THE POSSIBILITY OF A SOCIAL WELFARE FUNCTION

Abstract

Ever since 1951, when Kenneth Arrow published his monograph showing the paradox that social welfare functions generate, there has been interest in overcoming or bypassing this paradox.' The paradox is that, given certain simple and very persuasive conditions for collective rationality, there can be no decision rule which meets these conditions. The conditions, simply stated, are these: 1. Between three alternatives, the social welfare function must give rise to a unique social ordering, no matter how individual members of the group choose to order the three alternatives. 2. The social ordering must correspond positively, or at least not negatively, to changes in the ordering of any one individual. 3. The elimination of any one alternative shall not affect the ranking of the other alternatives in the social welfare function. 4. Voters can choose freely among all alternatives. S. No one individual's choice can dictate the social ordering independently of the choices of others. It is easy to show that even with three voters and three alternatives, a situation can exist in which these conditions are not met by a simple majority vote. For consider three voters, X, Y, and Z, and three alternatives, A, B, and C. The rankings given by X, Y, and Z are:

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 112 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.