A stability property in social choice theory: Stability property in social choice

A social choice function g is stable if whenever an alternative x is selected at profile u and then profile u* is constructed from u by only switching x with yfor one individual i who has y just below x at u, then rule g selects either x or y at u* and not some third alternative. Stability is strictly weaker than strategy†proofness but strong enough to establish two kinds of impossibility theorems.