Inequality Larry Temkin. Studied at UW Madison, Oxford, and Princeton Currently chair of Philosophy at Rutgers.

Inequality

Larry Temkin

Larry Temkin

• Studied at UW Madison, Oxford, and Princeton

• Currently chair of Philosophy at Rutgers

Central Question:

• When is one situation worse than another with respect to inequality?

Complaints

• Temkin introduces the idea of a “complaint with respect to inequality”

• If one situation is worse than another with respect to inequality, it will be worse for some person or persons in that situation.

• That person or those persons are then said to have a complaint.

Complaint 1:

• Any who are worse off than average have a complaint.– If society has n total welfare, then any who have

less than one nth of the total through no fault of their own have a complaint.

– One who is below the average then has less than their fair share, and a complaint seems warranted in a way that it does not from anyone with their fair share or more.

Complaint 2:

• All except the most well-off have a complaint.– Consider the following diagram:

• q has a complaint in each case, because q has less than p through no fault of q.

• The presence of r and s only seem to multiply the complaints.

• The situation for q even seems worse in C than in A or B, even though q is 10 units closer to average in C than in A.

Size of Complaints

• There are 3 plausible ways of judging the size of complaints:

1. How far below average is the one with the complaint

Size of Complaints



2. How far below the most well off is the one with the complaint

Size of Complaints




3. How those less well off compare with everyone who is better off than they

Size of Complaints

• The first two parallel our thinking concerning who has a complaint.




Size of Complaints

• The first two parallel our thinking concerning who has a complaint.

• The third requires some explanation…




Size of Complaints

• The third requires some explanation…

• If it is bad to be worse off than someone else through no fault of your own, it is worse to be worse off than more than one such person.




Principles of Equality

• The maximin principle of equality seeks to first, maximize the position of the least-well-off group, and then minimize the number of people in that group.

1. Maximin Principle

Principles of Equality

• The additive principle simply adds together the sizes of each complaint, and worlds with a greater total complaint are worse than worlds with less total complaint.

1. Maximin Principle2. Additive Principle

THE SEQUENCE

• Temkin’s main tool to think about inequality is a series of simple situations referred to as “The Sequence”.

THE SEQUENCE

• Temkin’s main tool to think about inequality is a series of simple situations referred to as “The Sequence”.

• The Sequence represents 999 distinct situations to be analyzed with respect to inequality

• Notice that both the total and average utility get worse and worse as the sequence progresses.

• Notice that both the total and average utility get worse and worse as the sequence progresses.

• For our purposes, this is an irrelevant feature. We simply want to know what inequality does over the course of the sequence.

• View 1: The sequence gets BETTER AND BETTER with respect to inequality.

• View 1: The sequence gets BETTER AND BETTER with respect to inequality.– The distance between those who have less and

the average decreases as the sequence progresses

• View 1: The sequence gets BETTER AND BETTER with respect to inequality.– The number of people better off than those who

are less well off decreases as the sequence continues.

• View 1: The sequence gets BETTER AND BETTER with respect to inequality.– It looks like someone is unjustly punished at the

beginning and someone is unjustly rewarded at the end, and unjust punishments are more objectionable than unjust rewards.

• View 1: The sequence gets BETTER AND BETTER with respect to inequality.– The maximin principle of equality prefers the

complaints to be more evenly distributed, instead of heaped upon a few or one.

• View 1: The sequence gets BETTER AND BETTER with respect to inequality.– The costs to the well-off to fix the inequality

increase as the sequence progresses, and the gain for the worse-off decreases as the sequence progresses, so the inequality is more egregious at the beginning and less so at the end.

• View 2: The sequence gets WORSE AND WORSE with respect to inequality.

• View 2: The sequence gets WORSE AND WORSE with respect to inequality.– The additive principle states that the more people

with a complaint, the worse a situation is.

• View 2: The sequence gets WORSE AND WORSE with respect to inequality.– At the beginning, the worse-off has a complaint

against the best-off. As the sequence progresses, more people have the same complaint.

• View 3: The sequence gets WORSE THEN BETTER with respect to inequality.– The endpoints are closer to absolute equality than

the middle, so as the sequence progresses, we move further from absolute equality, and then closer past the midpoint.

• View 3: The sequence gets WORSE THEN BETTER with respect to inequality.– If you look at complaints against all those who are better

off and use the additive principle, then the middle, where a large number have a large complaint will be worse than the beginning, where a small number have a large complaint, and the end where a large number have a small complaint.

• View 3: The sequence gets WORSE THEN BETTER with respect to inequality.– If you look at complaints of all those who are below

average and use the additive principle, then the middle, where a large number have a large complaint will be worse than the beginning, where a small number have a large complaint, and the end where a large number have a small complaint.

• View 4: The sequence gets BETTER THEN WORSE with respect to inequality.

• View 4: The sequence gets BETTER THEN WORSE with respect to inequality.– “By now it may seem that there are bound to be

several plausible positions supporting the judgment that the Sequence first gets better, then gets worse. If there are such elements, however, I am not aware of them.” (116)

• View 5: The worlds of the sequence are EQUIVALENT with respect to inequality.

• View 5: The worlds of the sequence are EQUIVALENT with respect to inequality.– If social institutions there are are responsible for

the presence of inequality, but not for the number of people in each group, then the worlds of the sequence are equivalent.

• View 5: The worlds of the sequence are EQUIVALENT with respect to inequality.– Temkin’s analogy: two judges who accept bribes

for all their cases are equally corrupt even if one has tried fewer cases than the other.

The Complexity of Inequality:

• If there are only two general principles of equality, and only three ways of having complaints with respect to inequality (which is surely false) then there are six different ways to explain what is happening with The Sequence, broken down as follows:

The Complexity of Inequality

below average

below best

below all better

Additive Principle

worse then better

worse and worse

worse then better

Maximin Principlebetter and better

worse and worse

better and better

Fractal Complexity

• There are surely additional plausible principles of equality, which, when combined with the reasons for complaint (which may well number more than three) yield further distinct analyses of inequality.

Fractal Complexity

• There are surely additional plausible principles of equality, which, when combined with the reasons for complaint (which may well number more than three) yield further distinct analyses of inequality.

• There are also specific modifications of both the principles of equality and the reasons for complaint that yield further variation.

Fractal Complexity

• Also, consider any situation more complex than The Sequence (e.g. real life) and you see that there are a great many plausible ways to think about when a situation is better or worse than another with respect to inequality.

Common Measures of Inequality

• Economists sometimes use the following measures of inequality:

Common Measures of Inequality

• Economists sometimes use the following measures of inequality:– Range: calculates the difference between the

highest and lowest observations of a particular variable of interest

Some Common Measures of Inequality

• Economists sometimes use the following measures of inequality:– Range: the difference between the highest and

lowest observations of a particular variable of interest




– Coefficient of Variation: the standard deviation of a variable divided by the mean.





– Gini Coefficient: a measure of the degree of deviation from perfect equality (see following)





– Gini Coefficient: a measure of the degree of deviation from perfect equality (see following)

Range:

A B0

1

2

3

4

5

6

pq


• Economists sometimes use the following measures of inequality:– Range: below best + maximin– Coefficient of Variation: the standard deviation of

a variable divided by the mean.– Gini Coefficient: a measure of the degree of

deviation from perfect equality (see following)

• The curve on the left has more people below the average and more people far below the average than does the much tighter curve on the right, so the sum totals of each individual complaint will be higher in blue than red.


• Economists sometimes use the following measures of inequality:– Range: below best + maximin– Coefficient of Variation: below average + additive– Gini Coefficient: a measure of the degree of

deviation from perfect equality (see following)

• Because the total area between the curve and perfect equality, each person with less is being compared to how many people have more and how much more they all have.


• Economists sometimes use the following measures of inequality:– Range: below best + maximin– Coefficient of Variation: below average + additive– Gini Coefficient: below all better + additive

Inequality Larry Temkin. Studied at UW Madison, Oxford, and Princeton Currently chair of Philosophy at Rutgers.

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