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Set-Valued Utilities for Strict Partial Orders.

Herrero1, Subiza

  • 1Universidad de Alicante

Journal of Mathematical Psychology
|November 30, 1999
PubMed
Summary
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This study introduces a novel numerical representation for strict partial orders, enabling the reconstruction of preference relations. This new method utilizes set-valued utilities, overcoming limitations of previous weak utility functions.

Area of Science:

  • Decision Sciences
  • Mathematical Economics
  • Set Theory

Background:

  • Existing weak utility functions inadequately represent strict partial orders.
  • Reconstructing the preference relation from weak utility functions is not feasible.

Purpose of the Study:

  • To introduce a numerical representation for strict partial orders.
  • To enable the recovery of the preference relation from the representation.

Main Methods:

  • Considered the strict partial order (2(Ropf), superset).
  • Introduced set-valued utilities (set-valued mappings).
  • Ensured set-valued utilities admit a selection that is a weak utility function.

Main Results:

  • Developed a novel numerical representation for strict partial orders.

Related Experiment Videos

  • Demonstrated that the preference relation can be recovered from this representation.

    • Conclusions:

    • Set-valued utilities offer a superior method for representing strict partial orders.
    • This approach facilitates a complete understanding of preference relations.