What Is Justice, and What Is Fair? The Rule That Can't See Your Name

You lent your brother forty dollars for a concert ticket last spring.

It's been months. He hasn't brought it up, and neither have you.

Then your family weighs in. Your mom, who watched you hand him the money, says, "I'll tell him he owes you." Your sister says, "I'll just cover it, so you two can drop it." Your brother, who has finally noticed the subject exists, says, "I helped your friend Dana move on Saturday. That's worth forty dollars. We're even."

Each of them is trying to make it right. Is any of them doing justice?

There's a second word hiding in the same house. Your mom has one ticket left for the next show and two kids who both want it. What would make the way she hands it out fair?

Justice and fairness are two of the biggest words in morality, and most of us can't say exactly what either one means. We only know when something has broken it. Reality's moral code gives each word an exact meaning, and this post works both out.

The short answer

Justice is a correction on the bond between two people, and both of them write it. Nobody outside the bond pays for it. A bond is the record's entry for a relationship. It's kept in two copies, one in each person's own books, and nobody writes in anyone else's books. So an act may change a bond only when both of its ends write the change. Your mom can say what she saw. Your sister can give you money. Your brother can help Dana. None of them writes your bond with your brother. Only the two of you can.

Fairness means the moral code can't see names. Swap who is who, and every verdict stays the same. For the code to give two cases different verdicts, they have to differ in a physical fact, never just in names. Two things follow. When a good divides, like a pot of soup, exactly one split is permitted, and for two kids with mirror-image claims it's the equal one. When a good doesn't divide, like one ticket, and the two claims are mirror images, the two ways of giving it tie, and either one is permitted.

The reason, in short: reality keeps a permanent record of every event, because the basic laws of physics never destroy information. A relationship between two people is a comparison, and it's recorded twice, once at each end. Every comparison has a cost, zero only when its two sides match. The code is a verdict on acts that reads only facts of the record: what an act does to the bonds, and who wrote it. A name isn't one of those facts. The section after the route gives each reason in full.

Here's the whole answer in seven steps. The rest of this post takes them one at a time and shows how we know each one.

1. What's due is read from what happened. You offered the loan, he accepted, you handed over the money, and nothing has come back. Two true records of a bond agree, so when two records disagree, at least one is false.
2. Justice is a correction both ends write. Bringing a bond back to level changes it, so both ends write the repair. Others can help. They can't write it.
3. Nobody outside pays, and nothing nets out. No act moves the burden of someone who didn't write it, and a benefit on one bond never settles a wrong on another.
4. A wrong stays written, and its correction takes two. The correction is a new line. If one end won't write, no act can move the bond, and both ends keep carrying its cost.
5. Fairness is name-blindness. The verdict reads what an act does and who wrote it. Two cases get different verdicts only when they differ in a physical fact.
6. One split, or a free tie. When a good divides, exactly one split is permitted, and for mirror-image claims it's the equal one. When it doesn't divide and the claims are mirror images, the two ways tie, and the choice is free.
7. Fair is judged on the whole record. Each end carries a bond's whole cost and the record counts it once, so an act isn't judged on each person's burden.

Why this matters: justice and fairness stop being feelings and become structure you can point at. A correction has two authors and one address, the bond it changes, so you can say whose writes it takes. Fairness is a property of the verdict, and you can test it: swap the names and see whether the verdict moves. For the ticket, it settles what your mom is stuck on. If the two claims are exact mirror images, either way of giving it out is permitted.

Here's the route. Each step ends with a line on why the next one comes next.

What this post stands on

Four starting claims, each with its reason.

The past still exists. Every event leaves a complete trace, and none is ever erased. The reason starts in known physics: the basic laws never destroy information. In quantum mechanics that's unitarity. The present fixes the past exactly, and running the laws backward recovers every earlier state. Inside the record the same holds by its own rule: writing a new entry never alters an earlier one.¹ What an entry is rests on a separate fact. Each entry is a comparison, one thing told apart from another, as every measurement and every perception is, and a comparison needs information about both of the things it compares. Earlier posts call this permanent record the Ledger, and Part 1 tells the full story.

A relationship is a comparison with two ends, and each end keeps its own books. A comparison needs both of its things, so the record's unit is a relation between two ends. The record's entry for a relationship is a bond, and its number is one end's amount divided by the other's: 1 when they match. Read from the other end, the number x becomes 1/x, and that changes nothing. Each end keeps its own record of the bond in its own books and writes only there. A write is an end's entry in its own books. An act is a change written in the actor's books, or in both ends' books when two people act together. Nobody writes in another's books.

A bond has a cost, and the formula is forced. A bond at 1 is level and costs nothing. Any other number costs: J(x) = (x + 1/x)/2 - 1, the number plus its flip, halved, minus 1. The cost measures imbalance, and it isn't a choice. A cost has to be zero only when the two sides match, grow as they differ, and be the same whichever side you put first. Add the rule for how the costs of combined comparisons add, and one calibration of how sharply the cost rises near level, and exactly one formula is left.² Meet in the Middle builds it from scratch.

A person's burden is the total cost of the bonds they're an end of, each counted in full.

There is one moral code, and it fits in a paragraph. An act is admissible when it meets four clauses: it touches only bonds that exist now, leaves every record of every bond true, changes a bond only when both of its ends write on it, and ends a bond only when one of its own two ends ends it. Of the admissible acts, the code permits exactly those that leave the least total cost on the complete record, which counts every moment still to come. Every other act is forbidden. That's the code's verdict on an act: permitted or forbidden. Doing nothing is always admissible, so something is always permitted.³ Right and Wrong Aren't Opinions works out the whole code on a promise to bring someone groceries. This post uses it on a debt and on shares.

Step 1: What's due is read from what happened

What one person owes another is read from what happened between them: the offer, the acceptance, the delivery, the repayment. Two true records of a bond agree, so when two records disagree, at least one is false.

Here's the loan as a bond. Count what each of you has paid for the other. Say that before last spring you were even, 40 dollars each way. Then you paid 40 dollars for his ticket. Now you're at 80 and he's at 40. The bond reads 80 to 40, which is the number 2. From his end it reads 1/2. The cost is 1/4 either way, the value in the table above.

What he owes is the 40 dollars that would bring the bond back to level. It comes from four kinds of event: you offered, he accepted, you handed over the money, and nothing has come back. Nobody has to rank who deserves what afterward. The events already say.

Now suppose he writes "even, 40 each" in his own book. Your book says 80 to 40. The two records of the bond disagree. Two true records agree, so one of these is false, and the events say which one: you handed over the money. A disagreement between two records isn't a claim against anyone. It means a record is false.

How we know. The arithmetic is the example's own, and a pencil checks it. That a debt is read from the events is the code's own reading: what's due comes from what happened,³ and a denial written in someone's book leaves it unchanged.⁴

One step here isn't derived yet: that the physical record carries what is due, with the two people as the bond's two ends. The dollars are a drawing of what a real debt compares, and which physical amounts those are belongs to the same step.

Next, and why: the debt is real, and it's still there. What does it take to put the bond right, and who writes it?

Step 2: Justice is a correction both ends write

Bringing a bond back to level changes it, so both of its ends write the repair. That's justice: a correction on one bond, written by both of its ends. Others can help. They can't write it.

Justice is the correction that's owed, carried out exactly, with nobody else carrying any of it. Step 1 found what's owed. This step is who carries it out. Step 3 is the "nobody else."

Say he pays you back. For the bond to read 80 to 80, his side moves and yours takes it. He writes "paid 40" in his book. You write "received 40" in yours. That's two writes and one correction.

Why can't one of you do it alone? Say you write "paid in full" in your book and he writes nothing. An end that doesn't write keeps its old record of the bond, and that record stays true only if the bond doesn't move. So your write alone can't move the bond, and your book is now the false one. The code excludes any act that leaves a record false, which is its second clause. On true books, its third clause says the same thing from the other side: an act may move a bond only when both of its ends write on it. That clause is about acts, and acts are what move bonds: a bond changes only through what someone sends, and sending is an act. A Favor Isn't a Yes works through the same rule with dinners, and shows why nobody can write your side.

An outsider isn't an end of the bond at all, so whatever they write goes in their own books. Your mom saw you hand over the money. She can say so, and what's due is read from what happened. Your sister can give you forty dollars. That's a new entry on her bond with you, written by her and by you. It's real help. It isn't the correction of your bond with your brother, because she isn't an end of it.

How we know. The rule comes from how the record is kept: each end writes only in its own books, so an act that changes a bond has to show up in both. "Both ends write" holds exactly when each person's record of a bond holds one exact state of it. That step isn't derived yet.

Next, and why: if only the two ends write the correction, can somebody else pay for it? Your sister has already offered.

Step 3: Nobody outside pays, and nothing nets out

No act moves the burden of anyone who didn't write it, so a bystander can't be made to pay for a correction. And a benefit on one bond never settles a wrong on another.

Suppose someone arranges things so that your sister pays, and she never agreed. Forty dollars of hers ends up with you anyway. That act changes her bond with you, and she wrote nothing. A push is a false entry in another person's own books. The code's third clause, that an act may change a bond only when both people on it write the change, excludes it. That holds at the step an act is done, on any books, and however much the push would save. Consent is a hard condition, not a price. Put any finite charge on a false record, and some push still comes out ahead, because the relief a push can buy grows without bound. So the clauses come first, and cost only compares the acts that pass them. Right and Wrong Aren't Opinions works through a settlement that lowers the total while a bystander pays.

Now your sister really does offer, and you both write it. That's allowed, and it's real. It's a new entry on her bond with you, and it leaves your bond with your brother exactly as it was. He still owes you forty.

Your brother's offer works the same way. Helping Dana move is a benefit on his bond with Dana. It doesn't touch his bond with you. Two acts on separate bonds, done together, are judged exactly as the two acts are. A wrong on one bond isn't settled by a benefit on another.

How we know. Both come from the clauses. An act may change a bond only when both of its ends write on it, and your sister and Dana aren't ends of your bond with your brother. No act of theirs, and nothing he does for them, changes it.

Next, and why: now put the pieces together. What does the code say to do about a wrong that has already happened?

Step 4: A wrong stays written, and its correction takes two

A wrong stays written. Its correction is a new line, and it takes both ends of the bond. If one end won't write, no act can move the bond. Nobody outside writes the correction or pays for it.

Say it has gone wrong: your brother accepted the loan, and now he says he won't pay it back. Here's what the code says.

• The wrong stays. Nothing recorded is erased. If he repays next month, that's a new line after this month, and this month stays written. Forgiving the debt is a new line too. Sorry Doesn't Rewind the Tape works through repair and forgiveness, and the exact shape a correction takes: carried out between the two people, with nobody else touched.
• The correction takes two. Bringing a bond to level changes it, so both ends write the repair (Step 2).
• One end can't close it alone. If he doesn't write, no act can move the bond. It stays at 2 and costs 1/4, and both of you keep carrying that. Writing "paid" in your own book doesn't change the bond. It makes your book false.
• Not writing doesn't move the cost off him. A bond at 2 and a bond at 1/2 cost the same 1/4, so the one who's owed carries exactly what the one who owes carries. Nobody comes out ahead in cost by leaving a bond lopsided.
• Cutting him off doesn't close it. You're one of the bond's two ends, so you can end it, and nobody outside can. But ending a lopsided bond removes the only way to repair it, and the ended bond stays on the record with all of its cost. An ended bond keeps its cost: no allowed act touches it, and nothing moves a bond between acts.
• Nobody outside writes it or pays for it. Others can say what happened, and they can give you what they have on their own bonds (Steps 2 and 3).

That's what the code says about correcting a wrong. The next question is punishment. At the step an act is done, a penalty that changes a wrongdoer's relationships without the wrongdoer's write breaks the clauses like any push. What a wrong calls for is repair, and a repair changes the relationship, so both ends write it. The wrong's charge stays on the record whatever follows.

How we know. Each line is the code at work: nothing recorded is erased, an act may change a bond only when both ends write, an end that doesn't write keeps its old record, J(2) = J(1/2), and no act moves the burden of someone who didn't write it.

Next, and why: that's justice. Now the other word. The same code gives it an exact meaning, and it starts with what the code can't see.

Step 5: Fairness is name-blindness

Rename the people, read any bond from its other end, or multiply every cost by the same positive number: no verdict changes. The code reads an act only through what it does and who wrote it, never through who's who. So two cases get different verdicts only when they differ in a physical fact.

Take any case and swap two names: Ann becomes Ben and Ben becomes Ann, in every bond and every act. Nothing physical has changed. Whoever held the bond at 2 still holds it, and whoever wrote an entry still wrote it. So no verdict changes: what was permitted for the one holding that bond is still permitted for them, whatever they're now called. Read a bond from its other end: 2 becomes 1/2, with the same cost, so the same verdict. Multiply every cost by 7: every act that was permitted still is, and every act that was forbidden still is.

Why can't the code read names? It reads only facts of the record. An act gets its verdict through what it does: how it changes the bonds it touches, which bonds it ends, and who wrote it. Two acts that leave the same world with the same authors get the same verdict. A name isn't a fact of the record. Swap every name and the record is the same record.

That's fairness, exactly: the same case gets the same verdict. It asks more than it sounds like. A different verdict needs a different fact: what was offered, who accepted, who wrote, what each bond reads. It isn't a rule that everyone gets the same. It's a rule that a name carries no weight.

Nobody added fairness to the code. It's what's left when a verdict reads only what happens.

How we know. Invariance is one of the code's six properties, and it follows from what the code is: a verdict on the record, and the record's facts are what happened, not what anyone is called. The preprint states the consequence in full: a different moral answer to the same case needs a different physical fact, or a judgment of a different form.³

Next, and why: what does name-blindness say when something has to be shared? First a good that divides, then one that doesn't.

Step 6: One split, or a free tie

When a good divides, exactly one split is permitted, and for two kids with mirror-image claims it's the equal one. When a good doesn't divide and the claims are mirror images, the two ways of giving it tie, and either is permitted.

Take Ann and Ben, two kids whose claims are mirror images: the same hunger, the same history with whoever is sharing, the same in everything the record holds about them.

A good that divides: a pot of soup. The pot holds 8 spoonfuls, all 8 get served, and they're served once, now. The soup divides: between any two ways of serving it, every way in between is available too. (The soup is a drawing. Which physical quantities a real claim compares is the open step from Step 1.)

There's only one best split. The cost curve is a bowl. Take a bond at 1 and a bond at 4. The one halfway between them is 2, because 1 to 2 is one doubling and 2 to 4 is another. The two ends cost 0 and 9/8, which average 9/16. The one halfway between costs 1/4, less than the average of the ends. That holds for any two different bonds. So suppose two different splits both left the least cost. The split halfway between them would cost less than their average, and their average is the least. That can't happen. Two different splits never tie when the good divides, so exactly one is permitted.

And it's the equal one. Suppose the permitted split were 5 spoonfuls to Ann and 3 to Ben. Swap the names. It's the same case, so the verdict swaps too, and 3 to Ann and 5 to Ben is permitted as well. Now two different splits are permitted, and exactly one is. So 5 and 3 isn't it. The only split that is its own mirror image is 4 and 4.

The equal bowls aren't a rule somebody chose. They're two facts multiplied: a cost that's a bowl, so there's one best split, and a code that can't see names, so the best split has to be its own mirror image.

A good that doesn't divide: one ticket. Ann and Ben have mirror-image claims on one ticket. Three acts are available: give it to Ann, give it to Ben, or give it to nobody. Giving it to nobody leaves two claims unmet, which costs more. Giving it to Ann leaves Ben's unmet, and giving it to Ben leaves Ann's. Those two acts are mirror images: swap the names and one turns into the other. The total cost reads only the bonds' numbers, never names, so mirror images cost the same, and they tie. The code permits every admissible act that leaves the least cost, and that's both.

Does any name-blind rule pick Ann? Whatever it says, swap the names and it says the swapped thing about the swapped case, and the swapped case is the same case. So it picks Ben too. A rule that can't see names can't pick one of two mirror images. That isn't a hole in the code. It's what not seeing names means.

This is where choice is free. The code's own line is that freedom exists only between acts that tie at the least cost. Flip a coin or go with a hunch. The code doesn't pick, and it doesn't require a lottery or any other method, because a coin and a hunch that both give the ticket to Ann leave the same world with the same authors, and the verdict reads only that.

If one of the two had a claim the other didn't, the claims wouldn't be mirror images, and something physical would differ between them. Which claim comes first then, and how a claim gets its authority, isn't derived yet.

How we know. That a bowl-shaped cost leaves exactly one permitted outcome when the acts divide is the code's own statement.³ The equal split is a deduction from that and Step 5, not a separate result. The tie follows from Step 5 and the judgment: permitted means least cost among admissible acts, so two equal least costs mean two permitted acts. That no name-blind rule picks one of two mirror images holds for any case that looks the same after the swap.

Next, and why: one more thing about how the code counts, because it decides what "fair" can't mean.

Step 7: Fair is judged on the whole record

Each end of a bond carries the bond's whole cost, and the record counts the bond once. So an act is judged on the record's cost, not on each person's burden.

Back to the loan. The bond reads 2 from your end and 1/2 from his, and costs 1/4 either way. Each of you is an end of it, so each of you carries the whole 1/4. The record's own total counts the bond once, so the loan adds 1/4 to the record, not 1/4 + 1/4.

What does counting once change? Here's an example. Take Ann and Ben again. Each has a bond of their own, a number for how heavy their own load is, and 1 is level there too. They share one bond. At the start their own bonds are level and cost nothing, and the shared bond reads 2 and costs 1/4. Each of them carries 1/4.

Now an act: each person's own bond goes from 1 to 2, and the shared bond goes from 2 to 1. Afterward each person's own bond costs 1/4 and the shared bond costs nothing. Each still carries exactly 1/4. Nobody's burden changed.

The record changed. Before, it cost 0 + 0 + 1/4 = 1/4. After, it costs 1/4 + 1/4 + 0 = 1/2. Doing nothing leaves it at 1/4, so another admissible act leaves less, and the code forbids this one.

So an act can leave every burden exactly where it was and still make the record worse. Fairness is the same verdict for the same case, and the case is the whole record, counted bond by bond, not each person's burden.

How we know. The symmetry J(x) = J(1/x) is the formula's own. The burden and the real-cost counts are the code's definitions.³ Why the code totals bond by bond and not person by person isn't derived yet, and neither is how much a person's own bond weighs.

Next, and why: what's still open, said plainly, and then the whole trip in one breath.

What's still being worked out

The code is proved in part and still being derived in part. Eight things touch this post:

• What's owed. That the physical record carries what is due, with the two people as a bond's two ends. The dollars, the soup and the ticket are drawings, and which physical amounts a real debt or claim compares is part of this step.
• Why both ends write. That each person's record of a bond holds one exact state of it. "An act may change a bond only when both ends write" holds exactly when it does.
• Reserves. One gap stays open at reserves: the clauses take an act's writes and books as handed over, so a taking from a reserve passes them with no write. Whether reading consent through the amounts an act moves closes it is being derived.
• Competing claims. Which claim comes first when two claims conflict and aren't mirror images, and how a claim gets its authority and loses it.
• Counting. Why the code totals cost bond by bond rather than person by person, and how much a person's own bond weighs.
• From charge to ought. The step from "the record charges this cost without bound" to "this ought not be done," which is what makes "forbidden" bind.
• One judgment. That the code's verdict at one moment and its verdict over time agree. The one-split and tie results here are for a single moment.
• Prices and wages. What a fair price or a fair wage is has no derived answer yet.

The whole trip, in one breath

Justice is a correction on the bond between two people. What's due is read from what happened between them. A bond lives in two books, and nobody writes in anyone else's books, so an act may change a bond only when both of its ends write the change. The correction is theirs: an outsider can say what happened or give what they have on their own bonds, and can't write it. Nobody outside pays, and a benefit on one bond never settles a wrong on another. A wrong stays written, its correction is a new line, and if one end won't write, no act can move the bond and both ends keep carrying its cost. Fair is the code's blindness to names: swap who is who and every verdict stays the same, so a different verdict needs a different fact. When a good divides, one split is permitted, and for mirror-image claims it's the equal one. When it doesn't divide and the claims are mirror images, the two ways tie and either is permitted. And the code counts the whole record, bond by bond, not each person's burden.

That's how reality is built: a record kept twice, one cost on every bond, and a code that reads only what happens. Justice has an address. Fairness has no names.