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Paper Summaries/Validity of the Hypergeometric Convergence Test: A Formal Defense of the Combinatorial Null in Cross-Regime Field Overlap Analysis
Paper #1018
Validity of the Hypergeometric Convergence Test: A Formal Defense of the Combinatorial Null in Cross-Regime Field Overlap Analysis
The paper defends the hypergeometric convergence test used in the Decision Accounting framework against three methodological objections: wrong test, coder dependence, and selection bias. It proves the test is correct, separates convergence from inter-rater reliability, shows coder dependence does not affect the null, and specifies a falsification condition. The convergence finding survives all objections.
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Theorem status: evidence-traced claim under the cited paper's assumptionsFalsification: show the same game preserving system welfare without changing the payoff structure
KEY FINDINGS
THEOREM
Theorem 1 (Invariance of the Convergence Statistic Under Coder Dependence). Let V = {v_1, ..., v_N} be a set of regime vectors produced by any coding process, including a process with arbitrary coder dependence. The convergence statistic C = |{j : v_ij = 1 for all i}| is a function of V only. The hypergeometric P-value P(C | H_0) is a function of C, M, and {k_i} only. Neither C nor P depends on the coding process that produced V.
PLAIN ENGLISH
The convergence statistic and its statistical significance depend only on the final set of regime requirement vectors, not on how those vectors were produced. Even if coders influenced each other, the test remains valid because it conditions on the observed vectors.
EVIDENCE & LIMITATIONS
- Theorem status: evidence-traced claim under the cited paper's assumptions
- Falsification: show the same game preserving system welfare without changing the payoff structure
REFERENCES / CITATION STATUS
References section
Detected
Bibliography entries
175
In-text citations
7
Unique citations
139
Footnote markers
131
Citation year span
1689-2026
Source hash
675776d5ce57
This page reports reference counts measured directly from the manuscript. Full reference entries render only when a curated source chapter carries a public References, Bibliography, Source Notes, Supplemental Reference Archive, Footnotes, or Source-Grounding Ledger section. The site does not synthesize citation entries. Literature-claim verification status: not evaluated.
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EXECUTIVE SUMMARY
The Decision Accounting framework reports that sixteen regulatory regimes converge on the same documentation fields with P < 0.001 under a hypergeometric null. A methods reviewer raised three objections: the hypergeometric test is inappropriate for hand-coded field overlap; coder non-independence contaminates the test; and regime selection biases the result. The paper addresses each objection. It proves that the hypergeometric distribution is the correct combinatorial null for the overlap-of-random-subsets problem, and that the test is conservative. It separates the convergence statistic from inter-coder reliability, explaining why they answer different questions. It proves the convergence statistic is invariant under coder dependence given fixed regime vectors. It shows the selection objection confuses selection on the independent variable with selection on the dependent variable. The paper also falsifies the institutional isomorphism alternative by demonstrating terminological divergence with structural convergence. A blind replication protocol is specified for independent verification. The convergence finding survives all three objections.
METHODOLOGY
The paper uses formal mathematical proof and logical argumentation to defend the hypergeometric convergence test. It states the null model, proves the correctness of the hypergeometric distribution, separates convergence from inter-rater reliability, proves invariance under coder dependence, and specifies a falsification condition. It also uses empirical evidence from the corpus (terminological divergence) to falsify the institutional isomorphism alternative.
SOURCE QUESTIONS
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WHY THIS MATTERS
For the economist
A structural claim about when bilateral optimization degrades the shared system. Read the formal statement and its stated axioms.
For the regulator
The constraint is physical or biological, so disclosure alone will not internalize it. The policy lever is to bound exposure, not to price it away.
For the executive
This is where a privately efficient decision can degrade the system the business depends on. The governance question is which decision records would make that system cost visible before it is normalized.
For the teacher
An on-site HTML deck and the expanded curriculum cover the argument, the evidence, and the measurement. Use the deck as a self-contained class session, then route deeper through the 45-50h core course or 100+h full curriculum.
For the affected community
In plain terms: who gains from the current arrangement, who pays for it, and what rule change would alter that split. The summary states each without jargon.
© 2026 Erik Postnieks · Independent Researcher · Salt Lake City