Minimum Description Length, or MDL, recovered the model that generated the data in 99% of 10,000 simulated datasets for each of two candidates. For one candidate, AIC and BIC recovered it in 48% of cases and cross-validation in 68%; for the other, all three exceeded 99%.
MDL treats model comparison as data compression, combining fit with a penalty based on the range of datasets a model can fit. The paper asks whether this can capture flexibility differences that parameter counts may miss. It uses NML throughout, with complexity depending on the model set rather than an additional prior or parameterization.
The comparisons produced different model choices
In a reanalysis of social-preference data from 96 subjects, predictive success and compression gain both selected a model labeled HM. Its area-based form had a predictive-success score of 0.177, while random-utility specifications had lower description length; the random-utility HM version achieved about 10% compression gain.
Risk simulations compared one-parameter model restrictions across three designs, each with 50 lotteries. For each experiment-model pair, the analysis generated 10,000 datasets, with parameters drawn uniformly from 0.2 to 0.8 and a noise scale of 0.1.
Across the designs, MDL selected the true risky-choice model in at least 94% of simulations. Cross-validation recovered the less-complex model in 56% and 49% of simulations in the two narrow designs, but recovered the more-complex model in 97% to 99% when that model was true.
The corresponding risky-choice reanalysis involved 179 subjects. Each provided 50 certainty equivalents, split between 25 gain-framed and 25 loss-framed lotteries, and models were compared separately for each subject. MDL was the most conservative criterion, favoring the one-parameter probability-weighting model; AIC and cross-validation favored the fully parameterized prospect-theory variant, while BIC most often selected an intermediate two-parameter weighting model.
Time-preference tests split the methods
Time-preference simulations compared hyperbolic and constant-sensitivity models using noisy present values at delays from 1 through 10, with a noise standard deviation of 0.05. When the hyperbolic model generated the data, MDL recovery exceeded 99%, compared with 62% for AIC and BIC and 58% for cross-validation. When constant sensitivity generated the data, MDL recovered it in 90%, compared with more than 99% for AIC and BIC and 90% for cross-validation.
The empirical time-preference analysis included 67 subjects at six delays ranging from three months to four years, with data pooled into 402 observations. Hyperbolic discounting had lower complexity than constant sensitivity, 7.31 versus 8.25, and higher completeness, 0.862 versus 0.850. MDL selected hyperbolic discounting, whereas AIC, BIC and cross-validation selected constant sensitivity.
The evidence stays within the designs tested
These are results within the candidate models, parameter ranges, noise levels and experimental designs studied. Simulation recovery depends on those choices and calibrations, while the empirical applications use one archival dataset or treatment per application and do not provide independent external validation.
Many complexity values rely on an asymptotic Fisher-information approximation that requires regularity conditions. In empirical comparisons with estimated noise, the choice of positive lower bounds can affect comparisons between models with different parameter counts. The main recovery and ranking results are reported without confidence intervals, hypothesis tests or other formal uncertainty estimates.
The manuscript is an arXiv version-1 preprint dated 25 August 2026, and no journal publication is listed. Whether the reported recovery patterns extend to other economic domains, datasets and experimental designs remains open.
Paper data and sources
Original title: Theory as data compression
Authors: Carlos Cueva
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
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