SOCIAL CHOICE THEORY
Have you ever thought about how it is difficult to make decisions in group? How tricky is to come
to an unanimity conclusion amid all the individuals that take part into a joint decision?
This topic makes us figure out how people can get decisions in order to achieve the best one for
everybody included in the cluster.
We can attribute the study above all to the french nobleman Nicolas de Condorcet and the
american Kenneth Arrow, which they contributed developing the theory through different
applications in welfare economics, social epistemology and political sciences.
The heart of the matter is to aggregate individual inputs to collective outputs, ranking different
social preferences into a Social Welfare Function, where we assign one point (the lowest) to each
individual’s most-preferred social state, two points to the second-best social state, and so on. It is
important to say that each individuals preferences must satisfy the axioms of completeness (we
can compare any two objects), asymmetry (we can only prefer one object over the other) and
transitivity (a transitive preference would be preferring apples to bananas, bananas to
cranberries, so apples to cranberries).
When we deal with the Social Choice Theory the main issue is to aggregate preferences, therefore
let’s start explaining the Condorcet Paradox by ordering preferences:
Suppose if Alfredo prefers a>b, and b<c (so a> c due to transitivity), Mario prefers b>c and c>a,
and Lorenza prefers c>a, and a>b. Simply counting sets out a social preference for a>b, for b> c
and for c>a.
As we see the group decisions may end up to be cyclic, so we approach this question using the
axiomatic method. The best known is certainly the ‘Impossibility Theorem’ of Kenneth Arrow,
which states an aggregation should satisfy at least this axiom:
If every individual ranks A over B in two different sets of individual preference ordering (D,E), then
so ought society. So we can talk about the impossibilities of SWF, where it shouldn’t be acceptable
that any individual might respect independence of irrelevant alternatives, Pareto, non-dictatorship
and the ordering condition, unless society has just one member or the number of social states is
fewer than three.
In order to prove Arrow’s impossibility theorem we have to explain ‘the Weak Pareto Condition’,
asserts that, if for any two alternatives a and b, all members of society agree that a is strictly
preferred to b, then as a final upshot, society should have exactly the same strict preference.
But have you ever thought about those irrelevant alternatives?
If society has to make a decision between A and B, it must not ponder any other alternatives, for
instance if I and Sara prefer having a pizza to a hamburger, the order of having french fries is
irrelevant:
Pizza>french fries>hamburger
French fries>pizza>hamburger
Moreover we don’t like absolutely to have in society a particolar person able to sway a decision
with his strict preference, this is called the “non-dictatorship” condition.
All these requirements explained so far, may make the world democratic! The social equality
should allow all members of the society to have freedom and independence over private matters,
the so-called ‘local decisiveness’.
Amartya Sen was the first to complete this idea into Arrow’s theorem. Sen’s Theorem, unlike
Arrow’s, does not counts on the finite number of individuals, he proposes a minimal condition of
liberalism. It assumes that there are at least two individuals in society such that for each of them
there is at least one pair of alternatives with respect to which she’s decisive, that is, there is a pair
a and b, such that if she prefers a to b, then society prefers a to b. Afterwards he showed another
important impossibility result that is ‘the impossibility of a Paretian liberal’. He showed that the
axiom of unrestricted domain, where all preferences of individuals are permitted, and the weak
Pareto principle are incompatible with the local dictatorship over purely private matters. In a
nutshell, there does not exist a SWF satisfying these conditions.
On the contrary the economist John Harsanyi rejects Arrow’s view that individual preference
orderings carry nothing but ordinal information. He explains us why we have to consider also
interval scale, so he defends a utilitarian solution to the problem of social choice, according to
which the social preference ordering should be entirely determined by the sum total of
individual utility levels in society.
An example can be the father of a family who has two separate preference orderings regarding a
trip with his wife and twenty-one sons, one personal preference ordering over all states (London,
Amsterdam, Milan), that reflects his personal preference ordering , as well as a separate
preference ordering over the same set of social states that reflects the social preference ordering
of all the family components.
The father’s social preference ordering must be a weighted sum of the individual preference
orderings, assigning equal utility units to everyone. This is known as the Equal treatment of all
individuals. In conclusion why should everybody be treated equally? This is a substantial ethical
question arisen when we usually have rational problems.
Bibliography
Arrow, K.J. (1951, 1963). Social Choice and Individual Values. New York: John Wiley.
Peterson Martin, An Introduction to Decision Theory, 2009.
Webliography
https://plato.stanford.edu/entries/social-choice/
http://www.academia.edu/5836739/Does_rational_choice_theory_aid_the_explanation_of_socia
l_phenomena
http://www.academia.edu/3197007/RATIONAL_CHOICE_THEORY_ASSUMPTIONS_STRENGHTS_A
ND_GREATEST_WEAKNESSES_IN_APPLICATION_OUTSIDE_THE_WESTERN_MILIEU_CONTEXT