"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.
Eliezer's conception of fairness does not account for a whole category of "fairnesses". Let me put the devil's shoes.
There are many ways to divide the pie fairly. You may divide it according to the amount of people. In which case each person gets 1/Nth. But my way is more fair. You should divide it according to the weight of each individual, in which case Big Joe gets more than Tiny Anny.
Agile Carlos stands up and says: No, the fair way is according to metabolic rates.
It is naïve to say that the pie should be divided equally between persons, since the numerical level of personhood is not the factor that best correlates with what food is useful for.
To decide what should a pie be divided according to, we would start to play Reference Class tennis, because it is hard to decide if fairness should be symmetric on the person, the metabolic, or the size level.
So even though arguments will stop Zaire from taking the whole pie, I am still not nearly convinced that it is obvious that 1/Nth is fair.
There's a technical definition in mechanism design: a mechanism (say for allocating goods) is Fair if all participants derive equal utility from participating.
Could you provide a reference for this? The use of interpersonal comparison of utility here surprises me.
I thought that the usual definition of fairness took into account both what you gain from your participation and what other people gain from your participation.
ETA: Are you referring to the same notion of fairness as in this famous paper by Rabin?
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 somethingI'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.
This whole pie-splitting story is an intuition pump that invites me to apply my embedded primate social judgments while pretending to some kind of objective analysis, which makes me distrust it.
That is: if Xannon, Yancy, and Zaire agree to give Zaire the whole pie, something deep in my primate soul howls "Unfair!" and all subsequent discussion is conducted in the context of that judgment.
This is true even when I conclude that the behavior is sensible. For example, if we specify that there's only enough pie to keep one of them from starving, such that giving each of them a third of the pie results in all three of them dying, I'll grudgingly agree that Zaire getting the whole pie is better than all three of them getting a third... but "grudgingly" is a key word. I resist this conclusion.
And I will feel better if we explicitly state that the process whereby Z got the whole pie lets me model it as something being equally shared, even if the something is as abstract as "the chance of getting the whole pie".
If we specify instead that Z likes blueberry pie 1000 times as much as Y and X do, I might similarly do a little mapping in my head from "pie" to "utility" and satisfy the howling primate by asserting that they are all getting equal "utility" when Z gets most of the pie. If we specify that Z is grateful for being given the whole pie, I can satisfy the primate by invoking some complicated notion of social contracts and indebtedness and that conveniently works out to everyone getting equal amounts of . If we tell an aesop where an hour later Z is by complete chance mauled by a lion (or better yet, is mauled by a lion because he smells so strongly of blueberry... or the pie turns out to be poisoned... or in some other way Z gets some of his "unfairly" obtained extra utilons taken away, preferably in a way that's causally linked to the pie-taking) my howling primate is mollified. If we tell an aesop where an hour later X and Y get extra utilons (say, God lets them into Heaven, again preferably because they showed by not getting any pie), my howling primate is mollified.
A notion of equity among sufficiently me-like things is important to my howling primate soul, it seems.
Whether I identify with that aspect of myself or not is a different question. (As is whether I ought to identify with it.) A lot of this discussion so far seems to take that as a given.
OTOH, if I reframe the story as three ants finding a crumb of pie-crust (and I refrain from anthropomorphising the ants, which is tempting), I notice that a lot of my intuitions about the importance of fairness change. If one of them eats the whole crumb and the other two don't interfere... well, OK. I'm curious as to how that resolution was computed, but I don't start out with the notion that it's WRONG WRONG WRONG. I suspect I'm more likely to think clearly about it.
Admittedly, had you written a story about three unanthropomorphized ants finding a crumb, not many people would care. Your whole goal here is to pump people's intuitions, and that's fine.
But for my own part, I distrust it.
among humans, I think, only people of good will can do complicated things without incurring large overhead costs from politics
That is a startlingly succinct summary of an important principle. I am likely to quote it a lot.
...when you encounter a pie in the forest, in the company of friends...
Happens to me all the time :)
Followup to: The Bedrock of Fairness
In "The Bedrock of Fairness", Xannon, Yancy, and Zaire argue over how to split up a pie that they found in the woods. Yancy thinks that 1/3 each is fair; Zaire demands half; and Xannon tries to compromise.
Dividing a pie fairly isn't as trivial a problem as it may sound. What if people have different preferences for crust, filling, and topping? Should they each start with a third, and trade voluntarily? But then they have conflicts of interest over how to divide the surplus utility generated by trading...
But I would say that "half for Zaire" surely isn't fair.
I confess that I originally wrote Zaire as a foil—this is clearer in an earlier version of the dialog, where Zaire, named Dennis, demands the whole pie—and was surprised to find some of my readers taking Zaire's claim seriously, perhaps because I had Zaire say "I'm hungry."
Well, okay; I believe that when I write a dialogue, the reader has a right to their own interpretation. But I did intend that dialogue to illustrate a particular point:
You can argue about how to divide up the pie, or even argue how to argue about dividing up the pie, you can argue over what is fair... but there finally comes a point when you hit bedrock. If Dennis says, "No, the fair way to argue is that I get to dictate everything, and I now hereby dictate that I get the whole pie," there's nothing left to say but "Sorry, that's just not what fairness is—you can try to take the pie and I can try to stop you, but you can't convince that that is fair."
A "fair division" is not the same as "a division that compels everyone to admit that the division is fair". Dennis can always just refuse to agree, after all.
But more to the point, when you encounter a pie in the forest, in the company of friends, and you try to be fair, there's a certain particular thing you're trying to do—the term "fair" is not perfectly empty, it cannot attach to just anything. Metaphorically speaking, "fair" is not a hypothesis equally compatible with any outcome.
Fairness expresses notions of concern for the other agents who also want the pie; a goal to take their goals into account. It's a separate question whether that concern is pure altruism, or not wanting to make them angry enough to fight. Fairness expresses notions of symmetry, equal treatment—which might be a terminal value unto you, or just an attempt to find a convenient meeting-point to avoid an outright battle.
Is it fair to take into account what other people think is "fair", and not just what you think is "fair"?
The obvious reason to care what other people think is "fair", is if they're being moved by similar considerations, yet arriving at different conclusions. If you think that the Other's word "fair" means what you think of as fair, and you think the Other is being honest about what they think, then you ought to pay attention just by way of fulfilling your own desire to be fair. It is like paying attention to an honest person who means the same thing you do by "multiplication", who says that 19 * 103 might not be 1947. The attention you pay to that suggestion, is not a favor to the other person; it is something you do if you want to get the multiplication right—they're doing you a favor by correcting you.
Politics is more subject to bias than multiplication. And you might think that the Other's reasoning is corrupted by self-interest, while yours is as pure as Antarctic snow. But to the extent that you credit the Other's self-honesty, or doubt your own, you would do well to hear what the Other has to say—if you wish to be fair.
The second notion of why we might pay attention to what someone else thinks is "fair", is more complicated: it is the notion of applying fairness to its own quotation, that is, fairly debating what is "fair". In complicated politics you may have to negotiate a negotiating procedure. Surely it wouldn't be fair if Dennis just got to say, "The fair resolution procedure is that I get to decide what's fair." So why should you get to just decide what's fair, then?
Here the attention you pay to the other person's beliefs about "fairness", is a favor that you do to them, a concession that you expect to be met with a return concession.
But when you set out to fairly discuss what is "fair" (note the strange loop through the meta-level), that doesn't put everything up for grabs. A zeroth-order fair division of a pie doesn't involve giving away the whole pie to Dennis—just giving identical portions to all. Even though Dennis wants the whole thing, and asks for the whole thing, the zeroth-order fair division only gives Dennis a symmetrical portion to everyone else's. Similarly, a first-order fair attempt to resolve a dispute about what is "fair", doesn't involve conceding everything to the Other's viewpoint without reciprocation. That wouldn't be fair. Why give everything away to the Other, if you receive nothing in return? Why give Dennis the whole first-order pie?
On some level, then, there has to be a possible demand which would be too great—a demand exceeding what may be fairly requested of you. This is part of the content of fairness; it is part of what you are setting out to do, when you set out to be fair. Admittedly, one should not be too trigger-happy about saying "That's too much!" We human beings tend to overestimate the concessions we have made, and underestimate the concessions that others have made to us; we tend to underadjust for the Other's point of view... even so, if nothing is "too much", then you're not engaging in fairness.
Fairness might call on you to hear out what the Other has to say; fairness may call on you to exert an effort to really truly consider the Other's point of view—but there is a limit to this, as there is a limit to all fair concessions. If all Dennis can say is "I want the whole pie!" over and over, there's a limit to how long fairness requires you to ponder this argument.
You reach the bedrock of fairness at the point where, no matter who questions whether the division is fair, no matter who refuses to be persuaded, no matter who offers further objections, and regardless of your awareness that you yourself may be biased... Dennis still isn't getting the whole pie. If there are others present who are also trying to be fair, and Dennis is not already dictator, they will probably back you rather than Dennis—this is one sign that you can trust the line you've drawn, that it really is time to say "Enough!"
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.
Now I'm sure there are some in the audience who will say, "You and perhaps some others, are merely doing things your way, rather than Dennis's." On the contrary: We are merely being fair. It so happens that this fairness is our way, as all acts must be someone's way to happen in the real universe. But what we are merely doing, happens to be, being fair. And there is no level on which it is unfair, because there is no level on which fairness requires unlimited unreciprocated surrender.
I don't believe in unchangeable bedrock—I believe in self-modifying bedrock. But I do believe in bedrock, in the sense that everything has to start somewhere. It can be turtles all the way up, but not turtles all the way down.
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." Is that sentence true? Is it false? It is neither; it doesn't mean anything because it is entirely wrapped up in itself, with no tentacle of relation to reality. If you're going to argue what is fair, there has to be something you're arguing about, some structure that is baked into the question.
Which is to say that you can't turn "fairness" into an ideal label of pure emptiness, defined only by the mysterious compulsion of every possible agent to admit "This is what is 'fair'." Forget the case against universally compelling arguments—just consider the definition itself: It has absolutely no content, no external references; it is not just underspecified, but entirely unspecified.
But as soon as you introduce any content into the label "fairness" that isn't phrased purely in terms of all possible minds applying the label, then you have a foundation on which to stand. It may be self-modifying bedrock, rather than immovable bedrock. But it is still a place to start. A place from which to say: "Regardless of what Dennis says, giving him the whole pie isn't fair, because fairness is not defined entirely and only in terms of Dennis's agreement."
And you aren't being "arbitrary", either—though the intuitive meaning of that word has never seemed entirely well-specified to me; is a tree arbitrary, or a leaf? But it sounds like the accusation is of pulling some answer out of thin air—which you're not doing; you're giving the fair answer, not an answer pulled out of thin air. What about when you jump up a meta-level, and look at Dennis's wanting to do it one way, and your wanting a different resolution? Then it's still not arbitrary, because you aren't being unfair on that meta-level, either. The answer you pull out is not merely an arbitrary answer you invented, but a fair answer. You aren't merely doing it your way; the way that you are doing it, is the fair way.
You can ask "But why should you be fair?"—and that's a separate question, which we'll go into tomorrow. But giving Dennis 1/Nth, we can at least say, is not merely and only arbitrary from the perspective of fair-vs.-unfair. Even if Dennis keeps saying "It isn't fair!" and even if Dennis also disputes the 1st-order, 2nd-order, Nth-order meta-fairnesses. Giving N people each 1/Nth is nonetheless a fair sort of thing to do, and whether or not we should be fair is then a separate question.
Part of The Metaethics Sequence
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