Classes of Models for Selected Axiomatic Theories of Choice
Abstract
Adding a reversibility axiom to the other axioms of Luce's (1959) probabilistic ranking theory results in an impossibility theorem - that all alternatives in an alternative set are equally likely to be chosen (i.e., that preferences are random). This impossibility theorem is generally avoided by removing the reversibility axiom. Using simple algebraic methods such a modified theory is shown to contain a theorem similar to the impossibility result. These results are discussed within the framework of mathematical model theory - model theory deals with the relations between sets of sentences (theories) and the structures which satisfy these sentences (models) - to illustrate the applicability of model theory as an analytic tool in theory development.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1973
- Accession Number
- AD0764874
Entities
People
- John Stever
- Stuart J. Thorson
Organizations
- Ohio State University