CAMBRIDGE – Human beings have always lived in
groups, and their individual lives have invariably depended on group decisions.
But the challenges of group choice can be daunting, particularly given the
divergent interests and concerns of the group’s members. So, how should
collective decision-making be carried out?
A dictator who wants to control every aspect
of people’s lives will seek to ignore the preferences of everyone else. But
that level of power is hard to achieve. More important, dictatorship of any
kind can readily be seen to be a terrible way to govern a society.
So, for both ethical and practical reasons,
social scientists have long investigated how the concerns of a society’s
members can be reflected in one way or another in its collective decisions,
even if the society is not fully democratic. For example, in the fourth century
BC, Aristotle in Greece and Kautilya in India explored various possibilities of
social choice in their classic books, Politics and Economics,
respectively (the Sanskrit title of Kautilya’s book, Arthashastra,
translates literally as “the discipline of material wellbeing”).
The study of social choice as a formal
discipline first came into its own in the late eighteenth century, when the
subject was pioneered by French mathematicians, particularly J. C. Borda and
Marquis de Condorcet. The intellectual climate of the time was greatly influenced
by the European Enlightenment, with its interest in reasoned construction of a
social order, and its commitment to the creation of a society responsive to
people’s preferences.
But the theoretical investigations of Borda,
Condorcet, and others often yielded rather pessimistic results. For example,
the so-called “voting paradox” presented by Condorcet showed that majority rule
can reach an impasse when every alternative is defeated in voting by some other
alternative, so that no alternative is capable of standing up to the challenge
of every other alternative.
Social choice theory in its modern and
systematic form owes its rigorous foundation to the work of Kenneth J. Arrow in
his 1950 Columbia University PhD dissertation. Arrow’s thesis contained his
famous “impossibility theorem,” an analytical result of breathtaking elegance
and reach.
Arrow’s theorem shows that even very mild
conditions of reasonableness in arriving at social decisions on the basis of
simple preference rankings of a society’s individuals could not be
simultaneously satisfied by any procedure. When the book based on his
dissertation, Social Choice and Individual Values, was published
in 1951, it became an instant classic.
Economists, political theorists, moral and
political philosophers, sociologists, and even the general public rapidly took
notice of what seemed like – and indeed was – a devastating result. Two
centuries after visions of social rationality flowered in Enlightenment
thinking, the project suddenly seemed, at least superficially, to be
inescapably doomed.
It is important to understand why and how
Arrow’s impossibility result comes about. Scrutiny of the formal reasoning that
establishes the theorem shows that relying only on the preference rankings of
individuals makes it difficult to distinguish between very dissimilar social
choice problems. The usability of available information is further reduced by
the combined effects of innocuous-seeming principles that are popular in
informal discussions.
It is essential, particularly for making
judgments about social welfare, to compare different individuals’ gains and
losses and to take note of their relative affluence, which cannot be
immediately deduced only from people’s rankings of social alternatives. It is
also important to examine which types of clusters of preference rankings are
problematic for different types of voting procedures.
Nonetheless, Arrow’s impossibility theorem
ultimately played a hugely constructive role in investigating what democracy
demands, which goes well beyond counting votes (important as that is).
Enriching the informational base of democracy and making greater use of
interactive public reasoning can contribute significantly to making democracy
more workable, and also allow reasoned assessment of social welfare.
Social choice theory has thus become a broad
discipline, covering a variety of distinct questions. Under what circumstances
would majority rule yield unambiguous and consistent decisions? How robust
are the different voting procedures for yielding cogent results? How can we
judge how well a society as a whole is doing in light of its members’
disparate interests?
How, moreover, can we accommodate
individuals’ rights and liberties while giving appropriate recognition to
their overall preferences? How do we measure aggregate poverty in view of
the varying predicaments and miseries of the diverse people who comprise the
society? How do we arrive at social valuations of public goods such as the
natural environment?
Beyond these questions, a theory of justice
can draw substantially on the insights and analytical results emerging from
social choice theory (as I discussed in my 2009 book The
Idea of Justice). Furthermore, the understanding generated by social
choice theorists’ study of group decisions has helped some research that is not
directly a part of social choice theory – for example, on the forms and
consequences of gender inequality, or on the causation and prevention of
famines.
The reach and relevance of social choice
theory is extensive. Rather than undermining the pursuit of social reasoning, Arrow’s
deeply challenging impossibility theorem, and the large volume of literature
that it has inspired, has immensely strengthened our ability to think
rationally about the collective decision-making on which our survival and
happiness depend.
Amartya Sen is a Nobel Prize-winning economist.