Correction, 30 October 2026. Proposition (Sequential Truth-Telling, corrected). Let S be strictly proper, let outcomes be independent conditional on the agent's beliefs, and let the agent's payoff be affine in R_T, u(R_T) = a + bR_T with b > 0, or more generally additively separable across periods in the per-period scores. A summary of this correction is on the papers page at https://www.susarb.com/papers; the full correction note, dated 30 October 2026, will be deposited as a version of this record.
| title: "The Incentive Compatibility of the Disclosure Incentive: A Mechanism Design Foundation for the Judgment Market" |
| author: "Gregory Caldwell Beier" |
| institute: "Susarb LLC, Cambridge, Massachusetts" |
| date: "April 2026" |
Computer Science, Mathematics, and Physics
by Gregory Caldwell Beier (forthcoming 2026).}
{
The companion paper (Beier, 2026d) resolves the Grossman-Stiglitz paradox by introducing track record capital as a second return channel alongside trading profit. The resolution depends on two assumptions the companion paper did not formally establish: that honest disclosure is incentive-compatible in the multi-agent, multi-period setting the mechanism requires, and that the judgment market's return to calibration quality is independent of price efficiency. This paper provides both foundations. Truth-telling about report content is dominant under any strictly proper scoring rule (the classical result, extended here to sequential reporting). The strategic selection problem - agents publishing only where they expect high scores - is addressed through a coverage-adjusted score weighting accuracy at \(\alpha\) and coverage at \(1-\alpha\). The central result: under any strictly proper scoring rule with bounded range \([0,1]\) and \(\alpha < 1/2\), honest comprehensive disclosure strictly dominates all withholding strategies for every agent regardless of calibration quality. The proof uses a worst-case analysis over all possible score profiles and is tight at \(\alpha = 1/2\). The judgment market's independence from price efficiency is derived from a principal's delegation problem: the demand for calibrated judgment about future constraint environments is structurally independent of current price informativeness.
Keywords: mechanism design, incentive compatibility, proper scoring rules, calibration, delegation, judgment market, track record capital
JEL Codes: D82, D86, C72, D47, D02
--
The Disclosure Incentive (Beier, 2026d) is a mechanism in which agents publish structured judgments about constraint dimensions of economic activity, scored against realized outcomes over time. The mechanism produces the multi-dimensional information that scalar price channels structurally cannot carry (Beier, 2026h). The companion paper showed that this mechanism resolves the Grossman-Stiglitz paradox in a CARA-normal general equilibrium framework, but left two formal questions open.
The first is whether truth-telling survives the transition from the single-agent, single-report setting where proper scoring rules have their classical dominance property to the multi-agent, multi-period, strategic environment that the Disclosure Incentive requires. In the textbook case (Savage, 1971; Gneiting and Raftery, 2007), an agent maximizes expected score by reporting true beliefs - but this assumes the agent reports every assessment and has no strategic choice about which dimensions to cover. Strategic selection - publishing only favorable assessments, analogous to the file-drawer problem (Rosenthal, 1979) - can undermine the informativeness of the track record even when individual reports are truthful. The question is whether the Disclosure Incentive's institutional structure - commitment to a disclosure domain, coverage scoring, and market discipline - restores the truth-telling property.
The second question is why the judgment market's return to calibration quality is independent of price efficiency - the assumption on which the companion paper's entire resolution depends. If this assumption is merely asserted rather than derived, the resolution follows trivially. This paper derives it from a micro-founded model of the principal's delegation problem.
Section 2 states the mechanism. Section 3 proves truth-telling for report content and extends it to sequential reporting. Section 4 addresses strategic selection under the commitment mechanism, including the central result on the coverage-adjusted score. Section 5 micro-founds the judgment market. Section 6 discusses robustness. Section 7 states limitations. Section 8 concludes.
The Disclosure Incentive consists of three components:
Message space. Structured assessments containing a probabilistic forecast \(r_t \in \Delta(\Omega)\) over a finite outcome space \(\Omega\), published before the outcome is realized. (The companion paper specifies a five-field format for the assessments; the formal results of this paper depend only on the probabilistic forecast and the scoring rule, not on the assessment structure.)
Outcome function. Each assessment is scored by a strictly proper scoring rule \(S(r_t, \omega_t)\) when the outcome \(\omega_t\) is realized. Scores are aggregated into a cumulative track record \(R_T = \frac{1}{T}\sum_{t=1}^T S(r_t, \omega_t)\).
Institutional structure. Agents commit publicly to a disclosure domain \(D_i\) specifying which types of assessments they will publish. A coverage-adjusted score (Definition ) incorporates both accuracy and coverage, penalizing agents who publish on only a subset of their committed domain. The number of assessable events \(|D_i|\) within the committed domain is assumed to be publicly observable - an institutional requirement that limits the mechanism to domains where event counts are verifiable by third parties.
The relevant incentive compatibility concept is dominant-strategy for report content (truth-telling is optimal regardless of what others do). For the coverage decision, Theorem establishes that honest comprehensive disclosure dominates all withholding strategies for all agents when \(\alpha < 1/2\).
Let \(\Omega\) be a finite outcome space and \(\Delta(\Omega)\) the set of probability distributions over \(\Omega\).
Definition (Strictly Proper Scoring Rule).
A scoring rule \(S: \Delta(\Omega) \times \Omega \to \mathbb{R}\) is strictly proper if for all distributions \(p\) in the interior of \(\Delta(\Omega)\):
\[
\mathbb{E}_p[S(p, \omega)] > \mathbb{E}_p[S(r, \omega)] \text{for all } r \neq p.
\]
Proposition (Dominant-Strategy Truth-Telling).
Let \(S\) be a strictly proper scoring rule. An agent with true belief \(p\) maximizes expected score by reporting \(r = p\). Truth-telling is strictly dominant.
Proof.
Define \(G(r, p) = \mathbb{E}_p[S(r, \omega)]\). By strict properness, \(G(p, p) > G(r, p)\) for all \(r \neq p\). No information about other agents enters the maximization, so truth-telling is dominant.
Two specific scoring rules are relevant. The Brier score (Brier, 1950): for binary outcomes \(\Omega = \{0, 1\}\), \(S_B(r, x) = 1 - (r - x)^2\). The expected Brier score under true belief \(p\) is \(\mathbb{E}_p[S_B(r, x)] = 1 - (r-p)^2 - p(1-p)\), maximized at \(r = p\). The logarithmic score (Good, 1952): \(S_L(r, x) = \log r(x)\), maximized at \(r = p\) by Gibbs' inequality.
Definition (Cumulative Track Record).
The cumulative track record score after \(T\) reports is \(R_T = \frac{1}{T}\sum_{t=1}^T S(r_t, \omega_t)\).
Proposition (Sequential Truth-Telling).
If \(S\) is strictly proper, future outcomes are independent conditional on the agent's beliefs, and the agent's per-period payoff is a weakly increasing function of \(R_T\), then truth-telling in every period maximizes the expected cumulative payoff.
Proof.
Since \(R_T\) is additively separable across periods and future outcomes are conditionally independent, the maximization decomposes: the agent maximizes \(\mathbb{E}[S(r_t, \omega_t)]\) at each \(t\) independently. By Proposition , truth-telling at each \(t\) is optimal.
The conditional independence assumption deserves scrutiny. If the agent's belief at time \(t\) depends on previous outcomes through Bayesian updating, conditional independence of future outcomes given current beliefs still holds. What could break the decomposition is strategic interaction: if the agent's score at time \(t\) affects other agents' behavior in a way that feeds back to the agent's future payoff. The coverage mechanism (Section 4) addresses this by making the scoring additively separable by construction.
Propositions and establish that truth-telling is dominant given that the agent reports. But the agent also chooses whether to report. An agent who makes ten assessments and publishes only the five that turned out well achieves a track record that overstates calibration quality. This strategic selection problem - related to the file-drawer problem in statistics (Rosenthal, 1979) and to strategic considerations in information elicitation more broadly (Witkowski and Parkes, 2012) - threatens the mechanism's incentive compatibility.
The Disclosure Incentive constrains strategic selection through a commitment structure. At the beginning of each period, the agent commits publicly to a disclosure domain \(D_i\) specifying which types of assessments the agent will publish. The commitment is timestamped and scored. The withholding decision analyzed in Theorem is ex ante: the agent decides which dimensions to cover before observing outcomes. Post-outcome selection (the file-drawer problem) is prevented by the commitment structure - the agent commits to \(D_i\) before the scoring period, and coverage is measured against the commitment. An agent who commits to "all capital allocation decisions above $10M in the energy sector" and subsequently publishes assessments of only three out of eight such decisions has a coverage gap that is observable.
Definition (Coverage-Adjusted Score).
The coverage-adjusted score for agent \(i\) with commitment domain \(D_i\) is:
\[ C_i = \alpha \cdot R_{D_i} + (1 - \alpha) \cdot \frac{|A_i|}{|D_i|} \]
where \(R_{D_i}\) is the average proper scoring rule score on published assessments within \(D_i\), \(|A_i|\) is the number of assessments actually published, \(|D_i|\) is the number of assessable events within the committed domain, and \(\alpha \in (0,1)\) weights accuracy against coverage.
Theorem (No-Withholding Under Bounded Scoring Rules).
Let \(S\) be any strictly proper scoring rule with range \([0, 1]\) (e.g., the Brier score \(S_B(r, x) = 1 - (r-x)^2\)). If \(\alpha < 1/2\), honest comprehensive disclosure - publishing all assessments within \(D_i\) with true beliefs - strictly dominates any strategy involving withholding, for every agent regardless of calibration quality.
Proof.
Three classes of deviation are analyzed.
Deviation 1 (Misreport). Holding the publication set fixed, expected accuracy is maximized by truth-telling (Proposition ). Strictly dominated.
Deviation 2 (Withhold \(k\) of \(n\) dimensions). Let \(q_1, \ldots, q_n \in [0, 1]\) be the agent's expected scores across \(n\) committed dimensions, with mean \(\bar{q}\). The agent considers withholding the \(k\) dimensions with the lowest expected scores. After withholding:
Accuracy component changes by \(\alpha(\bar{q}' - \bar{q})\) where \(\bar{q}' = (n\bar{q} - \sum_{i=1}^k q_{(i)})/(n-k)\).
Coverage component changes by \(-(1-\alpha) \cdot k/n\).
The net change in \(C_i\) is \(\Delta C = \alpha(\bar{q}' - \bar{q}) - (1-\alpha)(k/n)\).
The accuracy gain is maximized in the extreme case: the \(k\) withheld scores are 0 and the remaining \(n-k\) scores are 1, giving \(\bar{q} = (n-k)/n\) and \(\bar{q}' = 1\):
\[ \Delta C_{\max} = \alpha \cdot \frac{k}{n} - (1-\alpha) \cdot \frac{k}{n} = \frac{k}{n}(2\alpha - 1). \]
For \(\alpha < 1/2\), the factor \((2\alpha - 1) < 0\), so \(\Delta C_{\max} < 0\). Withholding any number of dimensions from any score profile reduces the coverage-adjusted score.
Deviation 3 (Joint). By additive separability of the scoring rule and linearity of the coverage term, misreporting and withholding are independent optimization problems. Since misreporting is dominated (Deviation 1) and withholding is dominated for \(\alpha < 1/2\) (Deviation 2), the joint deviation is dominated.
Remark.
The bound \(\alpha = 1/2\) is tight. The extreme case (one dimension at score 0, rest at 1) achieves exact indifference at \(\alpha = 1/2\). For agents with expected scores bounded away from the extremes (e.g., \(q_k \in [0.3, 0.8]\) for all \(k\)), the no-withholding condition is less restrictive and \(\alpha\) can exceed \(1/2\) without making withholding profitable.
Remark.
The condition \(\alpha < 1/2\) means coverage is weighted at least as heavily as accuracy. This is natural for a mechanism whose purpose is to elicit comprehensive constraint-dimension information. The mechanism rewards breadth of observation, with accuracy verified through the scoring rule. An agent who publishes narrow, high-accuracy assessments on easy dimensions while ignoring the difficult constraint dimensions where information is most valuable receives a lower score than an agent who covers the full domain with reasonable accuracy.
Corollary (Tighter Bound Under Truth-Telling).
Conditioning on truth-telling (which Deviation 1 establishes is dominant), the expected score on any dimension under a strictly proper scoring rule is \(q_k = \mathbb{E}_{p_k}[S(p_k, \omega_k)] \geq m_S > 0\), where \(m_S\) is the minimum expected score under truth-telling over all beliefs \(p\). The worst-case accuracy gain from withholding \(k\) dimensions becomes \(\alpha \cdot k(1-m_S)/n\), and the no-withholding condition tightens to:
\[ \alpha < \frac{1}{2 - m_S}. \]
For the Brier score, \(m_S = 3/4\) (achieved at \(p = 1/2\)), giving \(\alpha < 4/5\). This means accuracy can be weighted up to four times as heavily as coverage before withholding becomes profitable under the Brier score - substantially more permissive than the universal \(\alpha < 1/2\) bound.
Proof.
Under truth-telling, the expected Brier score on dimension \(k\) is \(\mathbb{E}_{p_k}[S_B(p_k, \omega_k)] = 1 - p_k(1-p_k)\), minimized at \(p_k = 1/2\) with value \(3/4\). The worst case for withholding has \(k\) dimensions at \(m_S = 3/4\) and \(n-k\) at \(1\), giving accuracy gain \(\alpha \cdot k(1-3/4)/n = \alpha k/(4n)\). The coverage penalty is \((1-\alpha)k/n\). No-withholding requires \(\alpha/4 < 1-\alpha\), giving \(\alpha < 4/5\).
Theorem establishes that, given a committed domain \(D_i\), no agent profits from withholding when \(\alpha < 1/2\). The theorem does not address the prior choice of \(D_i\) itself. An agent could commit to a narrow domain that excludes difficult dimensions. This ex-ante selection is constrained by three institutional features rather than by the scoring rule:
The commitment domain is public and timestamped. Principals hiring based on track records observe the commitment domain and discount narrow commitments. An agent who commits to "technology sector, large-cap equities only" when applying for a role covering all sectors reveals the limitation. The commitment's narrowness is itself a signal.
The judgment market (Section 5) prices calibration quality conditional on the commitment domain. Agents with broad commitments command higher returns because they provide more information to principals. The market return to breadth operates through the same channel as the market return to accuracy: principals pay for information that reduces the expected cost of delegated decisions, and broader coverage reduces that cost more.
Agents with very poor calibration may prefer not to disclose at all, and the mechanism does not prevent this. An agent whose calibration is so poor that honest disclosure would damage their track record has an incentive to remain silent - and the silence is informative. Principals who observe that an agent has operated for five years without accumulating a track record draw the appropriate inference. The mechanism differentiates signal quality through participation itself, not only through scores.
A principal must make decisions about the constraint environment - capital allocation, risk management, strategic planning - that require assessments of future states. Hiring an agent with demonstrated calibration quality reduces the expected cost of decisions made under uncertainty.
Let \(\theta\) be the uncertain state of the constraint environment (drawn from distribution \(F\)). The principal chooses an action \(a \in \mathcal{A}\) with loss \(\ell(a, \theta)\). Under delegation, the agent reports an assessment \(r\) and the principal chooses \(a(r) = \arg\min_a \mathbb{E}_r[\ell(a, \theta)]\).
Definition (Signal Quality).
The signal quality of an agent is \(q \in [0, 1]\), indexing a family of signal structures ordered by Blackwell (1953) dominance. The parameter ranges from \(q = 0\) (the agent's report carries no information beyond the prior) to \(q = 1\) (the agent reports the true posterior given all available constraint-dimension data). At intermediate values, the report is the true posterior corrupted by noise that decreases in \(q\), so that signal at \(q'\) is a garbling of signal at \(q\) for \(q' < q\). The parameter \(q\) captures informativeness (the Blackwell ordering), which is related to but distinct from calibration in the frequency-matching sense (Dawid, 1982; DeGroot and Fienberg, 1983).
Proposition (Value of Signal Quality).
The principal's expected loss from delegation is weakly decreasing in signal quality \(q\), and strictly decreasing whenever the optimal action depends on the state.
Proof.
By Definition , higher \(q\) corresponds to a more informative signal in the Blackwell (1953) sense. The Blackwell theorem gives \(L(q') \leq L(q)\) for \(q' > q\), with strict inequality when the optimal action depends on the state.
A note on terminology: calibration in the forecasting literature (Dawid, 1982; DeGroot and Fienberg, 1983) measures frequency-matching, which is distinct from Blackwell informativeness. A perfectly calibrated agent who always reports the base rate is calibrated but uninformative. The parameter \(q\) as used here captures informativeness (signal quality), not calibration in the narrow frequency-matching sense. The term "calibration quality" is retained for continuity with the companion paper but should be understood as signal quality ordered by Blackwell dominance.
Proposition (J4 Micro-Foundation).
If \(\theta_P\) and \(\theta_C\) are independent and the principal's loss function is additively separable or quadratic in \(\theta\), the principal's willingness to pay for signal quality \(q\) about \(\theta_C\) is independent of asset price informativeness about \(\theta_P\).
Proof.
Partition the information about \(\theta\) into \(\theta_P\) (reflected in the current price) and \(\theta_C\) (concerning future constraints the price cannot reflect because the states have not yet been realized). Under independence of \(\theta_P\) and \(\theta_C\) with quadratic loss \(\ell(a, \theta) = (a - \theta)^2\) where \(\theta = \theta_P + \theta_C\), the expected loss decomposes as \(\operatorname{Var}(\theta_P \mid \text{price}) + \operatorname{Var}(\theta_C \mid \text{disclosure})\). Improving the agent's signal about \(\theta_C\) reduces \(\operatorname{Var}(\theta_C \mid \text{disclosure})\) by an amount independent of \(\operatorname{Var}(\theta_P \mid \text{price})\). The willingness to pay \(W(q) = L(0) - L(q)\) is therefore independent of price efficiency.
For non-quadratic loss functions, the decomposition requires additive separability of \(\ell\) in the two information sources. Under non-separable loss (e.g., with binding budget constraints that link actions across \(\theta_P\) and \(\theta_C\)), the marginal value of \(\theta_C\) information may depend on the precision of \(\theta_P\) information. The result is exact for the quadratic-loss case and approximate when cross-terms are small relative to the direct effects.
The assumption that \(\theta_C\) is non-trivial - that the constraint environment has a forward-looking component the current price does not reflect - is empirically grounded (the social cost of carbon debate alone demonstrates that prices do not reflect constraint information) but not endogenized in this paper.
Remark.
The independence and quadratic-loss conditions are restrictive. In practice, the price-reflected component \(\theta_P\) and the constraint component \(\theta_C\) are often correlated (e.g., high-carbon firms have both high current earnings and high constraint exposure). Under non-separable loss with correlated components, the marginal value of \(\theta_C\) information depends on what the price already reveals, and the demand-side independence degrades. The rate of degradation with \(\operatorname{Corr}(\theta_P, \theta_C)\) is uncharacterized; Section 7 discusses this further.
Definition (Judgment Market).
The judgment market consists of principals who demand calibration quality and agents who supply it through disclosure. The market return per discloser when the fraction of disclosers is \(\lambda_D\) is \(\bar{r}_D(\lambda_D) = \int W(q) dG(q \mid \lambda_D)\), where \(G(q \mid \lambda_D)\) is the distribution of calibration quality among the \(\lambda_D\) disclosers.
The following conditions are assumed for the equilibrium result:
M2 is a sorting condition that requires the companion paper's two-channel resolution to hold: in the standard Grossman-Stiglitz framework, high-quality agents have higher opportunity cost of disclosure because they capture more trading profit. The companion paper (Beier, 2026d) resolves this by introducing track record capital as a second return channel whose value increases with signal quality. Under the two-channel model, high-quality agents enter the disclosure channel first because their track record capital grows faster. M2 is a derived consequence of the companion paper's resolution, not an independent assumption. The dependency structure between the papers is therefore as follows: this paper provides the incentive compatibility foundation (Theorem ) and the demand-side independence result (Proposition ) as self-contained results requiring no input from the companion paper. The judgment market equilibrium (Proposition ) additionally requires M2, which depends on the companion paper's two-channel model. The relationship at the equilibrium level is bidirectional rather than hierarchical. M3 is a congestion condition: as more agents disclose, the marginal discloser is of lower quality and the per-discloser return falls.
Remark.
Proposition establishes that the demand for calibrated judgment is independent of price efficiency. The equilibrium return depends on both demand and supply. If price efficiency affects agents' opportunity cost of disclosing (more efficient prices reduce trading profit, lowering the opportunity cost of disclosure, increasing supply, and thus lowering the equilibrium return), then the equilibrium return is not fully independent of price efficiency even though demand is. The companion paper addresses this through the two-channel model; the present paper establishes demand-side independence only.
Proposition (Judgment Market Equilibrium).
Under M1 -- M5, there exists a unique stable interior equilibrium \(\lambda_D^* \in (0,1)\).
Proof.
By continuity, strict monotonicity, and the intermediate value theorem applied to \(\bar{r}_D(\lambda_D) - c\). Uniqueness from strict monotonicity. Stability from the adjustment dynamics: below \(\lambda_D^*\) the return exceeds cost (entry); above it the return falls below cost (exit).
These conditions reproduce J1-J4 of the companion paper. J4 follows from Proposition : the principal's willingness to pay depends on \(\theta_C\), which prices do not reflect, so price informativeness does not enter the demand curve. The connection between the track record \(R_T\) and the signal quality \(q\) that principals value is asymptotic: by the Law of Large Numbers, \(R_T \to \mathbb{E}[S(p, \omega)] = g(q)\) as \(T \to \infty\), where \(g\) is strictly increasing in \(q\) for any strictly proper scoring rule. The cumulative track record therefore identifies signal quality in the large-sample limit, though finite-sample noise means principals must perform inference about \(q\) from observed \(R_T\) in practice.
The Disclosure Incentive differs from prediction markets (Hanson, 2003; Wolfers and Zitzewitz, 2004) in that the payoff accrues through cumulative track record capital rather than per-round trading profit, which decouples information production from the trading channel and avoids the Grossman-Stiglitz reflexive loop that prediction markets inherit.
Crawford and Sobel (1982) provide the baseline: in cheap talk, information transmission depends on sender-receiver preference alignment. Proper scoring removes this dependence by aligning the sender's payoff with honest reporting by construction. The commitment mechanism and coverage scoring address the strategic selection problem that single-report proper scoring does not.
Bergemann and Morris (2005) require mechanisms to perform well under uncertainty about higher-order beliefs. The Disclosure Incentive has partial robustness: the proper scoring rule is strictly proper regardless of beliefs about other agents. The commitment mechanism's effectiveness depends on the observability of the commitment domain, an institutional assumption.
On multiple equilibria: the judgment market has a unique interior equilibrium under (M1) -- (M5). The full game - in which agents simultaneously choose whether to trade, disclose, or remain uninformed - could in principle admit multiple equilibria if the judgment market return and the trading return interact. The companion paper's sequential structure (J4 ensures the judgment market clears independently of the asset market) prevents this.
Theorem addresses withholding given a committed domain. It does not formalize the ex-ante domain selection problem. The institutional constraints on narrow commitments (market discipline, principal observation of commitment breadth) are described but not proved. A formal treatment of the domain selection game, including pooling equilibria in which low-quality agents mimic high-quality commitment patterns, is deferred to companion work.
The \(\alpha < 1/2\) threshold applies to any proper scoring rule with bounded range \([0, 1]\), not just the Brier score. The result depends on the linear form of the coverage-adjusted score - a design choice, not an axiomatically derived functional form. Other coverage penalty functions (quadratic, step) would produce different thresholds.
The J4 micro-foundation depends on \(\theta_C\) being non-trivial and independent of \(\theta_P\). If all relevant constraint information were already in the price, the delegation problem would be trivial and J4 would fail. The independence assumption is the more restrictive condition: in practice, the price-reflected and price-unreflected components of value are often correlated. A firm's current profitability (\(\theta_P\)) and its exposure to unpriced carbon regulation (\(\theta_C\)) are not independent. Under non-separable loss with correlated \(\theta_P\) and \(\theta_C\), the marginal value of constraint-dimension information depends on what the price already tells the principal, and the demand curve shifts with price efficiency. The result is exact when \(\theta_P\) and \(\theta_C\) are orthogonal (as for constraint dimensions with no current price signal) and approximate when cross-terms are small. Quantifying how the bound degrades with correlation strength is an open problem that the research program must address.
The sequential truth-telling result (Proposition ) assumes additive separability and conditional independence. These exclude reputation effects, strategic timing, and inter-period learning. The proof is correct given its assumptions; the assumptions exclude the dynamic strategic interactions that make repeated information elicitation difficult in practice.
The scoring rule's effectiveness depends on outcome verification, which for long-horizon assessments may require years or decades. The mechanism is most effective for constraint dimensions with verifiable outcomes on 3-10 year horizons. Longer-horizon dimensions require intermediate outcome proxies, which introduce noise.
The mechanism does not address agents who refuse to participate. The incentive compatibility result applies to participating agents; inducing participation by reluctant agents depends on the cascade dynamics of the companion paper (Beier, 2026q) rather than on the mechanism design results established here. Under unbounded scoring rules, a nontrivial calibration threshold persists, and agents below it may find strategic selection profitable. Their silence is itself informative - conspicuous gaps in a committed domain signal low confidence on those dimensions - but formalizing the inference from silence requires a different framework.
The Disclosure Incentive is incentive-compatible within the domain defined by the commitment structure and proper scoring verification. The paper's main contribution is the no-withholding result: under the coverage-adjusted score with \(\alpha < 1/2\), honest comprehensive disclosure dominates all withholding strategies for any bounded \([0,1]\) scoring rule (Theorem ). Under Brier, conditioning on the dominant truth-telling strategy tightens the bound to \(\alpha < 4/5\) (Corollary ), allowing accuracy to be weighted up to four times coverage. On the demand side, the principal's willingness to pay for signal quality is independent of price efficiency under the stated conditions (Proposition ), though the equilibrium return additionally depends on supply-side dynamics addressed in the companion paper. These results, together with the sequential truth-telling extension (Proposition ) and judgment market equilibrium (Proposition ), micro-found the assumptions on which the companion paper's resolution of the Grossman-Stiglitz paradox depends.
The mechanism does not achieve universal participation - the ex-ante domain selection and the refusal to participate are constrained by market discipline and cascade dynamics rather than by the scoring rule. What the mechanism achieves is incentive-compatible information production within the disclosure channel: agents who participate are rewarded for calibration quality, the coverage-adjusted scoring identifies and penalizes withholding, and the disclosed information entering the public domain is produced by agents who have incentive to be honest and comprehensive.