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 on incentive compatibility (Beier, 2026r) proves that the Disclosure Incentive - with its specific combination of proper scoring rules, commitment mechanisms, coverage-adjusted scoring, and track record accumulation - is incentive-compatible within the conditions specified. But the Disclosure Incentive occupies a single point in a large design space. Alternative scoring rules, different commitment structures, different track record aggregation methods, different disclosure formats, and different verification architectures could produce different tradeoffs among truth-telling strength, adoption cost, adversarial robustness, and information richness. This paper maps that design space. Drawing on the market design literature (Roth, 2002) and the applied mechanism design tradition (Milgrom, 2004), it identifies the key design dimensions along which judgment market architectures vary, characterizes the tradeoffs each dimension involves, and derives design principles that any system for capturing, scoring, and aggregating human judgment must satisfy. The paper is honest that the Disclosure Incentive as currently specified is a design choice informed by analytical reasoning about the relevant tradeoffs, not a provably optimal mechanism. The design space is large, the tradeoffs are empirical as well as theoretical, and the optimal design may differ across constraint domains, institutional contexts, and stages of ecosystem maturity. Incentive architecture economics studies the design space rather than the single point the Disclosure Incentive occupies in it - and the study reveals both the robustness of the current design's core features and the dimensions along which alternative designs could improve on it.
Keywords: mechanism design, market design, incentive architecture, scoring rules, commitment mechanisms, track records, judgment markets, design space, tradeoffs, optimization
JEL Codes: D47, D82, C72, D02, L86
Roth (2002) argued that economics had entered an era of market design - the application of economic theory to the practical construction of market institutions. Auction design (Milgrom, 2004), matching market design (Roth and Peranson, 1999), and spectrum allocation (Milgrom, 2000) each demonstrated that the details of mechanism design matter enormously for outcomes, and that economic theory provides principles - though not always unique solutions - for navigating the design choices.
The Disclosure Incentive is a designed mechanism. Its components - the five-field disclosure format, proper scoring rules, the commitment mechanism, coverage-adjusted scoring, track record accumulation, and the judgment market return structure - were chosen to satisfy specific desiderata: truth-telling incentive compatibility, adversarial robustness, information richness, and practical implementability. The companion paper (Beier, 2026r) proves that the mechanism achieves incentive compatibility under stated conditions. The adversarial paper (Beier, 2026an) analyzes its robustness to attacks.
But mechanism design is not mechanism optimization. Proving that a mechanism works is not the same as proving that no alternative works better. The design space for judgment market architectures contains many mechanisms that could be incentive-compatible under various conditions, and they differ along dimensions that involve genuine tradeoffs. The present paper maps those dimensions and the tradeoffs they entail, treating the Disclosure Incentive as one well-analyzed point in a space that merits broader exploration.
Section 2 identifies the key design dimensions. Section 3 analyzes the tradeoffs along each dimension. Section 4 derives design principles that are robust across the space. Section 5 identifies the dimensions where the current design could be improved. Section 6 states limitations. Section 7 concludes.
Six dimensions define the design space for judgment market architectures.
The Disclosure Incentive uses strictly proper scoring rules (Brier, 1950; Good, 1952; Gneiting and Raftery, 2007), which maximize expected score at truth-telling. Within the class of strictly proper rules, the choice matters. The Brier score (quadratic) is bounded and symmetric - it penalizes overconfidence and underconfidence equally. The logarithmic score is unbounded below - it imposes catastrophic penalties for confident predictions that turn out wrong. The spherical score offers intermediate properties. Each choice produces different incentive gradients: the logarithmic score provides stronger incentives for honest reporting at extreme probabilities (near 0 or 1) but exposes agents to potentially devastating single-event losses that could discourage participation. The Brier score is gentler but provides weaker incentives at the extremes. The Brier score's bounded range [0,1] is not merely a convenience - it is what enables the tight calibration threshold proof (companion paper) to mathematically defeat the ex-post withholding problem. The logarithmic score's unbounded downside makes that proof impossible without additional assumptions about agent risk preferences.
Alternative approaches exist outside the strictly proper class. Prelec's (2004) Bayesian Truth Serum elicits honest reporting without requiring outcome observation - it works by comparing agents' reports to the distribution of reports across the population. Miller, Resnick, and Zeckhauser (2005) developed peer prediction methods that function when outcomes are subjective or unverifiable. These methods sacrifice the strict properness guarantee in exchange for applicability to domains where outcomes cannot be observed, which the standard proper scoring rule requires.
The Disclosure Incentive uses a public commitment mechanism: agents declare their disclosure domain and cadence in advance, and the track record scores adherence alongside calibration. The commitment structure constrains strategic selection (Beier, 2026r, Proposition 7) but imposes a rigidity cost - agents who commit to a domain cannot easily pivot when their interests or expertise shift.
Alternative commitment structures include no commitment (agents disclose whatever they choose, whenever they choose, with no pre-announced domain - maximizing flexibility but enabling strategic selection), domain commitment with flexible cadence (agents commit to a constraint domain but choose when to disclose - reducing the cadence signal from the companion temporal economics paper), and graduated commitment (agents begin with narrow commitments and expand as their track records grow - reducing the entry barrier while building toward comprehensive coverage).
The Disclosure Incentive aggregates scores into a cumulative track record using a simple average weighted by recency (the companion paper on judgment capital, Beier, 2026b, develops the depreciation dynamics). Alternative aggregation methods include exponential decay weighting (recent scores count more heavily, reflecting the intuition that current calibration matters more than historical calibration), domain-segmented records (separate calibration scores for each constraint domain rather than a single aggregate, preserving domain-specific quality information at the cost of a more complex record), and Bayesian calibration estimation (treating the track record as a sequence of observations from which calibration quality is estimated as a posterior distribution rather than a point statistic - providing uncertainty estimates around the calibration score that a simple average does not).
The five-field structure (Input, Method, Output, Identity, Scaling) is the Disclosure Incentive's specific format. Alternative formats could include fewer fields (only Output and Identity, minimizing the disclosure burden but losing the reasoning path that the Method and Scaling fields preserve), more fields (adding temporal horizon specification, uncertainty decomposition, or sensitivity analysis as required fields), or flexible fields (a core set of required fields with optional extensions that analysts in specific domains can add). The format choice involves a tradeoff between information richness (more fields preserve more of the original judgment) and adoption cost (more fields require more analytical effort per disclosure, raising the barrier to participation).
The Disclosure Incentive verifies through outcome-based proper scoring - disclosures are compared to what actually happened. Alternative verification architectures include peer evaluation (disclosures are scored by other experts in the domain, as in academic peer review), market-based verification (a prediction market prices the probability that the disclosure is accurate, aggregating the crowd's assessment of quality), and hybrid approaches (outcome scoring where outcomes are available, peer scoring where they are not, with the two scores combined into a quality estimate).
The judgment market in the companion paper (Beier, 2026b, 2026d) is modeled as a competitive market where principals hire agents based on track records. Alternative market structures include auction-based allocation (principals bid for access to specific analysts' disclosures, with revenue funding the epistemic infrastructure), subscription models (principals pay for access to a curated disclosure feed, with the curator selecting for quality), and public provision (disclosures are funded publicly and available to all, eliminating the market pricing of judgment quality in favor of universal access).
Each design dimension involves tradeoffs that the current Disclosure Incentive resolves in a specific way. Three cross-cutting tradeoffs deserve attention because they recur across multiple dimensions.
The first is truth-telling strength versus participation cost. Stronger truth-telling guarantees (stricter scoring rules, more demanding commitment structures, more detailed disclosure formats) come at higher participation costs - more effort per disclosure, higher risk from scoring, less flexibility to adapt. The logarithmic score provides stronger truth-telling incentives than the Brier score but exposes agents to unbounded losses that could deter risk-averse analysts from participating. A five-field format preserves more reasoning than a two-field format but requires more analytical work per disclosure. The design must balance the strength of the honesty incentive against the breadth of participation, because a mechanism with perfect truth-telling properties but no participants produces no information.
The second is information richness versus scalability. Richer disclosures (more fields, more detailed reasoning, more explicit uncertainty quantification) produce a more informative judgment data stream but are harder to produce at scale, harder to process (the rational inattention constraint binds more tightly on complex disclosures), and harder to score (multi-dimensional disclosures may require multi-dimensional scoring rules that are less well understood than scalar proper scoring rules). The design must balance the quality of individual disclosures against the volume and accessibility of the disclosure stream.
The third is adversarial robustness versus openness. Stronger adversarial defenses (stricter identity verification, more demanding commitment structures, more sophisticated detection algorithms) protect the judgment data stream's integrity but raise barriers to entry and may exclude legitimate participants whose institutional context does not support the verification requirements. The adversarial paper (Beier, 2026an) analyzes the attack surface; the present paper's contribution is to note that every defense mechanism has an adoption cost, and the design must balance integrity protection against the participation breadth that the mechanism's information value depends on.
Certain design principles hold across the entire design space - they are features that any judgment market architecture should incorporate regardless of where it sits on the tradeoff dimensions.
Principle 1: Outcome-based scoring where feasible. Whenever outcomes are observable and attributable within a reasonable horizon, proper scoring against outcomes should be the primary verification mechanism. No alternative - peer review, market-based assessment, self-report - provides the same immunity to conflicts of interest and the same direct linkage between stated beliefs and reality. This principle is robust because proper scoring's incentive properties are mathematical rather than institutional, and the mathematical guarantees hold regardless of the specific scoring rule chosen.
Principle 2: Public track records. The track record should be public, portable, and persistent. Private track records (visible only to the agent and their current employer) sacrifice the portability that gives track record capital its labor market value and the public-good properties that enable the collective learning dynamics from the companion paper (Beier, 2026al). This principle is robust because the public nature of the record is essential for every downstream property the companion papers identify: labor market signaling, collective learning propagation, principal-agent quality assessment, and adversarial detection.
Principle 3: Structured format with a scaling component. The disclosure should be structured enough to enable comparison across analysts and should include an assessment of interaction effects at scale. The specific structure can vary (more or fewer fields, different labeling, different granularity), but some structure is necessary for the scoring, comparison, and aggregation functions to operate, and some version of the Scaling field is necessary because scaling information is the type the price system most completely fails to carry (Beier, 2026ah).
Principle 4: Open-source specification. The disclosure format, scoring rules, and ontologies should be open-source rather than proprietary. Proprietary standards fragment the ecosystem, reduce network effects, and create rent-extraction opportunities that misalign the infrastructure's incentives with the information system's purpose. The open-source principle follows from the public good properties of the epistemic infrastructure (Beier, 2026aq) and from the Lerner-Tirole (2002) analysis of why open-source infrastructure outperforms proprietary alternatives when network effects are strong.
The Disclosure Incentive's current design occupies a reasonable point in the design space, but several dimensions merit further exploration.
The scoring rule choice could be domain-adaptive: using the logarithmic score in domains where extreme probabilities are common and consequential (tail-risk assessment, tipping-point analysis) and the Brier score in domains where probabilities cluster near the middle of the range (routine constraint monitoring). The companion paper uses proper scoring rules generically; domain-specific scoring rule selection could improve the calibration incentive gradient where it matters most.
The commitment structure could incorporate graduated entry, allowing new analysts to begin with narrow commitments (one constraint domain, quarterly cadence) and expand as their track records demonstrate calibration. The current design does not specify the commitment structure's flexibility at the entry margin, and a more welcoming entry path could increase participation at modest cost to the strategic selection protection.
The track record aggregation could move from simple averaging to Bayesian estimation, producing not only a calibration point estimate but a credible interval that reflects the estimation uncertainty. Principals making delegation decisions on the basis of track records would benefit from knowing not only the estimated calibration but the precision of the estimate - a distinction that matters most for analysts with short records, where the point estimate may be dominated by sampling noise.
The disclosure format could be modular: a core set of required fields (Output, Identity, Confidence) with optional fields (Method, Scaling, Sensitivity) whose completion adds depth to the disclosure and is rewarded in the coverage scoring. Modularity would reduce the entry barrier for analysts who have the calibration quality to contribute Output-level assessments but lack the domain expertise to produce full Scaling analyses.
The paper maps the design space but does not optimize over it. Optimization would require specifying an objective function (maximize information value? maximize participation? maximize adversarial robustness? some weighted combination?), formalizing the tradeoffs as constraints, and solving for the mechanism that achieves the best value of the objective given the constraints. This is a mechanism design problem of substantial difficulty, and the paper identifies it as the central open question in incentive architecture economics rather than resolving it.
The design principles in Section 4 are argued as robust across the space but are not proved to be necessary in a formal sense. A mechanism that violates one of the principles - using peer review instead of outcome scoring, or maintaining private track records - might still produce valuable information in specific contexts. The principles are design recommendations based on the analytical framework of the companion papers, not theorems.
The comparison across alternative designs is qualitative. Whether the logarithmic score or the Brier score produces better outcomes in a specific constraint domain is an empirical question that cannot be resolved by theoretical analysis alone. The paper identifies the tradeoffs but does not provide the data or simulations that would resolve them. Incentive architecture economics, like market design more broadly, will in the end require the combination of theoretical principles with empirical testing and iterative refinement that Roth (2002) described as the practice of economic engineering.
The Disclosure Incentive is a mechanism, and mechanisms are designed objects. The current design embodies specific choices about scoring rules, commitment structures, format, verification, and market structure - choices that resolve genuine tradeoffs in specific ways. Incentive architecture economics studies the space of possible designs rather than the single design the companion papers analyze, and the study reveals that the current design's core features (outcome-based scoring, public track records, structured format with scaling, open-source specification) are robust across the space while several implementation choices (scoring rule selection, commitment flexibility, aggregation method, format modularity) admit alternatives that could improve performance in specific domains and contexts.
The field's ultimate contribution is to establish that the design of judgment market architecture is an engineering problem in Roth's sense - one that admits principled design choices guided by theory and refined by empirical testing, not one that has a unique theoretically optimal solution. The Disclosure Incentive is a well-reasoned first design. The design space it occupies is large enough to sustain a research program.
This paper presents results from the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics (Beier, forthcoming 2026). Incentive architecture economics is the engineering companion to the theoretical foundation established in the companion papers on the Disclosure Incentive (Beier, 2026b) and its incentive compatibility (Beier, 2026r). The author invites engagement from the market design, mechanism design, and economic engineering communities.