On strongly consistent social choice functions (Q687046)

The paper analyses strongly consistent social choice functions (SCF) i.e., SCF's which yield a strong equilibrium for every preference profile of individuals. Similar to the elimination procedure introduced by \textit{B. Peleg} [Econometrica 46, 153-161 (1978; Zbl 0373.90002)] the paper introduces the key notion of an elimination scheme. A distribution of coalitions power (a blocking) is said to be eliminable, if an elimination scheme exists for every preference profile. In case a blocking is eliminable, each selector of its core correspondence is shown to be a strongly consistent SCF. Several characterizations and examples of eliminable blockings are provided.