PRIORITY FILING - INITIAL DRAFT
A fully revised and formatted version will follow.
Gregory Caldwell Beier
Susarb LLC, Cambridge, Massachusetts
March 19, 2026
From the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics by Gregory Caldwell Beier (forthcoming 2026).
© 2026 Gregory Caldwell Beier. Licensed under CC BY-NC-ND 4.0.
The companion paper (Beier, 2026b, Section 3.4) establishes that the Disclosure Incentive improves individual judgment quality through a feedback loop: the agent discloses, the disclosure is scored against outcomes, the scoring reveals calibration strengths and weaknesses, and the agent adjusts. Lichtenstein and Fischhoff (1980) demonstrated the mechanism experimentally; Ericsson, Krampe, and Tesch-Romer (1993) identified the conditions under which practice produces genuine skill improvement. These results concern individual learning. This paper develops what happens when the improvement is public. When an analyst's calibration improves through the disclosure-scoring feedback loop, the improved disclosures enter the public domain - they are available for every other agent to read, evaluate, and learn from. The improvement propagates: not mechanically, as though calibration were contagious, but informationally, because better disclosures raise the quality of the information environment in which every participant operates. A population of analysts whose individual calibration is improving simultaneously through scored disclosure produces a collective learning dynamic whose economics differ from the economics of individual skill acquisition. Arrow's (1962) learning by doing showed that productivity improves as a byproduct of production. The Disclosure Incentive produces learning by disclosing - calibration improves as a byproduct of the disclosure that the track record incentive motivates - and the public nature of the disclosure makes the learning a collective good rather than a private one.
Keywords: collective learning, calibration improvement, public disclosure, learning by doing, deliberate practice, population dynamics, information environment, feedback loops
JEL Codes: D83, J24, O33, D62
Arrow (1962) introduced the concept of learning by doing: workers become more productive through the experience of production itself, without formal training or deliberate investment in skill. The learning is a byproduct of the activity, not its purpose. The economic implications are substantial - learning by doing generates increasing returns because accumulated production experience improves future productivity, and the improvement is partially non-rival (one worker's experience benefits coworkers who observe and learn from it).
The Disclosure Incentive produces a parallel phenomenon that this paper calls learning by disclosing. An analyst who discloses structured constraint reasoning and receives calibration feedback improves through a mechanism the companion paper (Beier, 2026b, Section 3.4) develops in detail: the articulation forces explicit reasoning, the scoring reveals calibration gaps, and the iterative cycle of disclose-score-learn-repeat trains better judgment over successive rounds. The learning is a byproduct of the disclosure activity, not its primary purpose - the analyst discloses to build track record capital, and the calibration improvement is a side effect of the process.
What makes learning by disclosing economically distinct from learning by doing is the public dimension. Arrow's learning by doing produces productivity improvements that are partially observable to coworkers - other workers can watch and imitate. But the observation is informal, partial, and limited to the workers in physical proximity. Learning by disclosing produces calibration improvements that are fully public - the improved disclosures are available in the public information environment for every participant to read, evaluate, and learn from. The propagation path is not proximity-limited. It is network-wide.
Section 2 develops the individual learning mechanism. Section 3 analyzes the propagation from individual to collective. Section 4 characterizes the collective learning dynamics. Section 5 derives implications. Section 6 states limitations. Section 7 concludes.
The individual improvement mechanism rests on three empirically grounded components.
The first is calibration feedback. In Lichtenstein and Fischhoff's (1980) calibration experiments, subjects who received explicit feedback comparing their stated confidence levels to observed outcome frequencies became measurably better calibrated in subsequent assessments. The feedback is the essential input - without it, experience does not reliably improve calibration, as Einhorn (1980) showed: unstructured experience can worsen judgment through confirmation bias and selective memory.
The second is deliberate practice. Ericsson, Krampe, and Tesch-Romer (1993) identified three conditions under which repeated performance produces genuine skill improvement: a structured task, unambiguous feedback, and sufficient iteration. The Disclosure Incentive satisfies all three: the five-field format structures the task, proper scoring provides unambiguous feedback, and the rolling disclosure cadence generates iteration. The improvement mechanism is not a metaphor - it is a specific implementation of deliberate practice applied to probabilistic judgment.
The third is articulation forcing. The companion paper on performative economics (Beier, 2026ao) develops the stronger claim that the disclosure format generates reasoning that was not previously occurring. For the individual learning mechanism, the relevant property is milder: the articulation requirement forces the analyst to make explicit the reasoning that was previously implicit, and the explicit reasoning is what the scoring mechanism can evaluate and the analyst can correct. Implicit reasoning cannot be scored because it was never stated. The disclosure format converts implicit reasoning to explicit reasoning, making it available for the feedback loop that drives improvement.
The individual improvement trajectory follows a learning curve. Early disclosures in a new constraint domain tend to be poorly calibrated - the analyst is learning what confidence levels are appropriate, what data matters most, and what interaction effects to attend to. Calibration improves with scoring cycles as the analyst adjusts in response to feedback. The improvement rate diminishes as the analyst approaches their ceiling - the calibration quality that the analyst's underlying analytical capacity can support. Tetlock (2005) documented substantial and persistent cross-individual variation in this ceiling, suggesting that some analysts are structurally better calibrated than others, and that the improvement mechanism raises each analyst toward their individual ceiling rather than converging everyone to the same level.
Individual improvement becomes collective improvement through three channels.
The first is direct learning from improved disclosures. When analyst A improves their aquifer calibration from 0.6 to 0.8 over three years, their later disclosures carry more information than their earlier ones - more accurate probability estimates, better-specified conditional structure, sharper identification of the interaction effects that matter. Analyst B, reading A's improved disclosures, receives a higher-quality input for their own analysis than they would have received from A's earlier work. B's own assessments improve as a function of the improved quality of the inputs available in the information environment - not because B copied A's conclusions, but because B incorporated A's better-calibrated reasoning into their own analytical process.
The second is methodological learning. Disclosed reasoning paths reveal not only conclusions but methods. An analyst who achieves high calibration in aquifer assessment by incorporating a specific hydrological interaction model signals to other analysts that this model is productive. Other analysts can adopt the method, adapting it to their own domains and data, and the method propagates through the disclosure network. The propagation is evaluable: an analyst who adopts a new method can compare their calibration scores before and after adoption, providing empirical evidence of the method's value. Unscored methodological diffusion - the way analytical techniques propagate through academic papers and industry practice - lacks this empirical feedback. Scored methodological diffusion is faster and more reliable because the scoring mechanism identifies which methods actually improve calibration rather than merely appearing sophisticated.
The third is standard-setting through demonstrated calibration. As the best-calibrated analysts build visible track records, their calibration levels become de facto standards against which other analysts and principals benchmark. An analyst whose aquifer assessments are calibrated at 0.85 sets an expectation for the domain - principals who have seen 0.85-level calibration discount analysts operating at 0.65. The benchmark effect raises the calibration level that the market demands, which creates pressure on all participants to improve. The pressure is competitive (analysts below the benchmark lose market share to those above it) but the mechanism through which the benchmark was established is cooperative (the leading analyst's disclosed record is the public good that created the standard).
The three channels - input quality improvement, methodological diffusion, and standard-setting - interact to produce a collective learning dynamic with specific properties.
The first property is that the collective learning rate exceeds the average individual learning rate. Each individual improves at their own pace along their own learning curve. But the collective information environment improves faster than any individual because it aggregates the improvements of all participants simultaneously. When ten analysts each improve by a different amount along different dimensions of a constraint domain, the information environment available to the eleventh analyst reflects all ten improvements, even though no single analyst contributed all of them. The collective gains from disclosure mirror Arrow's (1962) insight about learning by doing - the accumulation of experience across the workforce produces productivity gains that exceed any individual's contribution - but with the additional feature that the gains are fully public and immediately available to every participant in the disclosure network.
The second property is domain-specific acceleration. The collective learning rate is highest in constraint domains where the disclosure density is greatest, because denser disclosure networks produce more feedback, more methodological cross-pollination, and more visible benchmarks. The companion paper on factorial coordination (Beier, 2026ag) shows that information value grows combinatorially with the number of disclosers in a domain. The collective learning dynamic reinforces this: more disclosers means more scored feedback, which means faster individual improvement, which means higher-quality disclosures, which means more valuable inputs for other disclosers. The acceleration is self-reinforcing within constraint domains that have achieved critical mass.
The third property is cross-domain spillover. An analyst who improves their calibration in one domain often improves in adjacent domains, because some calibration skills (appropriate uncertainty quantification, attention to base rates, resistance to overconfidence) are domain-general. When the improvement in the original domain is public and scored, analysts in adjacent domains can observe which calibration practices produced the improvement and adapt them. The cross-domain spillover extends the collective learning beyond the boundaries of any single constraint domain, though it operates more weakly across distant domains than within closely related ones.
The collective learning dynamic has three implications for the Disclosure Incentive's value.
The first is that the mechanism's value grows over time at a rate faster than the number of participants would suggest. Each participant's improvement feeds the improvement of others, which feeds further improvement, producing a compounding dynamic in the quality of the information environment. The early years of the Disclosure Incentive will produce modest information quality improvements as individual analysts begin their learning curves. The later years will produce accelerating improvements as the collective dynamics kick in - individual improvements propagate, methods diffuse, standards rise, and the information environment compounds.
The second is that the Disclosure Incentive produces a positive externality that compounds across generations of analysts. An analyst who enters the disclosure ecosystem in year ten encounters an information environment shaped by a decade of collective improvement - better methods, higher benchmarks, richer inputs. Their starting point is higher than the starting point of the analysts who built the ecosystem, and their improvement trajectory begins from a more advanced base. The intergenerational transmission of calibration quality through the public disclosure record is the human capital analog of the compounding returns that physical capital accumulation produces in the Solow growth model - but with the distinctive feature that the accumulated asset (the disclosure record) does not depreciate through physical wear, though it does require updating as constraint environments evolve (a dynamic addressed in the companion paper on depreciation).
The third is that the collective learning dynamic partially addresses the deep space problem identified in the companion paper on long-horizon constraint reasoning (Beier, 2026j). Long-horizon constraint assessment is the domain where individual calibration feedback is slowest (outcomes take decades to materialize). Collective learning accelerates the effective feedback rate by allowing analysts to learn from each other's assessments and from the interim scoring that becomes available as monitoring data accumulates. An analyst assessing fifty-year aquifer dynamics benefits from reading other analysts' shorter-horizon assessments of the same aquifer system, whose scoring arrives sooner and provides indirect evidence about the longer-horizon dynamics. This mechanism operates through intermediate milestones: the community decomposes a fifty-year forecast into overlapping three-year and five-year verifiable predictions, each scoreable on a timeline short enough for calibration feedback to function. The intergenerational transmission of judgment quality depends on this decomposition - without intermediate milestones, the collective learning loop cannot close on deep-horizon constraints. The collective learning network substitutes, imperfectly but meaningfully, for the slow direct feedback that deep space constraints impose.
The paper argues that collective learning through public disclosure is faster than individual learning but does not model the dynamics formally. A formal model would specify the network structure, the individual learning curves, the propagation mechanisms, and the interaction effects, then derive the collective learning rate as a function of these parameters. The paper's analysis is qualitative and directional rather than quantitative.
The claim that methodological diffusion through scored disclosure is faster and more reliable than methodological diffusion through academic publication is plausible but untested. The scoring mechanism provides an empirical signal about which methods improve calibration, which academic peer review does not. But academic methods are backed by theoretical justification and extensive testing, while disclosure-scored methods may perform well on historical scoring without generalizing to new conditions. The relative reliability of the two diffusion channels is an empirical question.
The collective learning dynamic assumes that analysts read each other's disclosures and learn from them. In practice, attention constraints (Sims, 2003) limit how many disclosures any individual analyst processes, and the collective learning rate is bounded by the attention the population allocates to cross-reading. If analysts produce disclosures but rarely read others' disclosures (because the direct track record return from producing disclosures exceeds the indirect benefit of reading others'), the propagation channels weaken and the collective learning rate converges toward the individual rate.
The intergenerational transmission claim assumes that the disclosure record remains accessible and interpretable over time. If the scoring infrastructure degrades, the ontology shifts, or the constraint environment changes enough that historical disclosures become irrelevant, the accumulated record loses value and the intergenerational transmission weakens. The companion paper on depreciation dynamics (Beier, 2026b) analyzes how track records depreciate as constraint environments evolve; the same depreciation applies to the collective information environment.
Private learning helps one agent. Public scored learning helps everyone who reads the improving disclosures - and the improvement compounds across the population in ways that private learning cannot replicate. The Disclosure Incentive produces learning by disclosing: calibration improves as a byproduct of the disclosure process the track record incentive motivates, and the public nature of the disclosure converts individual improvement into a collective good.
The collective learning dynamic is the mechanism through which the Disclosure Incentive produces returns that exceed the sum of individual returns. Each analyst improves individually through calibration feedback. Each improved disclosure raises the quality of the information environment for every other analyst. Each analyst operating in a higher-quality environment improves faster than they would have in isolation. The compounding is not a metaphor - it is a specific propagation mechanism operating through the same public information channels that the companion papers analyze for other purposes. The Disclosure Incentive was designed to resolve the Grossman-Stiglitz paradox. The collective learning dynamic is an emergent property of the resolution - a coordination improvement that arises from the mechanism's structure rather than from any explicit design for collective learning.
This paper presents results from the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics (Beier, forthcoming 2026). Collective learning economics extends the individual improvement mechanism from the companion paper (Beier, 2026b) to the population level, showing how the public nature of scored disclosure converts private skill acquisition into a collective good. The author invites engagement from the learning economics, human capital, and knowledge management communities.