## 1. Economics and Ethics



The role of ethics in economic theorizing is still a debated issue. In
spite of the reluctance of many economists to view normative issues as
part and parcel of their discipline, normative economics now
represents an impressive body of literature. One may, however, wonder
if normative economics cannot also be considered a part of political
philosophy.


### 1.1 Positive vs. Normative Economics



In the first half of the twentieth century, most leading economists
(Pigou, Hicks, Kaldor, Samuelson, Arrow etc.) devoted a significant
part of their research effort to normative issues, notably the
definition of criteria for the evaluation of public policies. The
situation is very different nowadays. "Economists do not devote
a great deal of time to investigating the values on which their
analyses are based. Welfare economics is not a subject which every
present-day student of economics is expected to study", writes
Atkinson (2001, p. 195), who regrets "the strange disappearance
of welfare economics". Normative economics itself may be partly
guilty for this state of affairs, in view of its repeated failure to
provide conclusive results and its long-lasting focus on impossibility
theorems (see
 SS 4.1).
 But there has also been a persistent ambiguity about the status of
normative propositions in economics. The subject matter of economics
and its close relation to policy advice make it virtually impossible
to avoid mingling with value judgments. Nonetheless, the desire to
separate positive statements from normative statements has often been
transformed into the illusion that economics could be a science only
by shunning the latter. Robbins (1932) has been influential in this
positivist move, in spite of a late clarification (Robbins 1981) that
his intention was not to disparage normative issues, but only to
clarify the normative status of (useful and necessary) interpersonal
comparisons of welfare. It is worth emphasizing that many results in
normative economics are mathematical theorems with a primary
analytical function. Endowing them with a normative content may be
confusing, because they are most useful in clarifying ethical values
and do not imply by themselves that these values must be endorsed.
"It is a legitimate exercise of economic analysis to examine the
consequences of various value judgments, whether or not they are
shared by the theorist." (Samuelson 1947, p. 220) The role of
ethical judgments in economics has received recent and valuable
scrutiny in Sen (1987), Hausman and McPherson (2006) and Mongin
(2001b).


### 1.2 Normative Economics and Political Philosophy



There have been many mutual influences between normative economics and
political philosophy. In particular, Rawls' difference principle
(Rawls 1971) has been instrumental in making economic analysis of
redistributive policies pay some attention to the maximin criterion,
which puts absolute priority on the worst-off, and not only to
sum-utilitarianism. (It has taken more time for economists to realize
that Rawls' difference principle applies to primary goods, not
utilities.) Conversely, many concepts used by political philosophers
come from various branches of normative economics (see below).



There are, however, differences in focus and in methodology. Political
philosophy tends to focus on the general issue of social justice,
whereas normative economics also covers microeconomic issues of
resource allocation and the evaluation of public policies in an unjust
society (although there is now philosophical work on non-ideal
theory). Political philosophy focuses on arguments and basic
principles, whereas normative economics is more concerned with the
effective ranking of social states than the arguments underlying a
given ranking. The difference is thin in this respect, since the
axiomatic analysis in normative economics may be interpreted as
performing not only a logical decomposition of a given ranking or
principle, but also a clarification of the underlying basic principles
or arguments. But consider for instance the "leveling-down
objection" (Parfit 1995), which states that egalitarianism is
wrong because it considers that there is *something* good in
achieving equality by leveling down (even when the egalitarian ranking
says that, *all things considered*, leveling down is bad). This
kind of argument has to do with the reasons underlying a social
judgment, not with the content of the all things considered judgment
itself. It is hard to imagine if and how the leveling-down objection
could be incorporated in the models of normative economics. A final
difference between normative economics and political philosophy,
indeed, lies in conceptual tools. Normative economics uses the formal
apparatus of economics, which gives powerful means to derive
non-intuitive conclusions from simple arguments, although it also
deprives the analyst of the possibility of exploring issues that are
hard to formalize.



There are now several general surveys of normative economics, some of
which do also cover the intersection with political philosophy: Arrow,
Sen and Suzumura (1997, 2002, 2011), Fleurbaey (1996), Hausman and
McPherson (2006, rev. and augmented in Hausman et al. 2016), Kolm
(1996), Moulin (1988, 1995, 1998), Roemer (1996), Young (1994).


## 2. Inequality and Poverty Measurement



Focusing traditionally on income inequality and poverty, this field
has been first built on the assumption that there is a given
unidimensional measure of individual advantage. The gist of the
analysis is then about the distribution of this particular notion of
advantage.



More recently, partly due to the emergence of data about living
conditions, there has been growing interest in the measurement of
inequality and poverty when individual situations are described by a
multidimensional list of attributes or deprivations. This has
generated the field of "multidimensional inequality and poverty
measurement".



So far most of this literature has remained disconnected from the
welfare economics literature in which interpersonal comparisons of
well-being in relation to individual preferences is a key issue. The
typical multidimensional indices do not refer to well-being or
preferences. But the connection is being made and the welfare
economics literature will eventually blend with the inequality and
poverty measurement literature.



Excellent surveys of the unidimensional part of the theory include:
Chakravarty (1990, 2009), Cowell (2000), Dutta (2002), Lambert (1989),
Sen and Foster (1997), Silber (1999). The multidimensional approach is
surveyed or discussed in Weymark (2006), Chakravarty (2009), Decancq
and Lugo (2013), Aaberge and Brandolini (2015), Alkire et al. (2015),
Duclos and Tiberti (2016). The link between inequality and poverty
measurement and welfare economics is discussed in Decancq et al.
(2015) and in several chapters of Adler and Fleurbaey (2016). For a
comprehensive handbook on economic inequality, see Atkinson and
Bourguignon (2000, 2015).


### 2.1 Indices of Inequality and Poverty



The study of inequality and poverty indices started from a
statistical, pragmatic perspective, with such indices as the Gini
index of inequality or the poverty head count. Recent research has
provided two valuable insights. First, it is possible to relate
inequality indices to social welfare functions, so as to give
inequality indices a more transparent ethical content. The idea is
that an inequality index should not simply measure dispersion in a
descriptive way, but would gain in relevance if it measured the harm
to social welfare done by inequality. There is a simple method to
derive an inequality index from a social welfare function, due to Kolm
(1969) and popularized by Atkinson (1970) and Sen (1973). Consider a
social welfare function which is defined on distributions of income
and is symmetrical (i.e., permuting the income of two individuals
leaves social welfare unchanged). For any given unequal distribution
of income, one may compute the egalitarian distribution of income
which would yield the same social welfare as the unequal distribution.
This is called the "equally-distributed equivalent" (or
"equal-equivalent") distribution. If the social welfare
function is averse to inequality, the total amount of income in the
equal-equivalent distribution is less than in the unequal
distribution. In other words, the social welfare function condones
some sacrifice of total income in order to reach equality. This drop
in income, measured in proportion of the initial total income, may
serve as a valuable index of inequality. This index may also be used
in a picturesque decomposition of social welfare. Indeed, an ordinally
equivalent measure of social welfare is then total income (or average
income - it does not matter when the population is fixed) times
one minus the inequality index.



This method of construction of an index of inequality, often referred
to as the *ethical approach* to inequality measurement, is most
useful when the argument of the social welfare function, and the
object of the measurement of inequality, is the distribution of
individual well-being (which may or may not be measured by income).
Then the social welfare function is indeed symmetrical (by requirement
of impartiality) and its aversion to inequality reflects its
underlying ethical principles. In other contexts, the method is more
problematic. Consider the case when social welfare depends on
individual well-being, and individual well-being depends on income
with some individual variability due to differential needs. Then
income equality may no longer be a valuable goal, because the needy
individuals may need more income than others. Using this method to
construct an index of inequality of *well-being* is fine, but
using it to construct an index of inequality of *incomes* would
be strange, although it would immediately reveal that income
inequality is not always bad (when it compensates for unequal needs).
Now consider the case when social welfare is the utilitarian sum of
individual utilities, and all individuals have the same strictly
concave utility function (strict concavity means that it displays a
decreasing marginal utility). Then using this method to construct an
index of income inequality is amenable to a different interpretation.
The index then does not reflect a principled aversion to inequality in
the social welfare function, since the social welfare function has no
aversion to inequality of utilities. It only reflects the consequence
of an empirical fact, the degree of concavity of individual utility
functions. To call this the ethical approach, in this context, seems a
misnomer.



In the field of multidimensional inequality or poverty measurement, a
key divide has separated the measures that evaluate the distribution
in every dimension (such as income, health, asset deprivation...)
before they aggregate over the dimensions, from the measures that
first evaluate individual situations, all dimensions included, before
aggregating over individuals. The latter has been praised (Decancq and
Lugo 2013) for being closer to the standard individualistic approach
in welfare economics, and for making it possible to have measures that
are sensitive to the correlation between disadvantages (e.g., the
positive correlation between income and health), and therefore more
accurately record the multidimensional suffering of the worst off. An
interesting feature of such measures is that a positive correlation
among attributes of advantage or disadvantage worsens inequalities
only if the elasticity of substitution between attributes, in the
measure of individual multidimensional advantage, is greater than the
inequality aversion in the social index. To illustrate, consider two
canonical distributions, with two individuals and two attributes:



(Perfect correlation) Ann: (1,1) and Bob: (2,2)



(Anti-correlation) Ann: (1,2) and Bob: (2,1)



If the attributes are deemed perfectly substitutable (meaning that
only the sum, potentially weighted, of the attributes matters for the
assessment of individual advantage), and the inequality aversion is
zero (meaning that only the sum of individual indexes of advantage
matters), the two distributions are considered equally good. But they
also appear equally good if there is no possible substitution (only
the value of the worst attribute matters) and inequality aversion is
infinite (only the worst-off individual matters). In contrast, the
first distribution appears worse if the attributes are substitutable
and inequality aversion is strong (the first distribution is then
unequal, unlike the second one); whereas it appears better if there is
no possible substitution and inequality aversion is weak (only one
individual has a bad attribute in the first distribution, whereas both
have one in the second).



The second valuable contribution of recent research in this field is
the development of an alternative ethical approach through the
axiomatic study of the properties of indices. The main ethical axioms
deal with transfers. The Pigou-Dalton principle of transfers says that
inequality decreases (or social welfare increases) when an even
transfer is made from a richer to a poorer individual without
reversing their pairwise ranking (although this may alter their
ranking relative to other individuals). Since this condition is about
even transfers, it is quite weak and other axioms have been proposed
in order to strengthen the priority of the worst-off. The principle of
diminishing transfers (Kolm 1976) says that a Pigou-Dalton transfer
has a greater impact the lower it occurs in the distribution. The
principle of proportional transfers (Fleurbaey and Michel 2001) says
that an inefficient transfer in which what the donor gives and what
the beneficiary receives is proportional to their initial positions
increases social welfare. Similar transfer axioms have been adapted to
the measurement of poverty. For instance, Sen (1976) proposed the
condition saying that poverty increases when an even transfer is made
from someone who is below the poverty line to a richer individual
(below or above the line). The other axioms with which the axiomatic
analysis has been made usually have a less obvious ethical appeal, and
relate to decomposability of indices, scale invariance and the like.
Characterization results have been obtained, which identify classes of
indices satisfying particular lists of axioms. The two ethical
approaches may be combined, when one takes as an axiom the condition
that the index be derived from a social welfare function with
particular features.


### 2.2 The Dominance Approach



The multiplicity of indices, even when a restriction to special
sub-classes may be justified by axiomatic characterization, raises a
serious problem for applications. How can one make sure that a
distribution is more or less unequal, or has more or less poverty,
than another without checking an infinite number of indices? Although
this may look like a purely practical issue, it has given rise to a
broad range of deep results, relating the statistical concept of
stochastic dominance to general properties of social welfare functions
and to the satisfaction of transfer axioms by inequality and poverty
indices. This approach, in particular, justifies the widespread use of
Lorenz curves in the empirical studies of inequality. The Lorenz curve
depicts the percentage of the total amount of whatever is measured,
income, wealth or well-being, possessed by any given percentage of the
poorest among the population. For instance, according to the Census
Bureau, in 2006 the poorest 20%'s share of total income was
3.7%, the poorest 40%'s share was 13.1%, the poorest 60%'s
share was 28.1%, the poorest 80%'s share was 50.6%, while the
top 5%'s share was 22.2%. This indicates that the Lorenz curve
is approximately as in the following figure.



![graph of lorenz curve](lorenz2006.png)


Considerable progress has been made in the development of dominance
techniques of the Lorenz type, with extensions to multidimensional
inequality and to poverty measurement (Aaberge and Brandolini
2015).


### 2.3 Equality, Priority, Sufficiency



Philosophical interest in the measurement of inequality has recently
risen (Temkin 1993). Most of this philosophical literature, however,
tends to focus on defining the right foundations for an aversion to
inequality. In particular, Parfit (1995) proposes to give priority to
the worse-off not because of their relative position compared to the
better-off, but because and to the extent that they are badly off.
This probably corresponds to defining social welfare by an additively
separable social welfare function, with diminishing marginal social
utility (a social welfare function is additively separable when it is
the sum of separate terms, each of which depends only on one
individual's well-being). Interestingly, if egalitarianism is
defined in opposition to this "priority view" by the
feature that it relies on judgments of relative positions, this means
that egalitarian values cannot be correctly represented by a separable
social welfare function. This seems to raise the ethical stakes
concerning properties of decomposability of indices or separability of
social welfare functions, which are usually considered in economics
merely as convenient conditions simplifying the functional forms
(although separability may also be justified by the subsidiarity
principle, according to which unconcerned individuals need not have a
say in a decision). The content and importance of the distinction
between egalitarianism and prioritarianism remains a matter of debate
(see, among many others, Tungodden 2003, and the contributions in
Holtug and Lippert-Rasmussen 2007). It is also interesting to notice
that philosophers are often at ease to work with the notion of social
welfare (or social good, or inequality) as a numerical quantity with
cardinal meaning, whereas economists typically restrict their
interpretation of social welfare or inequality to a purely ordinal
ranking of social states. Beside egalitarian and prioritarian
positions one must also mention the "sufficiency view",
defended e.g. by Frankfurt (1987) who argues that priority should be
given only to those below a certain threshold. One may consider that
this view supports the idea that poverty indices might summarize
everything that is relevant about social welfare.


## 3. Welfare Economics



Welfare economics is the traditional generic label of normative
economics, but, in spite of substantial variations between authors, it
now tends to be associated with a particular subcontinent of this
domain, maybe as a result of the development of
"non-welfarist" approaches and of approaches with a
broader scope, such as the theory of social choice.



Surveys on welfare economics in its restricted definition can be found
in Graff (1957), Boadway and Bruce (1984), Chipman and Moore (1978),
Samuelson (1981). Many topics of welfare economics are addressed in
the more recent handbooks by Arrow, Sen and Suzumura (2002, 2011),
Atkinson and Bourguignon (2000, 2015) and Adler and Fleurbaey (2016).
Accessible introductions are given by (book-length) Adler (2019) and
(article-length) Fleurbaey (2019).


### 3.1 Old and New Welfare Economics



The proponents of a "new" welfare economics (Hicks,
Kaldor, Scitovsky) have distanced themselves from their predecessors
(Marshall, Pigou, Lerner) by abandoning the idea of making social
welfare judgments on the basis of interpersonal comparisons of
utility. Their problem was then that in absence of any kind of
interpersonal comparisons, the only principle on which to ground their
judgments was the Pareto principle, according to which a situation is
a global improvement if it is an improvement for every member of the
concerned population (there are variants of this principle depending
on how individual improvement is defined, in terms of preferences or
some notion of well-being, and depending on whether it is a strict
improvement for all members or some of them stay put). Since most
changes due to public policy hurt some subgroups for the benefit of
others, the Pareto principle remains generally silent. The need for a
less restrictive criterion of evaluation has led Kaldor (1939) and
Hicks (1939) to propose an extension of the Pareto principle through
compensation tests. According to Kaldor's criterion, a situation
is a global improvement if ex post the gainers could compensate the
losers. For Hicks' criterion, the condition is that ex ante the
losers could not compensate the gainers (a change from situation A to
situation B is approved by Hicks' criterion if the change from B
to A is not approved by Kaldor's criterion). These criteria are
much less partial than the Pareto principle, but they remain partial
(that is, they fail to rank many pairs of alternatives). This is not,
however, their main drawback. They have been criticized for two basic
flaws. First, for plausible definitions of how the compensation
transfers could be computed, these criteria may lead to inconsistent
social judgments: the same criterion may simultaneously declare that a
situation A is better than another situation B, and conversely.
Scitovsky (1941) has proposed to combine the two criteria, but this
does not prevent the occurrence of intransitive social judgments.
Second, the compensation tests have a dubious ethical value. If the
compensatory transfers are performed in Kaldor's criterion, then
the Pareto criterion alone suffices since after compensation everybody
gains. If the compensatory transfers are not performed, the losers
remain losers and the mere possibility of compensation is a meager
consolation to them. Such criteria are then typically biased in favor
of the rich whose willingness to pay is generally high (i.e., they are
willing to give a lot in order to obtain whatever they want, and
therefore they can easily compensate the losers; when they do not
actually pay the compensation, they can have the cake and eat it
too).



Cost-benefit analysis has more recently developed criteria which are
very similar and rely on the summation of willingness to pay across
the population. In spite of repeated criticism by specialists (Arrow
1951, Boadway and Bruce 1984, Sen 1979, Blackorby and Donaldson 1990),
practitioners of cost-benefit analysis and some branches of economic
theory (industrial organization, international economics) still
commonly rely on such criteria. More sophisticated variants of
cost-benefit analysis (Layard and Glaister 1994, Dreze and
Stern 1987) avoid these problems by relying on weighted sums of
willingness to pay or even on consistent social welfare functions.
Adler (2012) offers a comprehensive study of the foundations of the
social welfare function approach to cost-benefit analysis. Many
specialists of public economics (e.g. Stiglitz 1987) have considered
that the Pareto criterion was the core ethical principle on which
economists should buttress their social evaluations, and that they
should focus on denouncing all sources of inefficiency in social
organizations and public policies.



A subfield of welfare economics focused on the possibility of making
social welfare judgments on the basis of national income. An increase
in national income may reflect an increase in social welfare under
some stringent assumptions, most conspicuously the assumption that the
distribution of incomes is socially optimal. Although very
restrictive, this kind of result has a lasting influence, in theory
(international economics) and in practice (the salience of GDP growth
in policy discussions). There exists a school of social indicators
(see the *Social Indicators Research* journal) which fights
this influence and the number of alternative indicators (of happiness,
genuine progress, social health, economic well-being, etc.) has soared
in the last decades (see e.g. Miringoff and Miringoff 1999, Frey and
Stutzer 2002, Kahneman et al. 2004 and Gadrey and Jany-Catrice
2006).



Bergson (1938) and Samuelson (1947, 1981) occupy a special position,
which may be described as a third way between old and new welfare
economics. From the former, they retain the goal of making complete
and consistent social welfare judgments with the help of well-defined
social welfare functions. The formula
*W*(*U*1(*x*),...,*Un*(*x*))
is often named a "Bergson-Samuelson social welfare
function" (*x* is the social state;
*Ui*(*x*), for
*i*=1,...,*n*, is individual *i*'s
utility in this state). With the latter, however, they share the idea
that only ordinal non-comparable information should be retained about
individual preferences. This may seem contradictory with the formula
of the Bergson-Samuelson social welfare function, in which individual
utility functions appear, and there has been a controversy about the
possibility of constructing a Bergson-Samuelson social welfare
function on the sole basis of individual ordinal non-comparable
preferences (see in particular Arrow (1951), Kemp and Ng (1976),
Samuelson (1977, 1987), Sen (1986) and a recent discussion in
Fleurbaey and Mongin (2005)). Samuelson and his defenders are commonly
considered to have lost the contest, but it may also be argued that
their opponents have misunderstood them. Indeed, individual utility
functions in the
*W*(*U*1(*x*),...,*Un*(*x*))
formula are, according to Bergson and Samuelson, to be constructed out
of individual preference orderings, on the basis of fairness
principles. The logical possibility of such a construction has been
repeatedly proven by Samuelson (1977), Pazner (1979), Mayston (1974,
1982). The fact that such a construction does not require any other
information than ordinal non-comparable preferences is indisputable.
Bergson and Samuelson acknowledged the need for interpersonal
comparisons, but considered that these could be done, in an ethically
relevant way, on the sole basis of non-comparable preference
orderings. They failed, however, to be more specific about the
fairness principles on which the construction could be justified. The
theory of fair allocation (see
 SS 6)
 may fill the gap.


### 3.2 Harsanyi's Theorems



Harsanyi may be viewed as the last representative of the old welfare
economics, to which he made a major contribution in the form of two
arguments. The first one is often called the "impartial observer
argument". An impartial observer should decide for society as if
she had an equal chance of becoming anyone in the considered
population. This is a risky situation in which the standard decision
criterion is expected utility. The computation of expected utility, in
this equal probability case, yields an arithmetic mean of the
utilities that the observer would have if she became anyone in the
population. Harsanyi (1953) considers this to be an argument in favor
of utilitarianism. The obvious weakness of the argument, however, is
that not all versions of utilitarianism would measure individual
utility in a way that may be entered in the computation of the
expected utility of the impartial observer. In other words, ask a
utilitarian to compute social welfare, and ask an impartial observer
to compute her expected utility. There is little reason to believe
that they will come up with similar conclusions, even though both
compute a sum or a mean. For instance, a very risk-averse impartial
observer may come arbitrarily close to the maximin criterion.



This argument has triggered controversies, in particular with Rawls
(1974), about the soundness of the maximin criterion in the original
position, and with Sen (1977b). See Harsanyi (1976) and recent
analyses in Weymark (1991), Mongin (2001a). There is a related, but
different controversy about the consequences of the veil of ignorance
in Dworkin's hypothetical insurance scheme (Dworkin 2000).
Roemer (1985) argues that if individuals maximize their expected
utility on the insurance market, they insure against states in which
they have low marginal utility. If low marginal utility happens to be
the consequence of some handicaps, then the hypothetical market will
tax the disabled for the benefit of the others, a paradoxical but
typical consequence of utilitarian policies. It is indeed well known
that insurance markets have strange consequences when utilities are
state-dependent (that is, when the utility of income is affected by
random events). For a recent revival of this controversy, see Dworkin
(2002), Fleurbaey (2008) and Roemer (2002a).



Harsanyi's second argument, the "aggregation
theorem", is about a social planner who, facing risky prospects,
maximizes expected social welfare and wants to respect individual
preferences about prospects. Harsanyi (1955) shows that these two
conditions imply that social welfare must be a weighted sum of
individual utilities, and concludes that this is another argument in
favor of utilitarianism. Recent evaluation of this argument and its
consequences may be found in Broome (1991), Weymark (1991). In
particular, Broome uses the structure of this argument to conclude
that social good must be computed as the sum of individual goods,
although this does not preclude incorporating a good deal of
inequality aversion in the measurement of individual good. Diamond
(1967) has raised a famous objection against the idea that expected
utility is a good criterion for the social planner. This criterion
implies that if the social planner is indifferent between the
distributions of utilities, for two individuals, (1,0) and (0,1), then
he must also be indifferent between these two distributions and an
equal probability of getting either distribution. This is paradoxical,
this lottery being ex ante better since it gives equal prospects to
individuals. Broome (1991) raises another puzzle. An even better
lottery would yield either (0,0) or (1,1) with equal probability. It
is better because ex ante it gives individuals the same prospects as
the previous lottery, and it is more egalitarian ex post. The problem
is that it seems quite hard to construct a social criterion which
ranks these four alternatives as suggested here. Defining social
welfare under uncertainty is still a matter of bafflement. See
Deschamps and Gevers (1977), Ben Porath, Gilboa and Schmeidler (1997),
Fleurbaey (2010). Things are even more difficult when probabilities
are subjective and individual beliefs may differ. Harsanyi's
aggregation theorem then transforms into an impossibility theorem. On
this, see in particular Hylland and Zeckhauser (1979), Mongin (1995),
Bradley (2005), Mongin and Pivato (2016, 2020), Dietrich (2021).


## 4. Social Choice



The theory of social choice in its modern incarnation originated in
Arrow's pioneering work. Arrow himself described it as a
'subversive' attempt to 'operationalize' the
Bergson-Samuelson approach (Arrow 1983, 26), but it could equally be
viewed as extending the tradition of earlier work on voting and
committee decisions, going back to Condorcet and Black. It has
developed into an immense literature, with many ramifications to a
variety of subfields and topics. The social choice framework is,
potentially, so general that one may think of using it to unify
normative economics. In a restrictive definition, however, social
choice is considered to deal with the problem of synthesizing
heterogeneous individual preferences into a consistent ranking.
Sometimes an even more restrictive notion of "Arrovian social
choice" is used to name works which faithfully adopt
Arrow's particular axioms.



There are many surveys of social choice theory, in broad and
restrictive senses: Arrow, Sen and Suzumura (1997, in particular chap.
3, 4, 7, 11, 15; 2002, in particular chap. 1, 2, 3, 4, 7, 10; 2011, in
particular chap. 13, 14, 17-20), Sen (1970, 1977a, 1986, 1999,
2009), Anand, Puppe and Pattanaik (2009). See also the entry on
 social choice theory.


### 4.1 Arrow's Theorem



In an attempt to construct a consistent social ranking of a set of
alternatives on the basis of individual preferences over this set,
Arrow (1951) obtained: 1) an impossibility theorem; 2) a
generalization of the framework of welfare economics, covering all
collective decisions from political democracy and committee decisions
to market allocation; 3) an axiomatic method which set a standard of
rigor for any future endeavor.



The impossibility theorem roughly says that there is no general way to
rank a given set of (more than two) alternatives on the basis of (at
least two) individual preferences, if one wants to respect three
conditions: (Weak Pareto) unanimous preferences are always respected
(if everyone prefers A to B, then A is better than B); (Independence
of Irrelevant Alternatives) any subset of two alternatives must be
ranked on the sole basis of individual preferences over this subset;
(No-Dictatorship) no individual is a dictator in the sense that his
strict preferences are always obeyed by the ranking, no matter what
they and the other individuals' preferences are. The
impossibility holds when one wants to cover a great variety of
possible profiles of individual preferences. When there is sufficient
homogeneity among preferences, for instance when alternatives differ
only in one dimension and individual preferences are based on the
distance of alternatives to their preferred alternative along this
dimension (think, for instance, of political options on the left-right
spectrum), then consistent methods exist (the majority rule, in this
example; Black 1958).



Arrow's result clearly extends the scope of analysis beyond the
traditional focus of welfare economics, and nicely illuminates the
difficulties of democratic voting procedures such as the Condorcet
paradox (consisting of the fact that majority rule may be
intransitive). The analysis of voting procedures is wide domain. For
recent surveys, see e.g. Saari (2001) and Brams and Fishburn (2002),
as well as the entry on
 Arrow's Theorem.
 This analysis reveals a deep tension between rules based on the
majority principle and rules which protect minorities by taking
account of preferences in a more extended way (see Pattanaik
2002).



Specialists of welfare economics once claimed that Arrow's
result had no bearing on economic allocation (e.g. Samuelson 1967),
and there is some ambiguity in Arrow (1951) about whether, in an
economic context, the best application of the theorem is about
individual self-centered *tastes* over personal consumptions,
in which case it is indeed relevant to welfare economics, or about
individual ethical *values* about general allocations. It is
now generally considered that the formal framework of social choice
can sensibly be applied to the Bergson-Samuelson problem of ranking
allocations on the basis of individual tastes. Applications of
Arrow's theorem to various economic contexts have been made (see
the surveys by Le Breton 1997, Le Breton and Weymark 2011).


### 4.2 The Informational Basis



Sen (1970a) proposes a further generalization of the social choice
framework, by permitting consideration of information about individual
utility functions, not only preferences. This enlargement is motivated
by the impossibility theorem, but also by the ethical relevance of
various kinds of data. Distributional issues obviously require
interpersonal comparisons of well-being. For instance, an egalitarian
evaluation of allocations needs a determination of who the worst-off
are. It is tempting to think of such comparisons in terms of
utilities. This has triggered an important body of literature which
has greatly clarified the meaning of various kinds of interpersonal
utility comparisons (of levels, differences, etc.) and the relation
between them and various social criteria (egalitarianism,
utilitarianism, etc.). This literature (esp. d'Aspremont and
Gevers 1977) has also provided an important formal analysis of the
concept of welfarism, showing that it contains two subcomponents. The
first one is the Paretian condition that an alternative is equivalent
to another when all individuals are indifferent between them. This
excludes using non-welfarist information about alternatives, but does
not exclude using non-welfarist information about individuals (one
individual may be favored because of a physical handicap). The second
one is an independence condition formulated in terms of utilities. It
may be called Independence of Irrelevant Utilities (Hammond 1987), and
says that the social ranking of any pair of alternatives must depend
only on utility levels at these two alternatives, so that a change in
the profile of utility functions which would leave the utility levels
unchanged at the two alternatives should not alter how they are
ranked. This excludes using non-welfarist information about
individuals, but does not exclude using non-welfarist information
about alternatives (one may be preferred because it has more freedom).
The combination of the two conditions excludes all non-welfare
information. Excellent surveys are given in d'Aspremont (1985),
d'Aspremont and Gevers (2002), Bossert and Weymark (2004),
Mongin and d'Aspremont (1998). In spite of the important
clarification made by this literature, the introduction of utility
functions essentially amounts to going back to old welfare economics,
after new welfare economics and authors such as Bergson, Samuelson and
Arrow failed to provide appealing solutions with data on consumer
tastes only.



A related issue is how the evaluation of individual well-being must be
made, or, equivalently, how interpersonal comparisons must be
performed. There is now a growing interest in exploring concrete ways
of measuring individual well-being, as illustrated by happiness
studies (section 7.5 below) and the handbook published by Adler and
Fleurbaey (2016). Welfare economics traditionally relied on
"utility", and the extended informational basis of social
choice is mostly formulated with utilities (although the use of
extended preference orderings is often shown to be formally
equivalent: for instance, saying that Jones is better-off than Smith
is equivalent to saying that it is better to be Jones than to be
Smith, in some social state). But utility functions may be given a
variety of substantial interpretations, so that the same formalism may
be used to discuss interpersonal comparisons of resources,
opportunities, capabilities and the like. In other words, one may
separate two issues: 1) whether one needs more information than
individual preference orderings in order to perform interpersonal
comparisons; 2) what kind of additional information is ethically
relevant (subjective utility or objective notions of opportunities,
etc.). The latter issue is directly related to philosophical
discussions about how well-being should be conceived and to the
"equality of what" debate. This debate, which originates
with Sen (1980), focuses on seeking the appropriate metric of
advantage that should be used by theories of justice that are
egalitarian or that give priority to the worst-off.



The former issue is still debated. Extending the informational basis
by introducing numerical indices of well-being (or equivalent extended
orderings) is not the only conceivable extension. Arrow's
impossibility is obtained with the condition of Independence of
Irrelevant Alternatives, which may be logically analyzed, when the
theorem is reformulated with utility functions as primitive data, as
the combination of Independence of Irrelevant Utilities (defined
above) with a condition of ordinal non-comparability, saying that the
ranking of two alternatives must depend only on individuals'
ordinal non-comparable preferences. Arrow's impossibility may be
avoided by relaxing the ordinal non-comparability condition, and this
is the above-described extension of the informational basis by relying
on utility functions. But Arrow's impossibility may also be
avoided by relaxing Independence of Irrelevant Utilities only. In
particular, it makes sense to rank alternatives on the basis of how
these alternatives are considered by individuals in comparison to
other alternatives. For instance, when considering to make a transfer
of consumption goods from Jones to Smith, it is not enough to know
that Jones is against it and Smith is in favor of it (this is the only
information usable under Arrow's condition). It is also relevant
to know if both consider that Jones has a better bundle, or not, which
involves considering other alternatives in which bundles are permuted,
for instance. In this vein, Hansson (1973) and Pazner (1979) have
proposed to weaken Arrow's axiom so as to make the ranking of
two alternatives depend on the indifference curves of individuals at
these two alternatives. In particular, Pazner relates this approach to
Samuelson's (Samuelson 1977) and concludes that the
Bergson-Samuelson social welfare function can indeed be constructed
consistently in this way. Interpersonal comparisons may be sensibly
made on the sole basis of indifference curves and therefore on the
sole basis of ordinal non-comparable preferences. This requires
broadening the concept of interpersonal comparisons in order to cover
all kinds of comparisons, not just utility comparisons (see Fleurbaey
and Hammond 2004).



The concept of informational basis itself need not be limited to
issues of interpersonal comparisons. Many conditions of equity,
efficiency, separability, responsibility, etc. bear on the kind and
quantity of information that is deemed relevant for the ranking of
alternatives. The theory of social choice gives a convenient framework
for a rigorous analysis of this issue.


### 4.3 Around Utilitarianism



The theory of social choice with utility functions has greatly
systematized our understanding of social welfare functions. For
instance, it has shown how to construct a continuum of intermediate
social welfare functions between sum-utilitarianism and the maximin
criterion (or its lexicographic refinement, the leximin criterion,
which ranks distributions of well-being by examining first the
worst-off position, then the position which is just above the
worst-off, and so on; for instance, the maximin is indifferent between
the three distributions (1,2,5), (1,3,5) and (1,3,6), whereas the
leximin ranks them in increasing order). Three other developments
around utilitarian social welfare functions are worth mentioning.



The first development is related to the application of theories of
equality of opportunity, and involves the construction of mixed social
welfare functions which combine utilitarianism and maximin. Suppose
that there is a double partition of the population, such that one
would like the social welfare function to display infinite inequality
aversion within subgroups of the first partition, and zero inequality
aversion within subgroups of the second partition. For instance,
subgroups of the first partition consist of equally deserving
individuals, for which one would like to obtain equality of outcomes,
whereas subgroups of the second partition consist of individuals who
have equal opportunities, so that inequalities among them do not
matter. Van de gaer (1993) proposes to apply average utilitarianism
within each subgroup of the second partition, and to apply the maximin
criterion to the vector of average utilities obtained in this way. In
other words, the average utilities measure the value of the
opportunity sets offered to individuals, and one applies the maximin
criterion to such values, in order to equalize the value of
opportunity sets. Roemer (1998) proposes to apply the maximin
criterion within each subgroup of the first partition, and then to
apply average utilitarianism to the vector of minimum utilities
obtained in this way. In other words, one tries to equalize outcomes
for equally deserving individuals first, and then applies a
utilitarian calculus. These may not be the only possible combinations
of utilitarianism and maximin, but they are given an axiomatic
justification which suggests that they are indeed salient, in Ooghe,
Schokkaert and Van de gaer (2007) and Fleurbaey (2008). For a survey
on the applications of Roemer's criterion, see Roemer (2002b)
and, more recently, Ferreira and Peragine (2016), Roemer and Trannoy
(2016), Ramos and Van de gaer (2016).



A second interesting development deals with intergenerational ethics.
With an infinite horizon, it is essentially impossible to combine the
Pareto criterion and anonymity (permuting the utilities of some
generations does not change social welfare) in a fully satisfactory
way, even when utilities are perfectly comparable. This is a similar
but more basic impossibility than Arrow's theorem. The intuition
of the problem can be given with the following simple example.
Consider the following sequence of utilities: (1,2,1,2,...).
Permute the utility of every odd period with the next one. One then
obtains (2,1,2,1,...). Then permute the utility of every even
period with the next one. This yields (2,2,1,2,...). This third
sequence Pareto-dominates the first one, even though it was obtained
only through simple permutations. This impossibility is now better
understood, and various results point to the "catching up"
criterion as the most reasonable extension of sum-utilitarianism to
the infinite horizon setting. This criterion, which does not rank all
alternatives, applies when the finite-horizon sums of utilities, for
two infinite sequences of utilities, are ranked in the same way for
all finite horizons above some finite time. Interestingly, this topic
has seen parallel and sometimes independent contributions by
economists and philosophers (see e.g. Lauwers and Liedekerke 1997,
Lauwers and Vallentyne 2003, Roemer and Suzumura 2007).



A third development worth mentioning has to do with population ethics.
Sum-utilitarianism appears to be overly populationist, since it
implies the "repugnant conclusion" (Parfit 1984) that we
should aim for an unhappy but sufficiently large population in
preference to a small and happy one. Conversely, average
utilitarianism is "Malthusian", preferring a happier
population, no matter how small, to a less happy one, no matter how
large. Here again there is an interesting tension, namely, between
accepting all individuals whose utility is greater than zero,
accepting equalization of utilities, and avoiding the "repugnant
conclusion". This tension is shown in this way. Start with a
given affluent population of any size. Add any number of individuals
with positive but almost zero utilities. This does not reduce social
welfare. Then equalize utilities, which again does not reduce social
welfare. One then obtains, compared to the initial population, a
larger population with lower utilities. One sees that these lower
utilities may be arbitrarily low, if the added individuals are
sufficiently numerous and have sufficiently low initial utilities,
thus yielding the repugnant conclusion (see Arrhenius 2000). Average
utilitarianism disvalues additional individuals whose utility is below
the average, which is very restrictive for affluent populations. A
less restrictive approach is that of critical-level utilitarianism,
which disvalues only individuals whose utility level is below some
fixed, low but positive threshold. For an extensive overview and a
defense of critical-level utilitarianism, see Blackorby, Bossert and
Donaldson (1997, 2005), as well as Broome (2004). For an original
proposal relying on a different social welfare function (inspired by
the Gini function), see Asheim and Zuber (2014).


## 5. Bargaining and Cooperative Games



At the time when Arrow declared social choice to be impossible, Nash
(1950) published a possibility theorem for the bargaining problem,
which is the problem of finding an option acceptable to two parties,
among a subset of alternatives. Interestingly, Nash relied on the
axiomatic analysis just like Arrow, so that both can be given credit
for the introduction of this method in normative economics. In the
same decade, a similar contribution was made by Shapley (1953) to the
theory of cooperative games. The development of such approaches has
been impressive since then, but some questioning has emerged regarding
the ethical relevance of this theory to issues of distributive
justice.


### 5.1 Nash's and Other Solutions



Nash (1950) adopted a welfarist framework, in which alternatives are
described only by the utility levels they give to the two parties. His
solution consists in choosing the alternative which, in the feasible
set, maximizes the product of individual utility gains from the
disagreement point (this point is the fallback option when the parties
fail to reach an agreement). This solution is therefore related to a
particular social welfare function which is somehow intermediate
between sum-utilitarianism and the maximin criterion. Contrary to
these, however, it is invariant to independent changes in utility
zeros and scales, which means that it can be applied with utility
functions which are defined only up to an affine transformation (i.e.,
no difference is made between utility function *Ui*
and utility function *ai Ui* +
*bi*), such as Von Neumann-Morgenstern utility
functions. Nash uses this invariance property in his axiomatic
characterization of the solution. He also uses another property, which
holds for any solution maximizing a social welfare function, namely,
that removing non-selected options does not alter the choice.



This particular property is criticized in Kalai and Smorodinsky
(1975), because it makes the solution ignore the relative size of the
sacrifices made by the parties in order to reach a compromise. They
propose another solution, which consists of equalizing the
parties' sacrifice relative to the maximum gain they could
expect in the available set of options. This solution, contrary to
Nash's, guarantees that an enlargement of the set of options
that is favorable to one party never hurts this party in the ultimate
selection. It is very similar to Gauthier's (1986)
"minimax relative concession" solution. Many other
solutions to the bargaining problem have been proposed, but these two
are by far the most prominent.



The relevance of bargaining theory to the theory of distributive
justice has been questioned. First, if the disagreement point is
defined, as it probably should, in relation to the relative strength
of parties in a "state of nature", then the scope for
redistributive solidarity is very limited. One obtains a theory of
"justice as mutual advantage" (Barry 1989, 1995) which is
not satisfactory at the bar of any minimal conception of impartiality
or equality. Second, the welfarist formal framework of the theory of
bargaining is poor in information (Roemer 1986b, 1996). Describing
alternatives only in terms of utility levels makes it impossible to
take account of basic physical features of allocations. For instance,
it is impossible to find out, from utility data alone, which of the
alternatives is a competitive equilibrium with equal shares. As
another illustration, Nash's and Kalai and Smorodinsky's
solutions both recommend allocating an indivisible prize by a
fifty-fifty lottery, whether the prize is symmetric (a one-dollar bill
for either party) or asymmetric (a one-dollar bill if party 1 wins,
ten dollars if party 2 wins).



Extensive surveys of bargaining theory can be found in Peters (1992),
Thomson (1999).


### 5.2 Axiomatic Bargaining and Cooperative Games



The basic theory of bargaining focuses on the two-party case, but it
can readily be extended to the case when a greater number of parties
are at the table. However, when there are more than two parties, it
becomes relevant to consider the possibility for subgroups
(coalitions) to reach separate agreements. Such considerations lead to
the broader theory of cooperative games.



This broader theory is, however, more developed for the relatively
easy case when coalition gains are like money prizes which can be
allocated arbitrarily among coalition members (the "transferable
utility case"). In this case, for the two-party bargaining
problem the Nash and Kalai-Smorodinsky solutions coincide and give
equal gains to the two parties. The Shapley value is a solution which
generalizes this to any number of parties and gives a party the
average value of the marginal contribution that this party brings to
all coalitions which it can join. In other words, it rewards the
parties in proportion to the increase in coalition gain that they
bring about by gathering with others.



Another important concept is the core. This notion generalizes the
idea that no rational party would accept an agreement that is less
favorable than the disagreement point. An allocation of the total
population prize is in the core if the total amount received by any
coalition is at least as great as the prize this coalition could
obtain on its own. Otherwise, obviously, the coalition has an
incentive to "block" the agreement. Interestingly, the
Shapley value is not always in the core, except for "convex
games", that is, games such that the marginal contribution of a
party to a coalition increases when the coalition is bigger.



The basics of this theory are very well presented in Moulin (1988) and
Myerson (1991). Cooperative games are distinguished from
non-cooperative games by the fact that the players can commit to an
agreement, whereas in a non-cooperative game every player always seeks
his interest and never commits to a particular strategy. The central
concept of the theory of non-cooperative games is the Nash equilibrium
(every player chooses his best strategy, taking others'
strategies as given), which has nothing to do with Nash's
bargaining solution. It has been shown, however, that Nash's
bargaining solution can be obtained as the Nash equilibrium of a
non-cooperative bargaining game, in which players make offers
alternatively, and accept or reject the other's offer.


## 6. Fair allocation



The theory of fair allocation studies the allocation of resources in
economic models. The seminal contribution is Kolm (1972), where the
criterion of equity as no-envy is extensively analyzed with the
conceptual tools of general equilibrium theory. Later the theory
borrowed the axiomatic method from bargaining theory, and it now
covers a great variety of economic models and encompasses a variety of
fairness concepts.



There are several surveys of this theory: Thomson and Varian (1985),
Moulin and Thomson (1997), Maniquet (1999), Thomson (2011).


### 6.1 Equity as No-Envy



An allocation is envy-free if no individual would prefer having the
bundle of another. An egalitarian distribution in which everyone has
the same bundle is trivially envy-free, but is generally
Pareto-inefficient, which means that there exist other feasible
allocations that are better for some individuals and worse for none. A
competitive equilibrium with equal shares (i.e., equal budgets) is the
central example of a Pareto-efficient and envy-free allocation. It is
envy-free since all agents have the same budget options, so that
everyone could buy everyone's bundle. It is Pareto-efficient
because, by an important theorem of welfare economics, any perfectly
competitive equilibrium is Pareto-efficient (in absence of asymmetric
information, externalities, public goods). A non-technical
presentation of this theorem can be found in Hausman and McPherson
(2006, 5.2).



This concept of equity does not need any other information than
individual ordinal preferences. It is not welfarist, in the sense that
from utility data alone it is impossible to distinguish an envy-free
allocation from an allocation with envy. Moreover, an envy-free
allocation may be Pareto-indifferent (everyone is indifferent) to
another allocation that has envy. On the other hand, this concept is
strongly egalitarian, and it is quite natural to view it as capturing
the idea of equality of resources (Dworkin 2000). When resources are
multi-dimensional, for instance when there are several consumption
goods, and when individual preferences are heterogeneous, it is not
obvious to define equality of resources, but the no-envy criterion
seems the best concept for this purpose. It guarantees that no
individual will consider that another has a better bundle than his. It
has been shown by Varian (1976) that, if preferences are sufficiently
diverse and numerous (a continuum), then the competitive equilibrium
with equal shares is the only Pareto-efficient and envy-free
allocation.



This concept can also be related to the idea of equality of
opportunities (Kolm 1996). An allocation is envy-free if and only if
the bundles granted to everyone could have been chosen by each
individual in the same opportunity set, such as, for instance, the set
containing all the bundles of the allocation under consideration.
Along this vein, the concept of no-envy can also be shown to have a
close connection with incentive considerations. A no-envy test is used
in the theory of optimal taxation in order to make sure that no one
would have interest to lie about one's preferences (Boadway and
Keen 2000). Consider the condition that, when an allocation is
selected and some individuals' preferences change so that their
bundle goes up in their own preference ranking, then the selected
allocation is still acceptable. A particular version of this condition
plays a central role in the theory of incentives, under the name of
Maskin monotonicity (see e.g. Jackson 2001), but it can also be given
an ethical meaning, in terms of neutrality with respect to changes in
preferences. Notice that envy-free allocations satisfy this condition,
since after such a change of preferences every individual's
bundle goes up in his ranking, thereby precluding any appearance of
envy. Conversely, it turns out that this condition implies that the
selected allocation must be envy-free, under the additional assumption
that, in any selected allocation, individuals with identical
preferences must have equivalent bundles. If one also requires the
selection to be Pareto-efficient, then one obtains a characterization
of the competitive equilibrium with equal shares (Gevers 1986).


### 6.2 Extensions



Kolm's (1972) seminal monograph focused on the simple problem of
distributing a bundle of non-produced commodities, and on equity as
no-envy. Other economic problems, and other fairness concepts, have
been studied later. Here is a non-exhaustive list of other economic
problems that have been analyzed: sharing labor and consumption in the
production of a consumption good; producing a public good and
allocating the contribution burden among individuals; distributing
indivisible commodities, with or without the possibility of making
monetary compensations; matching pairs of individuals (men-women,
employers-workers...); distributing compensations for
differential needs; rationing on the basis of claims; distributing a
divisible commodity when preferences are satiable. In the main stream
of this theory, the problem is to select a good subset of allocations
under perfect knowledge of the characteristics of the population and
of the feasible set. There is also a branch which studies cost and
surplus sharing, when the only information available are the
quantities demanded or contributed by the population, and the cost or
surplus may be distributed as a function of these quantities only (see
Moulin 2002). The relevance of this literature for political
philosophers should not be underestimated. Even models which seem to
be devoted to narrow microeconomic allocation problems may turn out to
be quite relevant, and some models are addressing issues already
salient in political philosophy. This is the case in particular for
the model of production of a private good when individuals have
unequal skills, which is a rough description of a market economy, and
for the model of differential needs. Both models are especially
relevant for analyzing the issue of responsibility, talent and
handicap, which is now prominent in egalitarian theories of justice. A
survey on these two models in made in Fleurbaey and Maniquet (2011a),
and a monograph connecting the various relevant fields of economic
analysis to theories of responsibility-sensitive egalitarianism is in
Fleurbaey (2008).



Among the other concepts of fairness which have been introduced, two
families are important. The first family contains principles of
solidarity, which require individuals to be affected in the same way
(they all gain or all lose) by some external shock (change in
resources, technology, population size, population characteristics).
For instance, if resources or technology improve, then it is natural
to hope that everyone will benefit. The second family contains welfare
bounds, which provide guarantees to everyone against extreme
inequality. For instance, in the division of non-produced commodities,
it is very natural to require that nobody should be worse-off than at
the equal-split allocation (i.e. the allocation in which everyone gets
the per capita amount of resources).



Let us briefly describe some of the insights that are gained through
this theory and seem relevant to political philosophy. A very
important one is that there is a conflict between no-envy and
solidarity (Moulin and Thomson 1988, 1997). This conflict is well
illustrated by the fact that in a market economy, typically any change
in technology benefits some agents and hurts others, even when the
change is a pure progress which could benefit all. Solidarity
principles are not obeyed by allocation rules which pass the no-envy
test, and these principles point toward a different kind of
distribution, named "egalitarian-equivalence" by Pazner
and Schmeidler (1978). An allocation is egalitarian-equivalent when
everyone is indifferent between his bundle in this allocation and the
bundle he would have in an egalitarian economy defined in some simple
way. For instance, the egalitarian economy may be such that everyone
has the same bundle. In this case, an egalitarian-equivalent
allocation is such that everyone is indifferent between his bundle and
one particular bundle. In more sophisticated versions, the egalitarian
economy is such that everyone has the same budget set, in some
particular family of budget sets. Egalitarian-equivalence is a serious
alternative to no-envy for the definition of equality of resources,
and its superiority in terms of solidarity is quite significant, in
relation to the next point.



The second insight, indeed, is that no-envy itself is a combination of
conflicting principles (Fleurbaey and Maniquet 2011a, Fleurbaey 2008).
This conflict is made apparent in models with talents and handicaps.
For instance, Pazner and Schmeidler (1974) found out that there may
not exist envy-free and Pareto-efficient allocations in the context of
production with unequal skills (when there are high-skilled
individuals who are strongly averse to labor). This results from an
incompatibility between a compensation principle saying that
individuals with identical preferences should have equivalent bundles
(suppressing inequalities due to skills), and a reward principle
saying that individuals with the same skills should not envy each
other (no preferential treatment on the basis of different
preferences). Both principles are a logical implication of the no-envy
test. This is obvious for the latter. For the former, notice that
no-envy among individuals with the same preferences means that they
must have bundles on the same indifference curve. Interestingly, the
compensation principle is a logical consequence of solidarity
principles and is therefore perfectly compatible with them. It is very
well satisfied by egalitarian-equivalent allocation rules. In
contrast, it is violated by Dworkin's hypothetical insurance
which applies the no-envy test behind a veil of ignorance (see Dworkin
2000, Fleurbaey 2008, and
 SS 3.2).
 A recent philosophical analysis of the no-envy approach has been
developed in Olson (2020). The relation between envy and theories of
justice is also scrutinized in the entry on
 envy.



The theory of fair allocations contains many positive results about
the existence of fair allocations, for various fairness concepts, and
this stands in contrast to Arrow's impossibility theorem in the
theory of social choice. The difference between the two theories has
often been interpreted as due to the fact that they perform different
exercises (Sen 1986, Moulin and Thomson 1997). The theory of social
choice, it is said, seeks a ranking of all options, while the theory
of fair allocation focuses on the selection of a subset of
allocations. This explanation is not convincing, since selecting a
subset of fair allocations is formally equivalent to defining a
full-blown albeit coarse ranking, with "good" and
"bad" allocations. A more convincing explanation lies in
the fact that the information used in fairness criteria is richer than
allowed by Arrow's Independence of Irrelevant Alternatives
(Fleurbaey, Suzumura and Tadenuma 2002). For instance, in order to
check that an allocation is envy-free while another displays envy, it
is not enough to know how individuals rank these two allocations in
their preferences. One must know individual preferences over other
alternatives involving permutations of bundles (an envious individual
would prefer an allocation in which his bundle is permuted with one he
envies). In this vein, one discovers that it is possible to extend the
theory of fair allocation so as to construct fine-grained rankings of
all allocations. This is very useful for the discussion of public
policies in "second-best" settings, that is, in settings
where incentive constraints make it impossible to reach
Pareto-efficiency. With this extension, the theory of fair allocation
can be connected to the theory of optimal taxation (Maniquet 2007),
and becomes even more relevant to the political philosophy of
redistributive institutions (Fleurbaey 2007). It turns out that the
egalitarian-equivalence approach is very convenient for the definition
of fine-grained orderings of allocations, which provides an additional
argument in its favor. A detailed study of fair social orderings is
made in Fleurbaey and Maniquet (2011b).


## 7. Related topics


### 7.1 Freedom and Rights



Sen (1970b) and Gibbard (1974) propose, within the framework of social
choice, paradoxes showing that it may not be easy to rank alternatives
when some individuals have a special right to rank some alternatives
that differ only in matters belonging to their private sphere, and
when their preferences are sensitive to what happens in other
individuals' private spheres. For instance, as an illustration
of Gibbard's paradox, individuals have the right to choose the
color of their shirt, but, in terms of social ranking, should A and B
wear the same color or different colors, when A wants to imitate B and
B wants to have a different color? There is a huge literature on this
topic, and after Gaertner, Pattanaik and Suzumura (1992), who argue
that no matter what choice A and B make, their rights to choose their
own shirt is respected, a good part of it examines how to describe
rights properly. The framework of game forms is an interesting
alternative to the social choice model. Recent surveys can be found in
Arrow, Sen and Suzumura (1997, vol. 2).



A related but different literature has focused on measuring the
freedom contained in a given menu from which a person may choose.
Inspired by Sen's (1985) remarks on how to value capabilities
(see section 7.2 below), this literature has offered characterizations
of various measures, starting from simple counting methods (Pattanaik
and Xu 1990) and later on including additional considerations such as
quality and diversity (e.g., Arlegi & Nieto 2001, Barbera et al.
2004). Surveys of this literature can be found in Dowding and van Hees
(2009) and Foster (2011).



Apart from this formal analysis of rights and measures of freedom,
economic theory is not very well connected to libertarian philosophy,
since economic models show that, apart from the very specific context
of perfect competition with complete markets, perfect information, no
externalities and no public goods, the laissez-faire allocation is
typically inefficient and arbitrarily unequal. Therefore libertarian
philosophers do not find much help or inspiration in economic theory,
and there is little cross-fertilization in this area.


### 7.2 Capabilities



The capability approach, developed in Sen (1985, 1992), is a
particular response to the "equality of what" debate, and
is presented by Sen as the best way to think about the relevant
interpersonal comparisons to be made for evaluations of social
situations at the bar of distributive justice. It is often presented
as intermediate between resourcist and welfarist approaches, but it is
perhaps accurate to present it as more general. A
"functioning" is any doing or being in the life of an
individual. A "capability set" is the set of functioning
vectors that an individual has access to. This approach has attracted
a lot of interest in particular because it makes it possible to take
into account all the relevant dimensions of life, in contrast with the
resourcist and welfarist approaches which can be criticized as too
narrow.



Being so general, the approach needs to be specified in order to
inspire original applications. The body of empirical literature that
takes inspiration from the capability approach is now numerically
impressive. As noted in Robeyns (2006) and Schokkaert (2007b), in many
cases the empirical studies are essentially similar, except for
terminology, to the sociological studies of living conditions. But
there are more original applications, e.g., when an evaluation of
development programs that takes account of capabilities is contrasted
with cost-benefit analysis (Alkire 2002) or when a list of basic
capabilities is enshrined in a theory of what a just society should
provide to all citizens (Nussbaum 2000). More generally, all studies
which seek to incorporate multiple dimensions of quality of life into
the evaluation of individual and social situations can be considered,
broadly speaking, as pertaining to this approach.



Two central questions pervade the empirical applications. The first
concerns the distinction between capabilities and functionings. The
latter are easier to observe because individual achievements are more
accessible to the statistician than pure potentialities. There is also
the normative issue of whether the evaluation of individual situations
should be based on capabilities only, viewed as opportunity sets, or
should take account of achieved functionings as well. The second
central question is the index problem, which has also been raised
about Rawls' theory of primary goods. There are many dimensions
of functionings and capabilities and not all of them are equally
valuable. The definition of a proper system of weights has appeared
problematic in connection to the difficulties of social choice
theory.



Recent surveys on this approach and its applications can be found in
Alkire (2016), Basu and Lopez-Calva (2011), Kuklys (2005), Robeyns
(2006), Robeyns and Van der Veen (2007), Schokkaert (2009).


### 7.3 Marxism



Roemer (1982, 1986c) proposes a renewed economic analysis of Marxian
concepts, in particular exploitation. He shows that, even if the
theory of labor value is flawed as a causal theory of prices, it may
be consistently used in order to measure exploitation and analyze the
correlation between exploitation and the class status of individuals.
However, he considers that this concept of exploitation is ethically
not very appealing, since it roughly amounts to requiring individual
consumption to be proportional to labor, and he suggests a different
definition of exploitation, in terms of undue advantage due to unequal
distribution of some assets. This leads him eventually to merge this
line of analysis with the general stream of egalitarian theories of
justice. The idea that consumption should be proportional to labor has
also received some attention in the theory of fair allocation (Moulin
1990, Roemer & Silvestre 1993). See Roemer (1986a) for a
collection of philosophical and economic essays on Marxism. There has
been a recent wave of analysis of the concept of exploitation in
economics, in particular under the impulsion of Veneziani and
Yoshihara (2015, forthcoming). See also Veneziani (2013), Fleurbaey
(2014) and Skillman (2014). For the references in philosophy, see the
entry on
 exploitation.


### 7.4 Opinions



In normative economics, theorists have often been wary of relying on
concepts which are disconnected from the lay person's intuition.
Questionnaire surveys, usually performed among students, have indeed
given some disturbing results. Welfarist approaches have been
questioned by the results of Yaari and Bar Hillel (1984), the
Pigou-Dalton principle has been critically scrutinized by Amiel and
Cowell (1992), the principles of compensation and reward have obtained
mixed support in Schokkaert and Devooght (1998), etc. It is of course
debatable how much theorists can learn from such results (Bossert
1998).



Surveys of this questionnaire approach are available in Schokkaert and
Overlaet (1989), Amiel and Cowell (1999), Schokkaert (1999), Gaertner
and Schokkaert (2011). Philosophers have also performed similar
inquiries (Miller 1992).


### 7.5 Altruism and Reciprocity



It is standard in normative economics, as in political philosophy, to
evaluate individual well-being on the basis of self-centered
preferences, utility or advantage. Feelings of altruism, jealousy,
etc. are ignored in order not to make the allocation of resources
depend on the contingent distribution of benevolent and malevolent
feelings among the population (see e.g. Goodin 1986, Harsanyi 1977).
It may be worth mentioning here that the no-envy criterion discussed
above has nothing to do with interpersonal feelings, since it is
defined only with self-centered preferences. When an individual
"envies" another in this particular sense, he simply
prefers the other's consumption to his own, but no feeling is
involved (he might even not be aware of the existence of the other
individual).



But positive economics is quite relevantly interested in studying the
impact of individual feelings on behavior. Homo oeconomicus may
be rational without being narrowly focused on his own consumption. The
analysis of labor relations, strategic interactions, transfers within
the family, generous gifts require a more complex picture of human
relations (Fehr and Fischbacher 2002). Reciprocity, in particular,
seems to be a powerful source of motivation, leading individuals to
incur substantial costs in order to reward nice partners and punish
faulty partners (Fehr and Gachter 2000). For an extensive survey of
this branch of the economic literature, see Gerard-Varet, Kolm
and Mercier-Ythier (2004).


### 7.6 Happiness studies



The literature on happiness has surged in the last decade. The
findings are well summarized in many surveys (see in particular Diener
(1994, 2000), Diener et al. (1999), Frey and Stutzer (2002), Graham
(2009), Kahneman et al. (1999), Kahneman and Krueger (2006), Layard
(2005), Oswald (1997), Van Praag and Ferrer-i-Carbonell 2008), and
reveal the main factors of happiness: personal temperament, health,
social connections (in particular being married and employed). The
impact of material wealth is debated, some arguing that it is more a
matter of relative position than of absolute comfort, at least above a
minimal level of affluence (Easterlin 1995, Clark et al. 2008), others
arguing that there is a positive (but logarithmic: doubling income
induces a constant increment on happiness) impact over the whole range
of observed living standards (Deaton 2008, Sacks et al. 2010) .



A hotly debated question is what to make of this approach in welfare
economics. There is a wide variety of positions, from those who
propose to measure and maximize national happiness (Diener 2000,
Kahneman et al. 2004, Layard 2005) to those who firmly oppose this
idea on various grounds (Burchardt 2006, Nussbaum 2008, among others).
There seems to be a consensus on the idea that happiness studies
suggest a welcome shift of focus, in social evaluation, from purely
materialistic performances to a broader set of values. Above all, one
can consider that the traditional suspicion among economists about the
possibility to measure subjective well-being is being assuaged by the
recent progress.



However, the fact that subjective well-being can be measured does not
imply that it ought to be taken as the metric of social evaluation.
Surprisingly, the literature on happiness refers very little to the
lively philosophical debates of the previous decades about welfarism,
and in particular the criticisms raised by Rawls (1982) and Sen (1985)
against utilitarianism. (Two exceptions are Burchardt (2006) and
Schokkaert (2007). Layard (2005) also mentions and quickly rebuts some
of the arguments against welfarism.) Nonetheless, one of the key
elements of that earlier debate, namely, the fact that subjective
adaptation is likely to hide objective inequalities, shows up in the
data, challenging happiness specialists. Subjective well-being seems
relatively immune in the long run to many aspects of objective
circumstances, individuals displaying a remarkable ability to adapt.
After most important life events, satisfaction returns to its usual
level and the various affects return to their usual frequency. If
subjective well-being is not so sensitive to objective circumstances,
should we stop caring about inequalities, safety, and
productivity?



These issues and the possible uses of subjective well-being data for
welfare analysis are discussed in detail in several chapters of Adler
and Fleurbaey (2016), in particular the chapters by Fujiwara and
Dolan, Bykvist, Haybron, Lucas, Graham, Clark, Decancq and
Neumann.


### 7.7 Animals



Normative economics, even more so than political and moral philosophy,
has traditionally been anthropocentric, but growing interest in animal
rights and animal interests is emerging, following the lead of
influential philosophers (see the entry on the
 moral status of animals)
 and, e.g., Sunstein and Nussbaum 2004). Interestingly, specialized
studies in animal welfare, in biology, adopt similar methods as
welfare economics to estimate animal preferences and conceptualize
various approaches to their needs and their well-being (e.g., Appleby
et al. 2018). Many arguments being developed against the current
farming practices are still based on anthropocentric considerations
such as climate change and ecosystem services. But the idea of carving
a place in the social welfare function for animals, alongside their
fellow humans, is gaining ground (Johansson-Stenman 2018, Carlier and
Treich 2020, Espinosa and Treich 2021; for the opposite view, see
Eichner and Pethig 2006). Budolfson and Spears (2020) propose a way to
compute an inclusive utilitarian social welfare function based on a
distinction between well-being potential and relative realized
well-being.