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How to deal with partially analyzable acts?

Jean-Yves Jaffray1, Meglena Jeleva2,3,4

  • 11LIP6, Université Pierre et Marie Curie-Paris 6, Paris, France.

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Area of Science:

  • Decision Theory
  • Behavioral Economics
  • Mathematical Psychology

Background:

  • Decisions are often made with incomplete information, where some outcomes are certain under specific conditions, while others remain vague.
  • Existing decision models struggle to fully capture the nuances of partial knowledge and varying attitudes towards uncertainty and ambiguity.

Purpose of the Study:

  • To develop an axiomatic decision model for incompletely analyzed acts.
  • To establish a representation theorem for this model.
  • To provide a framework accommodating diverse attitudes toward ambiguity and uncertainty.

Main Methods:

  • Formulation of an axiomatic decision model for incompletely analyzed acts.
  • Proof of a representation theorem for the proposed model.
  • Aggregation of partial evaluations including conditional expected utility and bounds on non-analyzed outcomes.

Main Results:

  • The model aggregates decisions by combining analyzed (probabilistic) and non-analyzed (vague) components.
  • The representation theorem allows for diverse decision criteria, reflecting varying knowledge and attitudes toward risk.
  • The framework incorporates existing models as sub-models, extending their applicability.

Conclusions:

  • The proposed decision model offers a unified approach to decision-making under partial knowledge and ambiguity.
  • It provides flexibility in representing beliefs, from precise probabilities to complete ignorance.
  • This framework enhances the understanding of decision-making processes in complex, uncertain environments.