Vertical Rule Coherence in Hierarchical Governance

• Vertical Rule Coherence is a framework that examines how institutional rules at operational, collective-choice, and constitutional layers maintain their intended effects and legal continuity.
• It employs syntactic and semantic formalizations using Institutional Grammar 2.0 to ensure consistent encoding and traceability of rules.
• Practical applications in digital governance and blockchain systems highlight its role in enhancing regulatory transparency and institutional adaptability.

Vertical Rule Coherence refers to the formal, empirical, and computational analysis of the alignment, compatibility, and traceability of institutional rules and norms across hierarchical layers of governance—namely operational, collective-choice, and constitutional levels—within the Institutional Grammar and the Institutional Analysis and Development (IAD) framework. This concept is central for evaluating how normative statements or formal regulations preserve their intent, constraints, and enforceability as they are instantiated, aggregated, or modified at different strata of institutional systems, such as laws, organizational policies, or digital protocols.

1. Conceptual Foundations: Layers of Institutional Rules

In Ostrom’s IAD framework and its formalizations, social systems are structured by rules that prescribe or proscribe the actions of actors (Attributes, $A$) under specific modalities (Deontic, $D$), aims (Aim, $I$), objects (Object, $O$), activation and execution conditions (Conditions, $C$), and sanctions ("Or Else", $S$) (Frantz, 19 May 2025). These rules are organized into three nested layers:

• Operational rules: Specify day-to-day permissible and forbidden behaviors (e.g., “how to submit a transaction”, “how to register attendance”) (Krafft et al., 2019).
• Collective-choice rules: Determine the allocation and permissible changes to operational rules (e.g., "who may change reporting requirements," "how a new safety protocol is adopted").
• Constitutional rules: Define meta-rules for the creation, modification, or replacement of collective-choice rules (e.g., voting procedures for amending bylaws, deployment of new governance modules in a protocol).

Vertical rule coherence, in this context, assesses whether rules at each layer logically and procedurally align with those at other layers, thus enabling transparency, dispute resolution, and institutional adaptability.

2. Syntactic and Semantic Formalization in Institutional Grammar 2.0

The Institutional Grammar (IG) 2.0 advances the formal analysis of rule coherence by providing a six-component structure for regulative rules:

$R = (A, D, I, O, C, S)$

and, for constitutive rules,

$K = (E, M, F, P, C, S)$

where $E$ is the constituted entity, $M$ is the modal, $F$ the constitutive function, $P$ the properties, and $(C, S)$ as above. Coherence between layers is facilitated by systematically encoding, decomposing, and comparing the instantiation of each component as rules percolate across layers (Frantz, 19 May 2025). For example, an operational rule requiring “officers must warn or fine drivers if speed exceeds limit” inherits its legitimacy and constraints from a collective-choice provision specifying which actor sets speed limits, and, ultimately, from constitutional definitions establishing who has authority over transportation regulation.

Vertical coherence thus depends on:

• Syntactic alignment: Consistency in the use and interpretation of IG components across rules at varying levels.
• Semantic congruence: Maintenance of meaning (e.g., matching deontic logics or conditions under which rules activate) as rules are instantiated or referenced hierarchically.

3. Parsing, Encoding, and Analytical Techniques

The IG Parser operationalizes vertical rule coherence by requiring that statements be coded in IG Script, a notation that explicitly marks the IG components via tags (e.g., A, D, I, O, C, S for regulative; E, M, F, P, C, S for constitutive) and supports nested structures (Frantz, 19 May 2025). The parser architecture includes:

• Lexical/syntactic validation: Ensures tags and nesting are correct, so that component-level correspondence between hierarchical statements can be structurally checked.
• Recursive decomposition and tree construction: Encoded rules are mapped to in-memory trees, whose parent-child relations reflect vertical derivation or reference between rule levels.
• Transformation and output: Parses can be serialized into CSV, JSON, XML, or RDF, enabling downstream computational or statistical analyses that track rule lineage and transformations through layers.

Coherence checks can be executed by traversing such trees to verify that, for a given atomic operational rule, its collective-choice and constitutional ancestors address the same actors, deontic modalities, and sanction structures.

4. Practical Applications: Case Studies and Computational Modeling

In digital institutions, vertical rule coherence is critical for resilience and adaptability. For example, in blockchain-based systems, operational code (e.g., validation rules) is ideally traceable to explicit on-chain or off-chain meta-rules about protocol amendments, and ultimately to constitutional choices about governance mechanisms (Krafft et al., 2019). The absence of formal meta-rules for protocol evolution (e.g., in early cryptocurrencies) has led to governance crises, demonstrating the need for constitutional layers that enforce vertical coherence.

Similarly, in regulatory informatics platforms such as METRC (medical cannabis tracking), operational requirements like tag scanning or data reporting are periodically revised through user group interventions—formal collective-choice and constitutional proceedings designed to realign operational practices with higher-level regulatory intent. Plugin architectures in digital games, such as Minecraft servers, reveal vertical rule coherence when governance plugins (constitutional layer) dynamically enforce or modify administrative rights, which in turn affect in-game permissions or sanctions.

Computational models such as the Action Situation Language (ASL) instantiate IAD framework elements explicitly as rules with boundary, position, choice, and control types (Montes, 2021). What-if analyses can be performed by altering collective choice or constitutional rules and observing the derived operational behavior in extensive-form games. This explicit mapping supports both formal and empirical analyses of vertical coherence by tracing modifications across layers and evaluating their equilibria and social welfare properties.

5. Benefits, Limitations, and Evaluation Metrics

Ensuring vertical rule coherence confers several analytic and operational advantages:

• Data consistency: Codified layers preclude ad hoc rule drift and ensure predictable transformation of norms through institutional hierarchies.
• Reproducibility and scalability: Deterministic parsing and encoding allow the assembly of large corpora where layer-to-layer correspondence can be batch-validated for compliance, traceability, or statistical modeling.
• Expressiveness and downgradeability: Nested and annotated IG Script can be projected onto simpler atomic substatements, permitting multi-scale analyses.

However, limitations persist:

• Ambiguity: Even with formal grammars, natural language legal or policy texts require human judgment for referent resolution and consistency checking.
• Jargon and semantic drift: Specialized domains may demand expansion of IG component sets or ontology-enhanced annotations to adequately maintain semantic coherence.
• Automation gaps: While APIs and semi-automated NLP pipelines assist in encoding, human expertise is indispensable for ensuring that the mapping from constitutional intent to operational effect is preserved and meaningful throughout transformation.

Regarding evaluation, although metrics such as “Oversight Integrity Score” (OIS) have been suggested for quantifying shifts across layers (e.g., before and after AI system deployment in clinical settings), no standard indices currently exist; research is ongoing to formalize such measures (Morgan et al., 2023).

6. Significance in AI, Governance, and Future Directions

Vertical rule coherence is of central importance not only in legal and policy domains but also across computational and AI-related governance regimes. As noted in the context of the NIST AI Risk Management Framework, the distinction between “Govern” (defining roles, boundaries, and aggregation at upper layers) and “Map” (charting operational choices, incentives, and information flows) is directly instantiated via IAD concepts (Morgan et al., 2023). Robust oversight structures for high-stakes AI require ensuring that operational decision-making, aggregation mechanisms, and accountability provisions remain aligned with their underlying collective-choice and constitutional mandates—a property that vertical rule coherence makes explicit and analytically tractable.

A plausible implication is that advancing formal DSLs for constitutional and collective-choice rules, empirical studies of governance resilience, and participatory design toolkits that emphasize meta-rule traceability will further the rigor and adaptability of institutional systems (Krafft et al., 2019).

In summary, vertical rule coherence provides a framework for diagnosing, enforcing, and evaluating the logical and procedural alignment of rules across institutional hierarchies, underpinning both the theoretical and practical sustainability of complex governance systems.