Intransitive social indifference and the Arrow dilemma

This paper deals with a proposal by Frederic Schick for resolving Arrow’s dilemma of social choice. Schick challenges Arrow’s assumption that rational social indifference is transitive. It turns out, however, that even if we drop this assumption, we still face a dilemma as embarrassing as Arrow’s. Any constitution which satisfies the remaining conditions is a liberum veto oligarchy. This means a unique set of individuals carries any issue on which it is unanimous, and engenders social indifference on any issue which divides it. A formal statement and proof of this theorem follows an informal presentation of the result.