Date of this Version
Published in Transactions of the Nebraska Academy of Sciences, Volume 3 (1976).
By a social welfare function, or "constitution," or arbitration scheme," or "conciliation policy," or "amalgamation method," or "voting procedure," is meant a rule which associates to each profile of individual preference orderings a preference ordering for the society itself. Is it possible to articulate such a social welfare function? If we demand that our social welfare function satisfy certain ethically acceptable constraints the answer to our question is not immediately obvious.
Kenneth Arrow, in his Social Choice and Individual Values, investigated the possibility of specifying a social welfare function which would satisfy certain socially desirable criteria.
Antecedent to this specification Arrow demanded of the individuals in the society that they be, in some sense, rational. That is, the individual's preference profile should exhibit transitivity of preference and indifference and connectedness.
Arrow's conditions imposed on the social welfare function were these:
(1) Unrestricted Domain: The domain of the social welfare function should include all logically possible combinations of individual orderings.
(2) The Pareto Principle: If all individuals in the society prefer one option to another or are indifferent as to these two options the social choice should reflect these relationships.
(3) The Independence of Irrelevant Alternatives: The introduction of new options should not alter the preference or indifference relationships already established within the individual profiles.
(4) Non-dictatorship: There is no individual such that in those situations in which he prefers one option to another society does likewise, regardless of the preferences of the other individuals.