Plural identities and preference formation

Abstract

This article explores under what conditions an agent can derive a transitive all-things-considered preference from a plurality of non-comparable objectives, values or judgements mirroring her plural identity. In contrast to existing contributions, the multiple values are reflected by partial (viz. incomplete) orderings. It is shown that a slight modification of the conditions employed by Arrow implies a spread of the dictate of one identity to its ‘incomplete parts’. The second result reveals that if one requires the decision making power to be spread a bit more equally across the various parts of a person’s identity, then even the derivation of an acyclic all-things-considered preference is rendered impossible. A third result shows that requiring some minimal consistency among a person’s plural identities, introduced via a domain restriction, allows the avoidance of the highlighted impossibilities.