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Probabilistic Choice as a Consequence of Nonlinear (Sub) Optimization

Marley1

  • 1Department of Psychology, McGill University

Journal of Mathematical Psychology
|February 25, 1998
PubMed
Summary
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This study introduces novel utility theories for decision-making, allowing for non-linear relationships in both choice and event probabilities. These theories address complex decisions by modeling multiple goals within a vector optimization framework.

Area of Science:

  • Decision Theory
  • Behavioral Economics
  • Mathematical Psychology

Background:

  • Existing research suggests probabilistic choice arises from utility maximization non-linear in choice probabilities.
  • Other theories propose utility functions non-linear in event probabilities.

Purpose of the Study:

  • To develop and motivate utility theories that are non-linear in choice probabilities, event probabilities, or both.
  • To integrate existing viewpoints on non-linear utility in decision-making.

Main Methods:

  • The study frames decision-making as a vector optimization problem with multiple, potentially incompatible goals.
  • This vector optimization problem is converted into a scalar optimization problem to find noninferior solutions.

Main Results:

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  • The proposed framework yields utility theories non-linear in choice and/or event probabilities.
  • In specific cases, the approach aligns with existing nonlinear utility theories.

Conclusions:

  • The presented vector-to-scalar optimization method provides a unified approach to nonlinear utility theories.
  • This framework offers a new perspective on modeling complex choices involving multiple objectives.