Social Choice Under Incomplete, Cyclic Preferences Majority/Minority-Based Rules, and Composition-Consistency

Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of “indifference” in individual preferences is misleading and should be replaced by andIn this context, ten types of and are studied which lead to social choice rules C: (;ℝ) ↦ (;ℝ) ∈ P()\{∅} that accept profiles R of reflexive relations. These rules are discussed by means of many familiar, and some new conditions, including Moreover, it is proved that every choice function satisfying two weak Condorcet-type conditions can be made both composition- consistent and idempotent, and that all the proposed rules have polynomial time complexity.