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
• There are 3 plausible
ways of judging the size
of complaints:
1. How far below
average is the one
with the complaint
2. How far below the
most well off is the
one with the
complaint
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
2. How far below the
most well off is the
one with the
complaint
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.
1. How far below
average is the one
with the complaint
2. How far below the
most well off is the
one with the
complaint
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.
• The third requires some
explanation…
1. How far below
average is the one
with the complaint
2. How far below the
most well off is the
one with the
complaint
3. How those less well
off compare with
everyone who is
better off than they
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.
1. How far below
average is the one
with the complaint
2. How far below the
most well off is the
one with the
complaint
3. How those less well
off compare with
everyone who is
better off than they
Principles of Equality
• The maximin principle
of equality seeks to
first, maximize the
position of the leastwell-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 Principle
2. 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
Additive Principle
Maximin Principle
below
average
worse
then
better
below
best
worse
and
worse
worse
better and and
better
worse
below all
better
worse
then
better
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
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.
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)
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)
Range:
6
5
4
p
3
q
2
1
0
A
B
Some Common Measures of Inequality
• 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.
Some Common Measures of Inequality
• 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.
Some Common Measures of Inequality
• Economists sometimes use the following
measures of inequality:
– Range: below best + maximin
– Coefficient of Variation: below average + additive
– Gini Coefficient: below all better + additive