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Reduction Invariance and Prelec's Weighting Functions.

R. Duncan Luce1

  • 1University of California, Irvine

Journal of Mathematical Psychology
|February 17, 2001
PubMed
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This study introduces reduction invariance, a simpler condition equivalent to Prelec's compound invariance in separable utility theory. It simplifies testing and generalizes weighting functions for decision-making under risk.

Area of Science:

  • Decision theory
  • Behavioral economics
  • Risk perception

Background:

  • Separable utility theory provides a framework for understanding decision-making under risk.
  • Prelec's (1998) work introduced compound invariance and derived specific weighting functions.
  • Understanding risk preferences is crucial in economics and psychology.

Purpose of the Study:

  • To introduce and validate reduction invariance as an alternative to compound invariance.
  • To demonstrate the equivalence between reduction invariance and Prelec's weighting functions.
  • To generalize existing weighting functions and explore their implications for decision-making.

Main Methods:

  • Utilizing separable utility theory as the foundational framework.
  • Developing and applying the concept of reduction invariance, a variant of gamble reduction.

Related Experiment Videos

  • Providing a simplified proof for the equivalence of reduction invariance and compound invariance.

    • Main Results:

    • Reduction invariance is shown to be equivalent to Prelec's (1998) 2-parameter weighting functions derived from compound invariance.
    • A simpler proof for this equivalence is presented, making the concept more accessible.
    • Generalizations of both conditions yield broader families of weighting functions, including Prelec's exponential-power and hyperbolic logarithm families.

    Conclusions:

    • Reduction invariance offers a more practical and testable condition for analyzing decision-making under risk.
    • The generalized weighting functions provide a richer set of tools for modeling risk preferences.
    • The power function, arising from simple probabilistic assumptions, is uniquely captured by Prelec's compound-invariance family.