Classes of models for selected axiomatic theories of choice

Stuart J. Thorson, John Stever

Research output: Contribution to journalArticle

3 Scopus citations

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 similiar 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.

Original languageEnglish (US)
Pages (from-to)15-32
Number of pages18
JournalJournal of Mathematical Psychology
Volume11
Issue number1
DOIs
StatePublished - Feb 1974

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

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