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Decision Rules in Choice Under Risk

Avner Seror

TL;DR

The paper develops a menu-specific, rule-based approach to binary risky choice, where observed choices are justified by local dominance after a rule-transformed perception of each lottery. The Maximum Rule Concentration Index (MRCI) summarizes how parsimoniously a dataset can be explained by a small set of rules, maximizing the Herfindahl-Hirschman index across admissible menu-by-menu assignments under First-Order Stochastic Dominance. It provides an exact MIQP formulation and a scalable heuristic to compute MRCI, plus a finite-sample permutation test to detect excess concentration beyond menu-independent randomness. Applied to the CPC18 data (686 subjects, 500–700 decisions each), the study finds a mean MRCI of 0.545 (effective rule count about 1.83) with 64.1% of subjects rejecting random choice at the 1% level, driven mainly by MAP (modal payoff) and SAL (salience) rules, with smaller contributions from regret and extremal heuristics. The framework offers a robust, interpretable way to compare broad behavioral mechanisms across menus, revealing substantial substitution among rules and providing a platform for extending revealed-preference analyses to procedure- and rule-based explanations of risky choice.

Abstract

We study choice among lotteries in which the decision maker chooses from a small library of decision rules. At each menu, the applied rule must make the realized choice a strict improvement under a dominance benchmark on perceived lotteries. We characterize the maximal Herfindahl-Hirschman concentration of rule shares over all locally admissible assignments, and diagnostics that distinguish rules that unify behavior across many menus from rules that mainly act as substitutes. We provide a MIQP formulation, a scalable heuristic, and a finite-sample permutation test of excess concentration relative to a menu-independent random-choice benchmark. Applied to the CPC18 dataset (N=686 subjects, each making 500-700 repeated binary lottery choices), the mean MRCI is 0.545, and 64.1% of subjects reject random choice at the 1% level. Concentration gains are primarily driven by modal-payoff focusing, salience-thinking, and regret-based comparisons.

Decision Rules in Choice Under Risk

TL;DR

The paper develops a menu-specific, rule-based approach to binary risky choice, where observed choices are justified by local dominance after a rule-transformed perception of each lottery. The Maximum Rule Concentration Index (MRCI) summarizes how parsimoniously a dataset can be explained by a small set of rules, maximizing the Herfindahl-Hirschman index across admissible menu-by-menu assignments under First-Order Stochastic Dominance. It provides an exact MIQP formulation and a scalable heuristic to compute MRCI, plus a finite-sample permutation test to detect excess concentration beyond menu-independent randomness. Applied to the CPC18 data (686 subjects, 500–700 decisions each), the study finds a mean MRCI of 0.545 (effective rule count about 1.83) with 64.1% of subjects rejecting random choice at the 1% level, driven mainly by MAP (modal payoff) and SAL (salience) rules, with smaller contributions from regret and extremal heuristics. The framework offers a robust, interpretable way to compare broad behavioral mechanisms across menus, revealing substantial substitution among rules and providing a platform for extending revealed-preference analyses to procedure- and rule-based explanations of risky choice.

Abstract

We study choice among lotteries in which the decision maker chooses from a small library of decision rules. At each menu, the applied rule must make the realized choice a strict improvement under a dominance benchmark on perceived lotteries. We characterize the maximal Herfindahl-Hirschman concentration of rule shares over all locally admissible assignments, and diagnostics that distinguish rules that unify behavior across many menus from rules that mainly act as substitutes. We provide a MIQP formulation, a scalable heuristic, and a finite-sample permutation test of excess concentration relative to a menu-independent random-choice benchmark. Applied to the CPC18 dataset (N=686 subjects, each making 500-700 repeated binary lottery choices), the mean MRCI is 0.545, and 64.1% of subjects reject random choice at the 1% level. Concentration gains are primarily driven by modal-payoff focusing, salience-thinking, and regret-based comparisons.
Paper Structure (59 sections, 10 theorems, 147 equations, 8 figures, 3 tables)

This paper contains 59 sections, 10 theorems, 147 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Model
  3. Bounded Rationality
  4. Identity (Id).
  5. MaxMin (MMn).
  6. MinMax (MMx).
  7. Max at $p$ (MAP).
  8. Probability Weighting (PW).
  9. Salience Thinking Rule (SAL).
  10. Regret Rule (REG).
  11. Disappointment Rule (DIS).
  12. Attention to $L^1$ (A1).
  13. Attention to $L^2$ (A2).
  14. Library choice, coarseness, and interpretation.
  15. Alternative libraries and nesting.
  16. ...and 44 more sections

Key Result

Proposition 1

For any $t\in\mathcal{T}$, we have $\mathcal{F}^{\mathrm{strict}}_t\neq\varnothing$.

Figures (8)

  • Figure 1: Mean rule coverage across subjects. For each subject and rule $f$, coverage is the share of that subject's observations for which applying $f$ makes the realized choice a strict FSD improvement in the perceived menu. Bars report cross-subject means; rules are ordered as in the baseline library.
  • Figure 2: Density of $N_{eff}$
  • Figure 3: Distribution of the p-values from the Permutation Test
  • Figure 4: Rule Importance Metrics. Error bars indicate 95% confidence intervals.
  • Figure 5: Gender Heterogeneity in Rule Usage. The figure compares the Concentration Gain (Panel A) and Stability Score (Panel B) for men (dark blue) and women (orange).
  • ...and 3 more figures

Theorems & Definitions (24)

  • Definition 1: First-Order Stochastic Dominance
  • Proposition 1
  • Definition 2: Admissible assignment
  • Definition 3: Maximum Rule Concentration Index
  • Proposition 2
  • Proposition 3: Monotonicity
  • Definition 4: Stability Score
  • Definition 5: Concentration Gain
  • Definition 6: Random Rule Model
  • Definition 7
  • ...and 14 more