Polynomial Conjoint Measurement - Polynomial Conjoint Measurement - Axioms


Let, and be non-empty and disjoint sets. Let " " be a simple order. Krantz et al. (1971) argued the quadruple is a polynomial conjoint system if and only if the following axioms hold.

  • SINGLE CANCELLATION. The relation " " satisfies single cancellation upon A whenever if and only if holds for all and . Single cancellation upon P and U is similarly defined.
  • DOUBLE CANCELLATION. The relation " " upon satisfies double cancellation if and only if for all and, and therefore is true for all . The condition holds similarly upon and .
  • JOINT SINGLE CANCELLATION. The relation " " upon satisfies joint single cancellation such that if and only if is true for all and . Joint independence is similarly defined for and .
  • DUAL DISTRIBUTIVE CANCELLATION. Dual distributive cancellation holds upon if and only if

, and implies is true for all and .

  • SOLVABILITY. The relation " " upon is solvable if and only if for all and, there exists and such that .

Read more about this topic:  Polynomial Conjoint Measurement, Polynomial Conjoint Measurement

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