Which Decision Rules Do People Use? A Mixture-of-Rules Model of Human Risky Choice with Context-Dependent Weights

Purpose. Recognising how people decide, and not only what they choose, requires models whose components correspond to decision rules. We ask whether a mixture of classic rules (expected value, mean–variance, cumulative prospect theory, the priority heuristic, maximin, equal weighting and a position bias), with mixture weights that depend on the decision context, predicts human choices in risky-choice problems better than a single rule or a regression on the same rule features, and what the fitted weights say about how the context changes the rules in use. Design and methods. We used the choices13k data set (242,859 choices in 14,568 problem-condition rows, 12,996 distinct two-option gambles with 15–33 participants each), where the target is the proportion of participants choosing option B. The mixture model gives each rule a choice probability and combines them with softmax weights that depend on four context variables (feedback, ambiguity, number of outcomes, presence of losses); parameters were fitted by maximum binomial likelihood with an L2 penalty on the weight parameters. Models were compared by five-fold cross-validation with folds grouped by distinct problem, and R² was referred to a noise ceiling computed from binomial sampling error. Comparators were a logistic model of expected value, a logistic regression on all rule features and gradient boosting on the same features. Findings. Cross-validated R² was 0.397 for expected value alone, 0.506 for the regression on all rule features, 0.604 for the mixture and 0.711 for gradient boosting, against a noise ceiling of 0.751. The mixture improved on the regression in all five folds (by 0.089 to 0.108) but was 0.106 below the flexible model. Fitted weights depended on context: expected value had a mean weight of 24.8% in problems with feedback against 15.2% without, while equal weighting and the position bias together had 47.3% in ambiguous problems against 21.0% overall. The priority-heuristic component converged to an error rate of 0.50, so it acted as an indifference component rather than as a deterministic heuristic, and the data do not support that heuristic as a rule in use. Originality. The paper separates what a rule-based model can explain from what a flexible predictor can, quantifies the gap against a noise ceiling, and reports a degenerate component and the limits of identification of the weights instead of treating fitted weights as a direct readout of the rules people use.