The Proven-Model Requirement: Existence Proofs, Selection Bias, and Falsification in the Intractability Taxonomy

The paper answers the survivorship objection to SAPM proven models

Critics say the taxonomy cherry-picks Australia on firearms, Portugal on drugs, the Nordic model on trafficking, Estonia on data governance, and Brazil on cash transfers while ignoring failures. The paper narrows the claim before defending it.

• SAPM reports 49-52 confirmed Intractability domains across the corpus, with zero counterexamples identified to date.
• The objection would be fatal only if the taxonomy claimed a reform always works or transfers unchanged everywhere.
• The paper turns the commitment into an auditable procedure for successes, failures, searches, and falsification.

One implemented reform is enough to reject institutional impossibility

The proven-model requirement says a reform lies inside the feasible set if a real polity implemented it and achieved measured superior outcomes. It does not claim the model is optimal, universal, or transferable without adaptation.

• Formal target: P = 'R is institutionally impossible,' meaning no polity can implement R and achieve superior outcomes.
• If at least one polity p implemented R and achieved superior outcomes, then P is false.
• Australia need not predict the United States; Portugal need not predict every drug market; feasibility and transfer are separate questions.

Intractability requires a proven model; Impossibility cannot have one

The requirement applies only where the binding constraint is institutional, political, or economic. It does not apply where the constraint is physical, chemical, biological, or nuclear.

• PFAS contamination is treated as Impossibility because the carbon-fluorine bond is 485 kJ/mol.
• Antimicrobial resistance is treated as Impossibility because natural selection cannot be repealed by institutional design.
• Plutonium-239 is treated as Impossibility because its half-life is 24,100 years.

The denominator must be reported, but it does not erase feasibility

The paper accepts the denominator problem and makes it part of the method. Each domain must identify the success case, attempted comparable reforms, failures, and causal reasons for failure.

• A large denominator weakens claims of easy generalization, not the narrower existence proof.
• The record must separate technical failure, implementation failure, and capture failure.
• Counts alone are insufficient; the paper requires causal analysis of each failed attempt.

Technical failures threaten classification; implementation and capture failures fit the diagnosis

The paper’s key move is to classify why reforms failed. A failure caused by the design producing worse outcomes is different from a failure caused by blocked implementation or capture by affected interests.

• Technical failure: implemented as designed, but produced worse outcomes than the status quo.
• Implementation failure: political opposition, bureaucracy, or resource constraints prevented the design from being carried out.
• Capture failure: the reform was carried out but neutralized by the interests it was meant to constrain.

The answer to Nordic exceptionalism is a large or heterogeneous case per reform pattern

The paper does not deny that small, high-trust societies create transfer risk. It requires the taxonomy to supply larger or more heterogeneous proven cases wherever they exist.

• Australia: firearms reform in a federal polity of 26 million with a gun-owning culture.
• European Union: platform monopoly remedies across 27 states, many languages, divergent legal traditions, and 450 million people.
• Brazil: Bolsa Família at 214 million people, continental scale, and extreme inequality.

Small-state proofs still refute impossibility, but they must be labeled honestly

The paper classifies proven models by scale and heterogeneity so a feasibility claim is not misread as a transfer guarantee.

• Large-scale proof: population over 50 million, federal structure, or culturally heterogeneous society; transfer risk low to moderate.
• Medium-scale proof: population 10-50 million, unitary system, or moderate homogeneity; transfer risk moderate.
• Small-scale proof: population under 10 million or high homogeneity; transfer risk high and labeled feasibility-in-principle.

An Intractability domain fails if every attempted reform failed for technical reasons

The paper gives the requirement a domain-level falsification test. A domain should move toward Impossibility, or lose its theorem, if no country or program anywhere has achieved the claimed outcome.

• Formal condition: for every p in the set of attempted reforms S, O(p) = false.
• The failure pattern must be technical unworkability, not lack of political will.
• The critic’s task is to identify universal technical failure or a newly recognized physical, chemical, or biological constraint.

Every proven-model entry must make the search reproducible

The documentation protocol converts 'zero counterexamples' from a bare count into a recorded search result. The program must show where it looked and what it found.

• Record the success case, outcome metric, attempted reforms, failures, and failure categories.
• Document databases, keywords, time period, inclusion criteria, and partial or abandoned attempts.
• Maintain a public registry and invite corrections so publication bias can be challenged.

Australia’s firearms reform is the paper’s complete protocol example

The example uses the 1996 National Firearms Agreement to show what a domain entry should contain: mechanism, outcomes, failure denominator, failure causes, and transfer risk.

• Mechanisms: mandatory buyback of 650,000 firearms, uniform licensing, and a 28-day waiting period.
• Outcomes reported: zero mass shootings in 24 years after reform versus 13 in 18 years before reform; 42% decline in firearm homicides; 57% decline in firearm suicides.
• Failure denominator reported: 12 attempts, 8 successes, 4 failures, all political and zero technical.

The Proven-Model Theorem links existence, feasibility, and classification

The formal theorem depends on four axioms: domain classification, feasibility, falsification, and search obligation. Its conclusion is narrow: a measured success case proves institutional feasibility and rejects impossibility.

• A1: Intractability means the binding constraint is institutional, political, or economic.
• A2: feasibility exists when at least one polity implemented R and achieved outcome O with measured superior outcomes.
• A3 and A4: all-technical failure falsifies the domain, and no-falsification claims require a documented search.

The requirement turns the General Game-Change Conjecture into a search procedure

The paper connects the method to the SAPM canon by making the zero-counterexamples claim auditable. Success shows the trap is not physical; repeated political failures support the fiscal-capture diagnosis.

• The conjecture predicts welfare-improving transformations that are blocked by institutional incentives until the incentive structure changes.
• A pattern of many political failures and at least one measured success is expected under Intractability.
• All existing and new Intractability domains must complete the protocol before the classification can stand.