be the appropriate division of something, with 'appropriateness' corresponding to a set of principles defining the relationship between effort, resources, and entitlement.

Sometimes equal division is seen as being fundamentally unfair. See the parable of the workers in the vineyard for a classic example.

The workers in the vineyard presumably expected that a different sort of equality was in effect - for instance, equal freedom to work at an equal rate.

When I say "equal division of something", the something isn't necessarily the pie itself.

Point taken, Lake, but it seems to me that one of the points of the parable was to contrast two different kinds of 'fairness': adherence to an agreement, and work-pay equivalence. The workers protested that those that did less work got the same pay as those that did, but the owner protested that they accepted the deal to work from an early hour to a later for a certain amount of money as 'fair' and had no grounds to complain about others receiving higher work-to-pay ratios.

Neither involves equal division of anything.

No, I suppose you're right, insofar as there's no fixed initial quantity to be divided. But both involve an equal *apportioning* of something: money to workers in the one case, and money to man-hours in the other. The parable doesn't undermine the notion that equality is essential to all concepts of fairness, even where different versions license different outcomes.

Hendrick,

That seems fair in pretty much the same sense that Eliezer's 1/N each is fair. It's just an incentive compatible way of implementing the 1/N rule.

(Also, you'd have to rule out enforceable side-deals, otherwise 1 could cut a deal with 2, such that they each get half: 1 cuts two 0 (or infitesimal) slices, leaving the entire pie for 2; in return 2 divides the whole pie with 1 (using the standard method). No, the side-deal isn't incentive compatible; that's why it needs to be enforceable. /nitpick.)

Fair is when 51% of a population can agree that they should sieze the possessions of the other 49% and divide it amongst themselves. Otherwise known as democracy. Thank god I live in a Constitutional Republic. But every day it looks more and more like a democracy.

Eliezer, I think you meant to say that "19 * 103 might not be 1957" instead of 1947. Either that or I'm misunderstanding that entire paragraph.

The setup's a little opaque, but I believe the correct reading is that the other person (characterized as honest) is correcting the faulty multiplication of the notional reader ("you").

If fairness is about something other than human agreement, what is it?

Suppose you have a rule that you say is always the fair one. And suppose that you apply it to a situation involving N people, and all N of them object, none of them think it's fair. Are you going to claim that the fair thing for them to do is something that none of them agrees to? What's fair about that?


When everybody involved in a deal agrees it's fair, who are you -- an outside kibitzer -- to tell them they're wrong?


Suppose a group all agrees, they think a deal is fair. And then you come in and persuade some of them that it isn't fair after all, that they should get more, and the agreement breaks down. Maybe they fight each other over it. Maybe some of them get hurt. And after some time contending, it's clear that none of them are better off than they were when they had their old agreement. Were you being fair to that group by destroying their agreement?

One very funny consecuence of defining "fair" as "that which everyone agrees to be "fair"" is that if you indeed could convince everyone of the correctness of that definition, nobody could ever know what IS "fair", since they would look at their definition of "fair", which is "that which everyone agrees to be "fair"", then they would look at what everyone does agree to be fair, and conclude that "that which everyone agrees to be "fair" is "that which everyone agrees to be "fair""", and so on!

An, I have no idea what you are saying here.

If a deal is fair when all participants freely agree to the deal, then there you are.

Are you saying that everybody has to agree to this definition of fairness before anybody can use it? I don't see why. People use the word "fair" when they are talking about deals. We don't all have to agree on the meaning of a word before any of us can use the word in conversation. If that was necessary, what would we say?

If some people freely agree to a deal but they still say it isn't fair -- perhaps it isn't fair to God, or to the pixies, or to somebody in Mali who isn't a party to the deal anyway -- then they can say that. Whether or not we all agree that the deal is fair, still we have a deal we all agree to.

What point is there to build an infinite regress of definitions? What is it good for?

If there was something that everyone agreed was xyblz, ...

Fixed that for you.

That's almost exactly the sort of answer I expected, except I don't see how it fixes anything.

If the definition consists of nothing but the observation that people agree, then it provides information about people, not the ostensible subject.

Depends on what we know in the beginning. If we knew the opinions of people, then it provides an information about the meaning of the word. This is the way how language is learned in the childhood - by observing what meaning other people attach to words. Even much later we learn to employ dictionaries and strict definitions.

If you define "red" as "whatever everyone agrees is red", it is for most people and everyday purposes more informative than the definition "emitting light of wavelength about 700 nm", and the definitions are practically equivalent. The difference is that we use a representative sample of population instead of a double-slit experimental setting.

Now that I've think about it more, even if we have the symmetric assumption (each person gets the same share), the pie share is not necessarily 1/n in that the utility of each person is different given a certain amount of pie.

for person 1 is not hungry at all, the pie is worth nothing to her and if she were to get 1/3 of the pie, she would not really even enjoy the consumption of it. Thus if person 1 were to get a tiny slice of pie, it could also be consider fair if we look at the symmetry in terms of utility instead of object. Well to achieve this, we can use a bidding system in which people bid for each infinitesimal part of the pie.

Either way, I believe that the argument that "each person gets 1/n of the pie is fair" is not sound because the worth of the pie is different for each person.

Hendrick, it could be argued that each person deserves to own 1/N of the pie because they are there. So if Doreen isn't hungry, she still owns 1/N of the pie which she can sell to anyone who is hungry.

Similarly it could be argued that the whole forest should be divided up and each person should own 1/N of it, and if the pie is found in the part of the forest that I own then I own that whole pie. But I have no rights to pies found in the rest of the forest.

Now suppose that all but one of the group is busy looking up into the trees at beautiful birds, which gives them great enjoyment. But Dennis instead has been working hard looking at the ground, searching for pies, and he finds one. Should he own the pie? Should he have the right to give or sell pieces to whoever he wants? Or should he have no special rights?

What if Dennis, knowing that the group will confiscate his pie if he shows it to them, eats it before they notice he has it. Is it then fair to pump his stomach so it can be divided equally?

Say it's 5 people walking through the woods, but they left 5 others back at base camp. Do the other 5 have any right to any of the pie?

If so, what if there are 5 starving children in india. Do they have any rights?

I say, Eliezer is wrong to say there is anything objectively fair about this.

If you and the others present get together and give Dennis 1/Nth of the pie - or even if you happen to have the upper hand, and you unilaterally give Dennis and yourself and all others each 1/Nth - then you are not being unfair on any level; there is no meta-level of fairness where Dennis gets the whole pie.

I agree that giving Dennis the whole pie when others disagree would not be fair. But when you disregard Dennis's opinion and dictate a solution, that isn't fair either. Just because Dennis is unable to explain his position so that you see it's right, and he does not suggest a compromise you can accept, does not make your alternative solution imposed on him fair.

There is no absolute standard of fairness here. It all depends. The concept that we should start with equal shares sounds right if you live in an egalitarian nation, otherwise not. Like, if it's a medieval english nobleman and four retainers walking through the woods, it would be idiotic to assert the pie must be split into 5 equal shares. The retainers would whip you for saying it, and they'd insist it was no more than you deserved, it was a fair response.

I say, fairness involves people who are making a deal, who are trying to be fair to each other. It is not about people who are not present, who cannot speak their minds. You aren't making a deal with starving children in india. You can be kind to them or unkind but until you can make a deal with them you can't be fair or unfair. It is not about the people back in base camp unless you made a deal with them that you will uphold or break.

If the people who are making the deal all agree it is fair, then it is fair. That's what it means for it to be fair. If some of them do not agree that it's fair then it isn't fair. It wouldn't be fair to give Dennis the whole pie, when somebody doesn't want to. It wouldn't be fair to give Dennis nothing, or 1/N of what he believes he deserves, when he doesn't agree. If you can't reach an agreement then you don't have a fair solution. Because that's what a fair solution isn't.

You can't say that just anything is fair. "Fair" isn't an empty concept that can apply to anything whatsoever. "Fair" is a concept that can apply to anything whatsoever that all participants of the deal freely agree to. If they don't agree, then it isn't fair.

Are you going to claim that the fair thing for them to do is something that none of them agrees to? What's fair about that?

Your question is only reasonable if you presume agreement is a major aspect of fairness. It only works if we already agree with the position you're forwarding, which would seem to limit its effectiveness.

Caledonian, thank you. I didn't notice that there might be people who disagree with that, since it seemed to me so clearly true and unarguable.

I guess in the extreme case somebody could believe that fairness has nothing to do with agreement. He might find a bunch of people who have a deal that each of them believes is fair, and he might argue that each of them is wrong, that their deal is actually unfair to every one of them. That each of them is deforming his own soul by agreeing to this horrible deal.

My thought about that is that there might be some deal that none of them has thought of, that would indeed be better for each of them. Maybe if they heard about the other deal they'd all prefer it. I'd want to listen to his proposals and see if I could understand them, or get new ideas from them.

But when somebody argues that a deal is unfair to somebody else, unfair to somebody who himself thinks it is not unfair to himself, it disrespects that person. It is a way to say that he doesn't know what he's doing, that he isn't competent to make his own deals, that he's a stupid or ignorant person who does not know what's good for him, that he needs you to take care of him and make his decisions for him. In general it is rude. And yet sometimes it could be true that people are stupid and agree to deals that are unfair to them because they don't know any better. There are probably 40 million american Republicans I'd suspect of that....

My sister used to be a teacher in a special education school. She would sometimes let some kids do things that other kids weren't allowed to do; a kid particularly prone to some kind of negative reaction to an otherwise mandatory activity might be allowed not to participate (I don't recall exactly). When the other kids protested that it wasn't fair, she would reply: "fair is when everyone gets what they need, not when everyone gets the same." Not totally satisfactory, but in my mind not totally bogus either. How hungry each person is *does* have some bearing on what's a fair division of the pie.

DJB:
Dr. Hanson's post today, mundane dishonesty, seems to beg the question in your scenario, "What if he's lying about how hungry he is?" There could be numerous explanations for this: power, more sex (sorry; I guess those two are the same), insurance against famine, assurance of the competition's demise, et al. In medicine, we have all sorts of tests, whether or not Dr. Hanson accepts that their interpretation leads to any meaningful intervention on health issues, to determine the status of one's nutritional state. As far as I know, we have no tests to determine the level of hunger. Is that what I see being called a "meta" issue? I can begin to see why the programming of an fAI has not been accomplished yet. Keep working, please.

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