Representation Capital Measurement Theory
Quantifying Computational Admissibility in AI-Mediated Markets
Evidence Status
Proposed hypothesis — not yet tested
This publication presents a conceptual hypothesis awaiting empirical validation.
Abstract
Representation Capital Measurement Theory supplies the measurement layer of the Representation Economy research program. This paper formalizes how Representation Capital—the accumulated stock of machine-readable qualities that increases computational admissibility probability—can be measured through observable primitives, composite indices, admissibility functions, Representation Yield, Allocation Influence, and threshold-based exclusion. The framework introduces six measurable primitives (Completeness, Accuracy, Verifiability, Freshness, Portability, Actionability), formalizes additive and multiplicative measurement approaches, defines computational admissibility functions with threshold-based exclusion, derives Representation Yield as the allocative return on representation investment, specifies Allocation Influence as the probability shift from representation changes, and provides testable predictions linking measurement outcomes to selection probability.
Executive Summary
Background
Representation Capital was introduced as a theoretical construct in Volume I, with Dynamics explored in a subsequent working paper. This paper completes the measurement layer by specifying how Representation Capital can be quantified, measured, and tested in practice.
Objectives
- Formalize six observable primitives that constitute Representation Capital
- Specify additive and multiplicative index construction methods
- Define computational admissibility functions with threshold-based exclusion
- Derive Representation Yield as the allocative return on representation investment
- Specify Allocation Influence as the probability shift from representation changes
- Provide testable predictions linking measurement to selection probability
Approach
Measurement-theoretic formalization building on Representation Capital (Volume I) and Representation Capital Dynamics. Defines primitive measurement scales, index construction rules, admissibility function specifications, and testable hypotheses linking representation quality to computational admissibility outcomes.
Main Findings
- Six primitives provide complete measurement basis: Completeness, Accuracy, Verifiability, Freshness, Portability, Actionability
- Additive indices support simple measurement; multiplicative indices capture interaction effects
- Threshold-based exclusion functions specify how admissibility depends on composite scores
- Representation Yield quantifies allocative return per unit of representation investment
- Allocation Influence measures the marginal probability effect of representation changes
- Testable predictions link measurement outcomes to observable selection frequency
Conclusions
- Representation Capital is measurable through the six-primitive framework
- Measurement choice (additive vs multiplicative) should reflect theoretical assumptions about interaction effects
- Threshold functions determine how representation quality translates to admissibility
- Representation Yield and Allocation Influence provide operational metrics for ROI assessment
- Empirical validation requires observing selection frequency across representation quality levels
Methodology
Research Type
measurement theory
Data Sources
Confidence Level
high
Description
Measurement-theoretic formalization specifying observable primitives, measurement scales, index construction rules, admissibility functions, and testable hypotheses.
Limitations
- Empirical validation required for definitive claims about measurement accuracy
- Primitive operationalization may vary across application domains
- Threshold calibration requires domain-specific validation
- Index weights may require empirical estimation
Key Findings
Six primitives provide complete measurement basis for Representation Capital.
Theoretical specification: Completeness, Accuracy, Verifiability, Freshness, Portability, and Actionability span all relevant dimensions of machine-readable representation quality.
Implications
- Each primitive is independently observable and measurable
- Composite indices can be constructed from primitive measurements
- Measurement framework is generalizable across asset classes
Additive and multiplicative indices capture different assumptions about primitive interaction.
Mathematical specification: additive indices assume independence; multiplicative indices capture interaction and compounding effects.
Implications
- Index choice should reflect theoretical assumptions
- Multiplicative indices may better capture real-world interactions
- Additive indices provide simpler measurement for baseline applications
Threshold-based exclusion determines how representation quality translates to admissibility.
Formal specification: P(admit | R) = f(Σᵢ wᵢpᵢ, τ) where τ is the exclusion threshold.
Implications
- Threshold calibration determines admissibility standards
- Different applications may require different thresholds
- Threshold analysis enables policy-relevant sensitivity assessment
Representation Yield quantifies allocative return on representation investment.
Derivation: RY = ΔP(select) / ΔRC Representation Quality—the expected increase in selection probability from a unit increase in Representation Capital.
Implications
- Representation Yield provides operational ROI metric
- Investment decisions can be evaluated using expected marginal returns
- Yield may vary across domains and contexts
AI Summary
One Sentence
Representation Capital Measurement Theory provides the measurement layer for the Representation Economy research program, formalizing how Representation Capital can be quantified through six observable primitives, composite indices, admissibility functions, Representation Yield, and Allocation Influence.
One Paragraph
This measurement-theoretic working paper completes the Representation Capital layer by specifying how RC can be measured in practice. The framework defines six observable primitives (Completeness, Accuracy, Verifiability, Freshness, Portability, Actionability), specifies additive and multiplicative index construction, formalizes threshold-based computational admissibility functions, derives Representation Yield as allocative return on investment, specifies Allocation Influence as marginal probability effect, and provides testable predictions linking measurement to selection frequency. All claims require empirical validation.
Key Takeaways
- · Six primitives provide complete measurement basis for Representation Capital
- · Additive and multiplicative indices capture different interaction assumptions
- · Threshold functions determine how representation translates to admissibility
- · Representation Yield quantifies allocative ROI on representation investment
- · Allocation Influence measures marginal probability effect of representation changes
- · Testable predictions link measurement to observable selection outcomes
Target Audience
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Citation
Patrone, M. (2026). Representation Capital Measurement Theory: Quantifying Computational Admissibility in AI-Mediated Markets. HomeSelf Research Publication Series.