Social
welfare functions have occupied the center stage of welfare economics since the philosopher Jeremy
Bentham and other utilitarian theorists advocated that humans should seek the
greatest total welfare, understood as the sum of individual utilities. The
noted economists Abram Bergson and Paul A. Samuelson generalized the concept.
Following the seminal work of the economic theorists Kenneth J. Arrow and
Amartya K. Sen, the theory of social choice has examined the various possible
forms of such functions in detail.
In the most
standard form, a social
welfare function is a mapping that determines the level of social welfare as a
function of individual levels of welfare. In fact, a numerical measure of
social welfare is not really needed for the evaluation of social situations;
the only relevant part of a social welfare function is how it ranks social
situations from the best to the worst.
The theory
of social choice analyzes two important
features of a social welfare function. The first feature is its degree of
aversion to inequalities between individual levels of welfare. For instance,
the utilitarian function, computed as the sum of individual indices of welfare,
is indifferent to inequalities because only the total matters. In contrast, the
maximin function, which identifies social welfare with the welfare of the
worst-off individuals in the population, displays an infinite aversion to
inequalities since it gives absolute priority to the worst off. There are
countless intermediate possibilities between these two extreme functions. The
second important feature of a social welfare function is the information about
individual indices that is used by the function. For instance, the utilitarian
function focuses on individual gains and losses when it compares two
situations: A situation is better than another if the sum of welfare gains when
one moves to it is greater than the sum of losses. By contrast, the maximin
function focuses on individual levels: A situation is better if the level of
welfare of the worst-off individuals is greater. The link between the two
features—inequality aversion and informational basis—has been thoroughly
scrutinized by the theory of social choice.
The link
between the measurement of social
welfare and the measurement of inequalities has also been clarified. The level
of social welfare in a given situation can be decomposed into the positive contribution
of total welfare and the negative contribution of inequalities. More precisely,
it is generally possible to write social welfare as the difference of two
terms. One is the sum of individual indices of welfare. The other, which comes
as a deduction, is computed as the product of an inequality index and the sum
of individual indices. In other words, one can typically say that inequalities
reduce social welfare by a certain percentage, and this percentage itself is
the value of an inequality index.
A
controversial issue has been the
possibility of constructing social welfare functions on the sole basis of
individual ordinal and non-comparable preferences over the social situations.
The standard social welfare function relies on individual indices of welfare,
but in its most general form it can simply define a ranking of social
situations as a function of the preference rankings of these situations for
each member of the population. This is important because there is much
skepticism in economics about the possibility of making interpersonal
comparisons of welfare in a consensual way.
Recent
developments have dealt with the refinements of social welfare functions to
incorporate a variety of fairness concepts or to make it possible not only to
compare social situations for a given population, but also to compare social
situations across different populations. The latter is important to make
judgments about the desirable size of the population, and deep dilemmas plague
this issue. A social welfare function such that every addition of an individual
with positive welfare is considered to improve the social situation will
generate extreme populationist evaluations—for example, the judgment that a
larger population always makes a situation better, provided the larger
population is large enough, no matter how low individual welfare is in this
situation. However, a social welfare function that is based on some notion of
average individual welfare is likely to be Malthusian because any addition of
an individual with less-than-average welfare is considered undesirable.
An important issue in fairness concepts has been the incorporation of considerations of freedom and individual responsibility, motivated by theories of justice such as that of John Rawls. Social welfare functions have been developed that are based on the idea of measuring individual situations in terms of opportunities or resources rather than ultimate welfare. A variety of functions have been proposed, in particular because there are different possible interpretations of the implications of individual responsibility. In one interpretation, individual responsibility removes the need for redistribution, which has motivated the construction of social welfare functions that disregard individual characteristics for which the individuals are responsible and focus on the compensation of inequalities for which individuals are not responsible. In another interpretation, individual responsibility removes the need for inequality aversion in the evaluation. Along this vein, social welfare functions have been proposed that are of the utilitarian sort along the responsibility dimensions of individual characteristics and of the maximin sort along the non-responsibility dimensions.
An important issue in fairness concepts has been the incorporation of considerations of freedom and individual responsibility, motivated by theories of justice such as that of John Rawls. Social welfare functions have been developed that are based on the idea of measuring individual situations in terms of opportunities or resources rather than ultimate welfare. A variety of functions have been proposed, in particular because there are different possible interpretations of the implications of individual responsibility. In one interpretation, individual responsibility removes the need for redistribution, which has motivated the construction of social welfare functions that disregard individual characteristics for which the individuals are responsible and focus on the compensation of inequalities for which individuals are not responsible. In another interpretation, individual responsibility removes the need for inequality aversion in the evaluation. Along this vein, social welfare functions have been proposed that are of the utilitarian sort along the responsibility dimensions of individual characteristics and of the maximin sort along the non-responsibility dimensions.