Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Non-Allais Paradox and Context-Dependent Risk Attitudes

Edward Honda, Keh-Kuan Sun

Abstract

We provide and axiomatize a representation for preferences over lotteries that generalizes the expected utility model. Since the representation uses different utility functions to evaluate different lotteries, the preferences can be interpreted as coming from individuals that have context-dependent attitudes toward risks. The model enables generating various violations of the independence axiom that are not compatible with some of the most prominent models of non-expected utility. Depending on the specification chosen, the model can range from being very flexible with many different utility functions to being parsimonious with few or just one utility function.

Non-Allais Paradox and Context-Dependent Risk Attitudes

Abstract

We provide and axiomatize a representation for preferences over lotteries that generalizes the expected utility model. Since the representation uses different utility functions to evaluate different lotteries, the preferences can be interpreted as coming from individuals that have context-dependent attitudes toward risks. The model enables generating various violations of the independence axiom that are not compatible with some of the most prominent models of non-expected utility. Depending on the specification chosen, the model can range from being very flexible with many different utility functions to being parsimonious with few or just one utility function.

Paper Structure

This paper contains 85 sections, 10 theorems, 95 equations, 10 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Related Literature and Experimental Evidence
  3. Expected Contextual Utility Representation
  4. Defining the Representation
  5. Discussion on the Disappointment Parameter
  6. Some Special Cases
  7. Preference for Stochastic Dominance
  8. Binary Utilities
  9. Disappointment Probability as Utility Parameters
  10. Resulting Behavior
  11. Worst-Outcome-Shift Problem
  12. Allais Paradox
  13. Violation of the Betweenness Axiom
  14. Violation of Negative Certainty Independence
  15. Illustrating Changes in Risk Attitudes
  16. ...and 70 more sections

Key Result

Proposition 1

If $\succsim$ has an ECU representation with a set of contextual functions that satisfies Conditions condition:non-decreasing-u and condition:monotone-pessimism, then $p\succsim q$ for any $p,q\in \mathcal{L}$ such that $p$ first-order stochastically dominates $q$.

Figures (10)

  • Figure 1: $u_\pi(x)=\left(\frac{x-w}{b-w}\right)^{0.5 +\pi }$ with $w=0, b=1$
  • Figure 2: Visual comparison of CC/CR/MX and the WS.
  • Figure 3: Marschak-Machina triangles under different threshold orderings.
  • Figure 4: Visual Comparison: EU, DA, and ECU
  • Figure 5: A screenshot of the experiment software displaying Stage 1.
  • ...and 5 more figures

Theorems & Definitions (33)

  • Definition 1
  • Definition 2
  • Proposition 1
  • proof
  • Example 1
  • Example 2
  • Example 3
  • Definition 3
  • Example 4
  • Definition 4
  • ...and 23 more