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.
A disclosed constraint assessment is valuable only if it reaches the agents whose decisions it should inform. A hydrologist's aquifer depletion analysis, however well-calibrated, produces no allocation improvement if no fund manager, regulator, or farmer reads it. The propagation of disclosed judgments through networks of economic agents - from the analyst who produced the assessment to the allocators, regulators, and operators whose decisions it would improve - is not automatic. It depends on the transmission infrastructure, the readers' attention allocation, and the institutional boundaries the information must cross. This paper develops the economics of this propagation, which it calls disclosure cascades. A disclosure cascade differs from the information cascades analyzed by Bikhchandani, Hirshleifer, and Welch (1992) in a fundamental respect. Their cascades are information-destroying: agents observe predecessors' actions, infer their information, and imitate - discarding their own private signals in favor of the inferred consensus. Disclosure cascades are information-preserving: agents read predecessors' disclosed reasoning, evaluate it against the discloser's track record and their own analysis, and incorporate the reasoning while retaining their own assessment. The imitation cascade compresses information by reducing N independent judgments to one herd behavior. The disclosure cascade enriches information by exposing N independent judgments to cross-evaluation. The economics of the two cascade types are structurally different, and the Disclosure Incentive is designed to produce the second while structurally inhibiting the first.
Keywords: cascades, information propagation, herding, disclosure, judgment transmission, institutional boundaries, attention, network effects, information preservation
JEL Codes: D82, D83, D85, G14
In the Bikhchandani, Hirshleifer, and Welch (1992) model, rational agents observing the sequential actions of predecessors can fall into information cascades - situations where each agent ignores their own private signal and imitates the actions of those who moved before them. The cascade is individually rational (the accumulated weight of predecessors' actions outweighs the agent's private signal) but collectively irrational (the cascade locks in a possibly incorrect action because the agents' private signals, which collectively contain enough information to identify the correct action, are never expressed). The cascade is fragile - a small amount of new public information can shatter it - but while it persists, it destroys the information content of the agents' private signals by preventing them from being expressed through action.
The Disclosure Incentive creates a different kind of cascade. When a hydrologist publishes a scored aquifer assessment and a fund manager reads it, the fund manager does not merely imitate the hydrologist's conclusion. The fund manager evaluates the assessment against the hydrologist's track record, weighs it against other information sources, and incorporates it into an allocation decision whose reasoning may itself be disclosed. The second disclosure - the fund manager's capital allocation assessment, which cites the hydrologist's aquifer analysis as an input - propagates the hydrologist's information further while adding the fund manager's own analytical layer. A regulator who reads both disclosures incorporates two perspectives. A farmer who reads the hydrologist's assessment directly adjusts irrigation practices. The information propagates through the network, gaining layers of evaluation and application at each step rather than losing information content through imitation.
The present paper analyzes the economics of this propagation - the factors that determine how far a disclosure travels, how much of its information content survives the journey, and what institutional barriers impede transmission across the boundaries between scientific communities, financial markets, regulatory bodies, and operational decision-makers.
Section 2 distinguishes the two cascade types. Section 3 analyzes propagation dynamics. Section 4 examines institutional boundary effects. Section 5 develops the economics of transmission loss. Section 6 states limitations. Section 7 concludes.
A fourth source of friction is strategic hoarding. An asset manager who discovers a valuable constraint insight in a disclosed assessment has an immediate incentive to trade on it quietly rather than propagate it. The Disclosure Incentive mitigates this because track record capital requires publication to accrue - the analyst who generated the insight captures reputational return only through the public scoring system, not through private trading on undisclosed reasoning. But downstream readers face no such constraint, and the competitive channel's incentive toward secrecy creates a propagation bottleneck that the cooperative channel's public scoring only partially offsets.
The distinction between herding cascades and disclosure cascades can be stated precisely through what each preserves and destroys at each link in the chain.
In a herding cascade, agent n observes the actions of agents 1 through n-1, infers their information from those actions, and chooses an action that maximizes expected payoff given the inferred information and their own private signal. When the accumulated weight of predecessors' inferred information exceeds the agent's private signal, the agent ignores their signal and imitates. The private signal is never expressed - it is destroyed at the point where the agent decides not to act on it. The information available to agent n+1 is the same as what was available to agent n (the sequence of actions, which now includes one more imitation), and the cascade is locked in.
In a disclosure cascade, agent n observes the disclosed reasoning of agents 1 through n-1, evaluates each disclosure against the discloser's track record, and forms an assessment that incorporates the predecessors' reasoning alongside their own. The agent's own assessment may then be disclosed, adding to the chain. At each link, the information available to the next agent grows rather than stagnates - the chain accumulates evaluated assessments rather than reducing to a sequence of imitative actions.
Three structural features of the Disclosure Incentive inhibit herding cascades and promote disclosure cascades.
The first is that proper scoring rewards calibration rather than consensus. In a herding cascade, the agent's payoff depends on choosing the correct action, and the cascade is rational because imitating predecessors is the best estimate of the correct action given the information available. In the Disclosure Incentive, the agent's payoff depends on calibration quality - the correspondence between stated confidence and outcomes - which is maximized by reporting true beliefs rather than by matching predecessors' conclusions. An agent who herds (reports the consensus probability rather than their own assessment) is scored against outcomes, not against the consensus, and herding degrades calibration whenever the agent's private signal diverges from the consensus.
The second is that disclosed reasoning is evaluable. In a herding cascade, the agent observes predecessors' actions but not their reasoning - the inference from action to information is indirect and lossy. In a disclosure cascade, the agent observes predecessors' full five-field reasoning, enabling direct evaluation. The agent who reads a hydrologist's aquifer assessment can identify which data the hydrologist consulted, which model was used, what assumptions were made, and where the confidence levels are weakest. This evaluability makes it possible to incorporate the predecessor's information selectively - accepting the data, questioning the model, adjusting the confidence - rather than accepting or rejecting the conclusion wholesale.
The third is that track records differentiate quality. In a herding cascade, agents treat predecessors as interchangeable - the cascade depends on the count of prior actions, not on the quality of the agents who performed them. In a disclosure cascade, track records enable quality weighting - a disclosure from an analyst with a ten-year record of well-calibrated aquifer assessments carries more weight than the same conclusion from an analyst with no track record. The quality differentiation prevents low-quality disclosures from driving the cascade in the way that low-quality early movers can drive a herding cascade.
A disclosed judgment propagates through the network of agents who encounter, read, evaluate, and act on it. The propagation has three measurable properties: reach (how many agents encounter the disclosure), absorption (what fraction of those who encounter it incorporate it into their analysis), and transformation (how the disclosure's information content changes as it passes through successive agents).
Reach depends on the transmission infrastructure - the platforms, data feeds, and communication channels through which disclosures travel from producer to consumer. A disclosure published on a specialized hydrology platform reaches hydrologists efficiently but may not reach the fund managers and regulators whose allocation decisions it should inform. Institutional boundaries limit reach, and the economics of the transmission infrastructure (the companion paper on epistemic infrastructure, Beier, 2026aq) determine how far disclosures travel.
Absorption depends on the reader's attention allocation. The rational inattention framework (Sims, 2003) predicts that agents process the signals with the highest return per unit of attention. A disclosure is absorbed when the reader's expected benefit from incorporating it (improved decision quality, weighted by the decision's stakes) exceeds the attention cost of reading and evaluating it. High-quality disclosures from well-calibrated analysts are absorbed at higher rates because the expected benefit is higher - the track record provides a quality signal that reduces the reader's uncertainty about whether the attention investment will pay off.
Transformation is the most distinctive property of disclosure cascades. As a disclosure propagates, each agent who incorporates it adds their own analytical layer. The hydrologist's aquifer assessment, when incorporated into a fund manager's capital allocation disclosure, is transformed - the aquifer depletion estimate becomes one input to a broader assessment of the agricultural company's value, combined with the fund manager's analysis of commodity prices, operating efficiency, and competitive position. The hydrologist's information is preserved but recontextualized. A regulator who reads both disclosures encounters the aquifer assessment twice - once in its original scientific form and once embedded in a financial valuation - and the dual perspective is more informative than either alone.
The cascade's information content at link n is not the original disclosure degraded by n steps of transmission loss (as in a game of telephone). It is the original disclosure enriched by n layers of cross-domain evaluation and application. This information-enriching property is the fundamental difference between disclosure cascades and herding cascades, and it connects to the factorial coordination paper's (Beier, 2026ag) argument that the interaction of multiple disclosures produces combinatorial information growth.
The most significant impediment to disclosure propagation is not distance or technology but institutional boundaries. A hydrologist's aquifer assessment must cross at least three institutional boundaries to produce its full allocation impact: from the scientific community to the financial community (where it informs capital allocation), from the financial community to the regulatory community (where it informs water policy), and from the regulatory and financial communities to the operational community (where it informs farming practices).
Each boundary imposes translation costs. The hydrologist speaks in depletion rates and recharge coefficients. The fund manager speaks in risk-adjusted returns and portfolio weights. The regulator speaks in compliance thresholds and permit conditions. The farmer speaks in irrigation schedules and crop yields. The same underlying constraint information must be translated into each community's vocabulary, analytical framework, and decision context. The translation is costly and lossy - each boundary crossing compresses the original information into the receiving community's format, destroying domain-specific nuance that the originating community would have preserved.
The five-field disclosure format mitigates some of this translation loss because the format is shared across institutional boundaries. A hydrologist's disclosure and a fund manager's disclosure use the same structure (Input, Method, Output, Identity, Scaling), which creates a common framework that reduces the translation cost of reading across institutional boundaries. The Scaling field is particularly important for cross-boundary propagation because it forces each discloser to address the aggregate constraint dynamics that every community needs to understand, even though each community frames the question differently.
The companion paper (Beier, 2026b) develops the machine-readable translation layer that further reduces cross-boundary transmission costs. When disclosures are available in both human-readable and machine-readable formats, AI systems can perform the cross-institutional translation automatically - extracting the constraint-relevant content from a hydrological disclosure and presenting it in the vocabulary and framework a fund manager or regulator uses. The Protocol is the infrastructure component designed specifically to reduce the institutional boundary costs that impede disclosure cascades.
Despite the Disclosure Incentive's design features, transmission loss occurs. Not every disclosure reaches every agent who would benefit from it. Not every agent who encounters a disclosure absorbs it. Not every agent who absorbs it transmits the full information content in their own subsequent disclosures or decisions. The cumulative transmission loss between the original disclosure and the allocation decision it was designed to inform determines how much of the disclosure's potential value is realized.
Transmission loss has three sources.
The first is attention scarcity. The rational inattention constraint means that agents cannot process every disclosure in every constraint domain. Even a well-calibrated, high-quality disclosure may go unread if the agents who would benefit from it are allocating attention to other signals they perceive as higher-return. The attention scarcity loss is largest for disclosures that address constraint domains remote from the reader's primary focus - an energy-sector fund manager may not allocate attention to an aquifer assessment even if the agricultural companies in their portfolio depend on the aquifer.
The second is trust friction. An agent encountering a disclosure from an unfamiliar analyst faces uncertainty about the disclosure's quality, even if the analyst has a scored track record. Building trust in a new information source requires evaluating the track record, assessing the analyst's domain expertise, and comparing the disclosure to other sources - an investment of attention that some agents will not make. The trust friction is highest for the first disclosure an agent encounters from a new analyst and diminishes with repeated exposure. The verification economics paper (Beier, 2026aq) analyzes how proper scoring reduces trust friction over time; the present paper's contribution is to note that the friction generates transmission loss during the period before trust is established.
The third is boundary compression. Each institutional boundary crossing compresses the disclosure's content into the receiving community's framework, losing domain-specific nuance. A fund manager who incorporates a hydrologist's aquifer assessment into a portfolio allocation decision preserves the bottom line (the aquifer is depleting at rate X with probability Y) but may lose the conditional structure (the rate depends on precipitation patterns that are shifting, and the probability is sensitive to the hydrological model used). The boundary compression is smaller when the receiving agent has domain expertise that overlaps with the discloser's (a fund manager with a geology background loses less aquifer nuance than one without), but some loss is inherent in any cross-domain translation.
The total transmission loss between production and final use determines the Disclosure Incentive's realized value. The theoretical value - the improvement in allocation that would result if every relevant agent fully absorbed every relevant disclosure - is an upper bound that transmission loss reduces. Reducing transmission loss is therefore a design objective for the epistemic infrastructure (Beier, 2026aq): platforms that match disclosures to relevant consumers, formats that reduce cross-boundary translation costs, and AI systems that perform institutional translation automatically all serve to narrow the gap between the theoretical and realized value of the disclosure system.
The paper distinguishes disclosure cascades from herding cascades conceptually but does not model the dynamics formally. A formal model would specify the network structure through which disclosures propagate, the attention allocation rule each agent follows, the transformation function that describes how information content changes at each link, and the equilibrium propagation pattern. The paper's analysis is qualitative - identifying the mechanisms and their direction without computing the equilibrium.
The claim that disclosure cascades are information-enriching assumes that each agent in the chain adds genuine analytical value when incorporating a predecessor's disclosure. If agents incorporate disclosures mechanically - copying the conclusion without evaluating the reasoning - the disclosure cascade degenerates toward a herding cascade with disclosed conclusions rather than inferred actions. The proper scoring mechanism provides some protection against mechanical copying (the agent who copies a conclusion without genuine analysis will have worse calibration than one who evaluates and adjusts), but the protection is imperfect for short track records.
The institutional boundary analysis (Section 4) identifies translation costs as a major impediment but does not estimate their magnitude. How much information is lost when a hydrological assessment crosses into a financial context? How much is lost when a financial assessment crosses into a regulatory context? These are empirical questions whose answers are domain-specific and not currently measurable with existing methods.
The paper assumes that the disclosure network's structure is exogenous - that the channels through which disclosures propagate are determined by the transmission infrastructure. In practice, network structure is endogenous: agents choose whom to follow, which platforms to use, and which constraint domains to monitor, and these choices are shaped by the same attention and incentive considerations the paper analyzes. A model of endogenous network formation in the disclosure ecosystem would produce richer predictions about cascade patterns but is beyond this paper's scope.
A disclosed judgment that stays where it was produced changes nothing. The value of disclosure is realized only when the judgment propagates - from the scientist to the allocator, from the allocator to the regulator, from the regulator to the operator whose daily decisions the constraint information should inform. The propagation is a cascade, and the cascade's economics are governed by reach, absorption, transformation, and the institutional boundaries the information must cross.
The Disclosure Incentive is designed to produce information-preserving cascades rather than information-destroying ones. Proper scoring inhibits herding by rewarding calibration rather than consensus. Disclosed reasoning enables evaluation rather than imitation. Track records differentiate quality rather than counting votes. But the design features cannot overcome the physical constraints of attention scarcity, trust formation, and institutional translation. The realized value of the disclosure system is the theoretical value minus the transmission loss, and reducing that loss - through better transmission infrastructure, lower-friction cross-boundary formats, and AI-mediated institutional translation - is as important for the Disclosure Incentive's impact as the mechanism design that produces the disclosures in the first place.
This paper presents results from the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics (Beier, forthcoming 2026). Cascade economics analyzes the propagation dynamics that determine how much of the Disclosure Incentive's theoretical value is realized in allocation decisions. The author invites engagement from the network economics, information cascade, and science communication communities.