In held-out private die-roll reports, about 45 percent read as honest, and this method cannot tell us why

In a private die or coin task a person sees a random outcome alone and is paid by the number they report, so a lie pays and cannot be caught. Payoff maximisation says everyone should claim the top outcome. We used the open meta-study data of Abeler, Nosenzo and Raymond: 252 first-round treatments from 58 papers with 27,039 subjects, split by paper so that 19 papers with 9,960 subjects were held out. On held-out tasks with three or more outcomes, reports read as 45 percent honest, 26 percent maximal and 29 percent partial.c1 Six preference models were fitted on the other papers and scored on the held-out ones. All six sit within 0.005 nats per report of each other, and no contrast against the fixed-cost model passes the false-discovery correction.c2 The planted check failed: on data simulated from the reputation model, the reputation model lost to the fixed-cost model by 0.0003 nats per report.c3 By the preregistered rule, no ranking among the models counts. Our subset's mean standardised report was 0.287 against the 0.234 published for the full data, outside the preregistered tolerance of 0.03.c4 The departure from strict self-interest is large; the mechanism behind it is not identified by report distributions.

Fischbacher and Föllmi-Heusi [3] made the private reporting taskDefinition: private reporting task (die-under-the-cup) experimental economics and psychology An experiment in which a person observes a random outcome in private, such as a die roll or coin toss, reports it, and is paid by the report, so a lie pays and cannot be caught for any one person. Lying shows only in the distribution of many reports. Excludes tasks where the experimenter can see each person's true outcome. full definition a standard tool. Subjects rolled a die under a cup, reported the number, and were paid by it. No single lie could be detected, and the honest distribution is known, so lying shows in the reports as a whole. They found many fully honest subjects, a smaller group who lied to the maximum, and a large group of partial liars who lied but did not claim the top payoff, which they read as a wish to keep a favourable self-image.

Gächter and Schulz [4] ran the die task in 23 countries and related intrinsic honesty to a national index of the prevalence of rule violations built from corruption, tax evasion and political fraud. They found more honest reporting in subject pools from countries with fewer violations.

Abeler, Nosenzo and Raymond [1] combined data from 90 studies across economics, psychology and sociology and found that people lie surprisingly little. They derived predictions that separate the leading models, tested them with new experiments, and concluded that a preference for being honest together with a preference for being seen as honest best explains the behaviour. They published their data [2].

This paper asks a narrower question of that public data. Without the designed treatments that Abeler and colleagues used to separate the models, can the plain report distributions of ordinary first-round tasks tell the models apart on papers the models have not seen? And what share of reports look honest, maximal or partial?

The design was written as a preregistrationDefinition: preregistration research method (metascience) A dated written plan for a study, fixed and hash-locked before any result is seen: the question, the data, the statistic, the controls, the forecasts and the kill conditions. Excludes a plan revised after looking at the outcome, and a protocol written only for the record after the run. full definition and hash-locked on 31 October 2026 at 22:02 UTC, before any model was fitted. Two things were seen first, and both are stated in the locked file. The publishers' site gives a mean standardised report of 0.234. Our parsing step printed pooled report distributions over all 252 treatments, held-out ones included, and printed a mean standardised report of 0.287. The forecasts of report shares are therefore not blind to the pooled shape.

The locked file names the data and its filters, the six models and two baselines, the score, the paper-level tests, the three-part reading, the planted checkDefinition: planted check research method; called a positive control in experimental science Data built so that the right answer is known, run through the same analysis before the real data, to show that the analysis can see the effect when it is there. Excludes any check made on the real data, which cannot show what the analysis misses. full definition, a reproduction check, a controlDefinition: control statistics and experimental design A version of the data with the structure under test removed (for example shuffled or pooled), scored the same way as the real data, so the real score has something to beat. Excludes a comparison with a different dataset or with a published number. full definition, the forecasts and the kill conditionsDefinition: kill condition research method (our usage, after Popper's falsification) A rule written in the preregistration that, when met, decides against the claim with no room for judgement after the run. Excludes reasons found after the run for setting a result aside. full definition. Its assumptions are listed in it: true outcomes are uniform; upward lies come from preference only and downward lies only from mistakes; one population spans countries and subject pools; only first rounds are used; and the norm model has no measured norm input. Nothing was added after the run.

Kill conditions, without discretion:

Reproduction check: the mean standardised report over the by-treatment set must lie within 0.03 of 0.234.

The data are the merged meta-study file and the data-and-programs archive published by Abeler, Nosenzo and Raymond [2] on their resources page and on figshare (files 16211150 and 16211414), downloaded on 31 October 2026. The site states that all its data are released under the CC BY licence, with credit and a link back. The files were read as data; no program in the archive was run. The publishers' site describes the full set as 429 treatments from 90 papers with over 44,000 participants in 47 countries.

A parsing step kept first-round reports from tasks with uniform true outcomes and 2, 3, 6 or 10 possible outcomes. It removed treatments coded in the data as internal lying or as having a victim, treatments that asked subjects about the report distribution, and treatments that told subjects what others reported. That left 252 treatments from 58 papers with 27,039 subjects. Papers were split by a hash of the citation, with 30 percent held out: the held-out papersDefinition: held-out papers statistics, cross-validation Papers kept out of all fitting, chosen by a hash of the citation (30 percent of papers), on which every model is scored once. All treatments from one paper fall on the same side. Excludes a split by treatment or subject, which would let one paper's design appear in both fitting and scoring. full definition were 19 papers with 9,960 subjects, and fitting used 17,079 subjects.

As a check on the parsing, the baseline treatment of Fischbacher and Föllmi-Heusi in our file has counts of 38, 44, 64, 76, 171 and 219 from the lowest to the top payoff. Our results summary records the top report at 36 percent, where honest reporting gives 17.

Let a task have $K$ outcomes, ranked by payoff, with ${\pi }_r$ the rank of report $r$ scaled from 0 for the lowest to 1 for the highest. A person who saw outcome $s$ and reports $r$ receives the scaled payoff times a stakes factor

where $G$ is the money at stake in the treatment in purchasing-power dollars and $ϵ$ is the stakes elasticityDefinition: stakes elasticity behavioural economics, our parametrisation The parameter epsilon in a stakes factor (G/5) to the power 1 minus epsilon, where G is the money at stake. At epsilon 1 the size of the payment has no effect on reports, and at 0 the pull to lie grows in proportion to the payment. Excludes the effect of payment on whether people take part. full definition. Each person also carries a lying cost $c$, drawn from a lognormal distribution, $\ln c=\mu +\sigma z$ with $z$ standard normal, evaluated on a grid of 25 quantiles. Each person picks the report with the highest utility

where $a_r$ is 1 when $r$ differs from $s$ and 0 otherwise, $d_r$ is the payoff distance $|{\pi }_r-{\pi }_s|$, and $R_r$ is the chance that a person making report $r$ is honest. Each model keeps some of these terms:

A trembleDefinition: tremble game theory and behavioural economics A parameter that mixes a share of uniformly random reports into a model's prediction, standing for mistakes and inattention. In these models it is the only source of downward lies. Excludes a preference, since the tremble does not depend on payoffs. full definition $\tau$ mixes in uniform reports, so a model's prediction for report $r$ is $q_r=(1-\tau )m_r+\tau /K$, with $m_r$ the share of the cost grid choosing $r$. The payoff model has no cost and no tremble. It is a logit choice on money alone with one scale parameter $\beta$:

Two baselines frame the models: everyone honest, which predicts uniform reports, and the training-average baselineDefinition: training-average baseline forecast verification, where it is called climatology A forecast that gives each held-out treatment the average report distribution of training treatments with the same number of outcomes. Excludes any theory of why people report as they do. full definition. Every model was fitted by maximum likelihoodDefinition: maximum likelihood statistics Fitting a model's parameters by choosing the values that make the observed data most probable under the model. Excludes choosing parameters by hand or by fit to the test data. full definition on the training papers.

Models are scored by log lossDefinition: log loss (nats per report) statistics and forecast verification Minus the average natural log of the probability a model gave to each report that was made. Lower is better, and the difference between two models in nats per report is how much better one predicts each report. Excludes an accuracy count, which ignores how much probability a model gave to what happened. full definition over the $N$ held-out subjects, with $n_{\mathrm{tr}}$ the count of report $r$ in treatment $t$:

A model's gain is the everyone-honest loss minus its own. Each theory model is compared with the fixed-cost model by a paper-level sign permutation testDefinition: paper-level sign permutation test statistics A test that sums each held-out paper's difference in log loss between two models, then flips the sign of each paper's difference at random 5,000 times to see how often a sum as large arises with no true difference. Excludes a test that treats subjects within one paper as independent. full definition, the p values adjusted together by the Benjamini-Hochberg correctionDefinition: Benjamini-Hochberg correction statistics, multiple testing A rule that adjusts a set of p values so that, among the tests called significant, the expected share of false calls stays at or below a chosen rate q, here 0.05. Excludes the stricter Bonferroni rule, which bounds the chance of any false call. full definition. The reputation and full models' differences from fixed cost also get a 95% intervalDefinition: 95% interval statistics The range that holds the middle 95 percent of the bootstrap or control draws for a number. We report it beside the number. Excludes a statement that the true value lies inside with 95 percent probability. full definition from a paper bootstrapDefinition: paper bootstrap statistics An interval made by recomputing a statistic 2,000 times on held-out papers drawn with replacement, so subjects from one paper stay together. Excludes resampling single subjects as if they were independent. full definition.

For each task size of 3, 6 or 10, reports are pooled and given a three-part readingDefinition: three-part reading experimental economics, after Fischbacher and Föllmi-Heusi A split of a report distribution into honest reporters, read as the number of outcomes times the share reporting the lowest outcome, maximal liars, the excess at the top over the honest share, and partial liars, the rest. Excludes an observation of any person's lie; it assumes the true outcomes are uniform and that no one lies downward on purpose. full definition. With $q_1$ the share reporting the lowest outcome and $q_K$ the share reporting the top,

with $h$ capped at 1, and the partial share is $1-h-m$. The three task sizes are combined weighted by subjects. Two-outcome tasks are left out, since they have no partial lie.

For the reproduction check each report is mapped to $x_r=-1+2(r-1)/(K-1)$, and the standardised reportDefinition: standardised report experimental economics; the measure Abeler, Nosenzo and Raymond report, computed here by our own code The mean report of a treatment after the outcomes are mapped evenly onto -1 for the lowest-paying report and +1 for the highest, so honest reporting gives 0 in expectation and everyone claiming the top gives 1. Here averaged over treatments without weights. Excludes a share of liars, which the mean alone does not give. full definition is averaged over the $T$ treatments without weights:

The planted check simulated report counts from the reputation model at known parameters on the same treatments, kept the same split by paper, fitted the fixed-cost, size-cost and reputation models to the simulated training papers and scored them on the simulated held-out papers. The reputation model had to beat both. The planted check failed: on data simulated from the reputation model, the reputation model lost to the fixed-cost model by 0.0003 nats per report.c3 It beat the size-cost model by 0.0005. The fitted reputation parameters also missed the planted ones: the log of the value on looking honest, $\rho$, was planted at 0.2 and fitted at -0.56. The method cannot recover a known model at this sample size, so by the kill condition no ranking of the real models counts.

The shuffle control permuted report labels within each held-out treatment, and the best model's gain over everyone-honest was recomputed 300 times to give a null distributionDefinition: null distribution statistics The spread of scores a control gives over many random draws. Its 95th percentile is the bar a real score must clear. Excludes a theoretical distribution assumed rather than drawn from the data. full definition. Its 95th percentile was -0.086 (mean -0.112). The real best gain of 0.072 lies far above it (p from drawsDefinition: p value (from draws) statistics The share of control draws scoring at or above the real score, with one added to the count and to the number of draws, so it is never zero. Excludes a p value from a textbook formula that assumes a distribution. full definition 0.003). The theories carry information beyond chance, and this kill condition did not fire.

The reproduction check failed. Our subset's mean standardised report was 0.287 against the 0.234 published for the full data, outside the preregistered tolerance of 0.03.c4 The two numbers come from different sets: ours uses first rounds only and drops several designs. Our filtered subset does not reproduce the publishers' headline figure, and the 0.287 was printed before the lock, so the outcome of this check was knowable when the plan was written.

Table 1 and Figure 1 give the held-out losses. Every model beats everyone-honest by about 0.07 nats per report. All six sit within 0.005 nats per report of each other, and no contrast against the fixed-cost model passes the false-discovery correction.c2 The reputation model's edge over fixed cost was 0.003 (95% interval -0.001 to 0.008, p 0.40), and the full model's 0.002 (-0.008 to 0.012, p 0.75). The training-average baseline, which has no theory in it, scored the same as the norm model to four places.

The payoff model was forecast to do worse than honest reporting. With its logit noise it did better, by 0.071 nats per report, and finished second. A model with no lying cost at all fits these reports almost as well as the cost models.

The fitted stakes elasticities were 0.89 to 0.96 across the five cost models, so the size of the payment hardly moved reports in these data.

On held-out tasks with three or more outcomes, reports read as 45 percent honest, 26 percent maximal and 29 percent partial.c1 The training papers gave 42, 24 and 34 percent. Table 2 and Figure 2 set those against the shares each fitted model predicts for the held-out tasks.

One held-out paper carries the full model's small edge. In Effron and colleagues' 2015 study (2,151 subjects), the full model beat fixed cost by 0.021 nats per report; without that paper, the full model's edge over fixed cost becomes -0.003. Across the 23 subject pools of Gächter and Schulz [4] in the data, the mean standardised report ranged from 0.18 to 0.58 (standard deviation 0.10).

Two sensitivity refits, scored on matching held-out subsets, are in Table 3. The fixed-cost model scored best of the three theories refitted in both. Among students the training average beat every theory; in the general population it lost to all three. The refit without hand-coded treatments was not run, because too few treatments remained.

Table 4 sets the forecasts written before the run against the outcomes.

The departure from strict payoffs is the part that holds. Payoff maximisation predicts that every report is the top one; held-out reports show a top share of about a quarter beyond the honest share and a large honest share, consistent with what Fischbacher and Föllmi-Heusi [3] and Abeler and colleagues [1] report. The reading of those shares rests on the uniform-truth assumption and on there being no deliberate downward lies.

The mechanism is not identified here. Six models built on different motives, and a training average with no motive at all, predict held-out reports to within 0.005 nats per report. The planted check places part of the problem in the design: when the reputation model was true, the method still could not pick it out. Report distributions from ordinary tasks constrain the shape of reporting and leave the motive open.

This does not contradict Abeler and colleagues [1]. Their conclusion rests on designed treatments that change what a report signals about the reporter, which this study did not refit. Our result says that the distributions alone are not enough, which is the reason such treatments are needed.

The payoff logit's second place deserves care. A logit with a single scale parameter puts most weight on high reports and spreads the rest, and on these data that shape matches the reports about as well as a cost model. Its predicted shares are the furthest from the observed ones (Table 2), so a fit on log loss and a fit on shares can disagree.