1
A pattern is a shape
A patterned principle says holdings should be distributed according to some measure, such as equally or by need. Whether a distribution satisfies it can be read off the final list of holdings alone.
Lesson · Justice and Collective Choice · Distributive justice
Entitlement, Patterns and the Gini Coefficient
Nozick argued that justice in holdings depends on history, not pattern, and that any pattern is upset by free transfers. The Gini coefficient measures the shape, and a small exchange can be followed to the number it produces. The wrong model is that a just distribution is one with a just shape.
pattern: justice is a shape of holdings
entitlement: justice is how they arose
Gini: 0 for equal shares, higher for more gap
a free transfer moves the Gini, wrongs no one
Shape against history
Core ideas
What this lesson establishes
Two views of what makes a distribution just, and a number that lets the difference between them be seen.
2
An entitlement is a history
An historical principle says holdings are just if they were acquired justly and passed on by just transfers. Two identical lists of holdings can differ in justice if they arose differently.
3
Gini measures shape
The Gini coefficient of “Priority, Equality and Levelling Down” is 0 when everyone holds the same and rises as the gaps between people grow. It is a measure of a pattern, and so it cannot by itself say whether a pattern is just.
The material
Wilt Chamberlain and the number
An exchange small enough to follow, a measure that tracks it, and the argument that grows out of both.
Nozick's challenge to the theories of the previous two lessons is that they judge only the final list of holdings. Suppose the list is the one you think just. Then people begin to spend what they have, freely, on what they want, and the list changes. If the new list is not just, something wrong must have happened in the exchanges. If nothing wrong happened, the new list is just, and a principle that forbids it is forbidding the outcome of choices that nobody had a right to prevent.
His example is a basketball player. Four people hold 10 units each. Three of them each pay 1 to watch Wilt Chamberlain play, and he keeps what they pay. Afterwards three hold 9 and one holds 13. The total is still 40, and the shares are no longer level.
Definition · Gini coefficient
For holdings x of n people with mean m, the Gini coefficient adds up the gap between every ordered pair of people and divides by 2·n²·m. It is 0 when all holdings are equal.
For the starting list, every gap is 0, so the Gini is 0. For the list after the game, each of the three at 9 is 4 away from the person at 13. There are three such pairs, counted in both orders, so the gaps add up to 24. The divisor is 2·16·10, which is 320. The Gini is 24 / 320, which is 3/40.
That is Nozick's point as a number. A single round of voluntary payments moved the Gini from 0 to 3/40, and no one was wronged. To keep the Gini at 0 the state would have had to stop the payments, or to take the money back, and either one is an interference with people who did nothing wrong. Nozick concluded that liberty upsets patterns, and that a theory which wants a pattern must keep interfering.
Example · Two rounds
If the same three pay again, they hold 8 each and Wilt holds 16. The gaps are 8, three pairs in both orders gives 48, and the Gini is 48 / 320, which is 3/20: twice the single-round figure. A pattern is not stable under free exchange, and the lab shows the drift as a number.
What the number does not show
Three replies deserve their strength. The first is about the premises: the argument assumes the starting list was just and that every payment was free, and a critic asks what made the first list just and whether a choice made under need is as free as the story imagines. The second is Rawls's own: the difference principle is a standard for the rules of the basic structure, the law of property and taxation under which people trade, and not a pattern to be restored after each exchange, so a tax on Chamberlain's receipts is one of the rules the fans paid under and not an interference after the fact. The third is that the Gini is not what every patterned theory is about: a theory that cares only about a floor is untouched by payments made above it. Nozick's rejoinder to the second, that a tax on earnings is on a par with forced labour, is where the dispute stands.
Redistribution moves the number back. The lab's second table starts with holdings (2, 4, 6, 28), whose Gini is 1/2, and ends with (6, 8, 10, 16), whose Gini is 1/5, with the total unchanged. The total rule calls the two equal, since it only adds. Whether the move was just is the dispute between the two views, and the number is the same under both of them.
The lab measures shape. It does not know who paid whom, and a history is what the entitlement view is made of, so no tile here can pass a verdict on it.
Interactive
Two distributions, six rules
the same people ranked by total, average, priority, the worst off, and sufficiency
Method
Measuring a transfer
Five moves, working from two lists of holdings to one number each.
1
Write the holdings before and after
Use one list per moment and the same people in the same order. The total should not change in an exchange.
2
Find the mean
Add the holdings and divide by the number of people. Here it is 10 in every list.
3
Add the gap between every ordered pair
Each pair of people counts twice, once in each order. Pairs with equal holdings contribute nothing.
4
Divide by twice the square of the count, times the mean
For four people with mean 10 the divisor is 320. The result runs from 0 for equal shares upward.
5
State what the number does and does not say
It says the shape changed and by how much. Whether the change was unjust depends on how it came about, which is a fact about the history and not about the list.
Pattern and history
Score 0 / 0Choose the answer you can justify.
The Gini after one round
Four people at 10, then three of them pay 1 each to the fourth.
before 10 10 10 10 every gap 0 Gini 0
after 9 9 9 13 3 pairs, gap 4
ordered pairs counted twice: 3 x 4 x 2 = 24
divisor 2 x 4 x 4 x 10 = 320
Gini after = 24 / 320 = 3/40
The total is 40 before and after, so a rule that adds holdings sees no change. The Gini sees the whole of it.
Common mistakes
1
Thinking a just distribution is one with a just shapeOn the historical view the same list of holdings can be just or unjust, depending on how it came about. The Gini of (9, 9, 9, 13) is 3/40 whether the fans paid freely or were robbed, so the number cannot tell the two apart. A defender of patterns must say why shape matters in itself.
2
Treating the Gini as a measure of injusticeIt measures the spread of holdings and nothing else. Both a fair market and a theft can leave the same spread. An egalitarian may care about the spread and a sufficientarian may not, and the coefficient is neutral between them.
3
Reading the argument as showing that no redistribution is justifiedNozick's argument tells against patterned principles that ignore history. It leaves open a rectification of past injustice, and it assumes the starting holdings were just. If they were not, the exchanges inherit that.
Check your understanding
✓
Finish when you can compute a Gini coefficient for a short list and say what it does and does not show.
Given holdings before and after a set of payments, compute the coefficient of each, report the change, and state which view of justice treats the change as significant and which treats it as irrelevant.
Note: The rule shipped here is the total, which is deliberately blind to shape; switch it to leximin and the verdicts on the first table change, because the worst-off person lost a unit. The Gini and the leximin ranking are measuring different things, and a distribution can improve on one and worsen on the other.