The Postnieks Impossibility Theorems

An impossibility theorem is a proof that a set of individually reasonable axioms cannot be simultaneously satisfied by any mechanism, rule, or institution. The impossibility is structural, not empirical: it does not claim that existing systems fail, but that no possible system can succeed.

The framework originates with Kenneth Arrow’s 1951 proof that no rank-order voting system can convert individual preferences into a community-wide ranking while simultaneously satisfying unrestricted domain, the Pareto principle, independence of irrelevant alternatives, and non-dictatorship. Arrow’s contribution was not the identification of a flawed mechanism but the demonstration that the flaw is inherent in the problem itself.

Every impossibility theorem since Arrow has followed the same logical architecture:

What distinguishes an impossibility theorem from an ordinary negative result is its generality: the proof holds for allmechanisms satisfying the stated assumptions, not merely existing ones. When the proof succeeds, it does not say “we have not found a solution”; it says “no solution exists under the stated axioms.” The claims on this page are working-paper claims presented for review against that standard.

From Condorcet’s 1785 voting paradox through List and Pettit’s judgment aggregation theorem in 2002, the fourteen impossibility theorems collected here are a representative selection of the major results in social choice theory and mechanism design.^† Every one proves an impossibility in the space of decision procedures operating on human preferences. The logical constraint is always informational or aggregative. None reaches outside the bilateral payoff space into the physical, biological, or geochemical world.

^† The set of impossibility theorems in social choice and mechanism design is open-ended, not a fixed canon; this is a curated selection of major results, not an exhaustive list. See Stanford Encyclopedia of Philosophy, “Social Choice Theory”, which treats these results as a continually growing cluster rather than a closed list.

The Stanford Encyclopedia of Philosophy states directly: Arrow’s conditions are “not supposed to express more or less indubitable truths.” Arrow himself characterized his axioms as “value judgments”that “express the doctrines of citizens’ sovereignty and rationality in a very general form.”

Many classical impossibility theorems were built on value judgments. The profession accepted them. A subset of the Postnieks domain theorems is built on conservation of mass, radioactive decay constants, carbon-fluorine bond energetics, and evolutionary selection pressure— physical laws confirmed by independent experimental replication. The broader domain program also includes institutional intractability theorems, where the constraint is policy architecture rather than natural law.

Whether these foundations meet the standard applied to the canonical fifteen is a question the profession will have to answer. The axioms are stated plainly so that the evaluation can proceed on their merits.

Eight classes of domain science describe the binding mechanism across these records. The mechanism is what decides the class: where a physical, chemical, biological, thermodynamic, geological, or informational law sets the welfare floor, the record is an impossibility; where the constraint is institutional and a proven reform model already exists in another jurisdiction, the record is an intractability; where the measured βW is already below 1, the record is a control.

Each Postnieks theorem has an expiry condition— a precisely specified state of the world under which the impossibility’s scope reduces. Arrow’s theorem has no expiry condition because it does not engage the actual world. The Postnieks theorems do.

If someone invents a non-limestone binder with equivalent performance at scale, the Calcination Floor expires. If a biological pathway is discovered that cleaves the C–F bond, the Molecular Persistence Floor narrows. If a viable antibiotic alternative eliminates selection pressure, the Efficacy Ceiling lifts.

The falsifiability is intentional. Each theorem states the conditions under which its scope would narrow, and welcomes the technical or scientific development that would narrow it.

The sixty-one studied-domain records divide into three classes by the binding mechanism. The class turns on why the welfare loss cannot be closed: a natural law, an institutional game with no borrowed cure, or a loss already small enough that no floor is reached. The foundational MST theorem is presented above as the theorem-paper result; it is not counted as another ranked-domain row.

Fourteen records classified as impossibility— a hard physical, chemical, biological, thermodynamic, geological, or informational law sets the welfare floor, so no institutional reform, however strong, pushes βW below 1. Cement (βW 3.21) is bound by calcination: CaCO₃ → CaO + CO₂ is conservation of mass. Deep-sea mining (βW 8.63) destroys benthic habitat that regenerates on million-year timescales. Antimicrobial resistance (βW 1.53) is an evolutionary floor: the molecular event that cures is the same event that selects for resistance. The floor is natural law, not a rule that reform could rewrite.

Thirty-four records classified as intractability— the binding constraint is institutional, and a working reform model already exists in at least one jurisdiction that can in principle be borrowed, so the right rule change can push βW below 1. Firearms (βW 21.98) has Australia’s 1996 buyback; tobacco (βW 6.50) has the WHO Framework Convention on Tobacco Control and plain-packaging regimes; cybercrime, human trafficking, and opioids each have enforcement and treatment models that have worked elsewhere. The damage persists because the institutional game has not been redesigned, not because physics forbids the fix.

Thirteen records classified as control— the measured βW is already below 1, so the welfare loss is smaller than annual industry revenue on the matched boundary. These records keep the panel honest: they show the method produces low-βW results when the measured welfare loss is small, rather than labelling every domain a floor. Several describe a genuine physical mechanism — PFAS at βW 0.96, nuclear waste half-lives — but the measured magnitude does not clear one, so they are reported as controls, not floors.

Across all sixty-two theorems, a consistent three-axiom architecture emerges:

This A1–A2–A3 architecture mirrors Arrow’s structure precisely. Arrow proved that no social welfare function can satisfy unrestricted domain, Pareto, independence of irrelevant alternatives (IIA), and non-dictatorship simultaneously. Each Postnieks theorem proves that no mechanism can satisfy necessity, identity, and reversibility simultaneously. The impossibility is the same: individually reasonable requirements that are mutually incompatible.

The seventy-five papers were released as a single corpus. They were not released as they were drafted, and the reason is methodological rather than rhetorical.

The program is interconnected by design. The Missing System Theory requires an empirical panel to test its range of application. The market-failure domain papers require a shared welfare-beta methodology so that their results can be compared. The foundational theory papers — the Reform Dividend, the Fiscal Capture Theorem, Disclosure Futility, Postnieks’s Law — depend on the completed empirical panel, because each of them makes a claim about the aggregate or about a pattern across the market-failure domains. Writing the theory papers before the empirical papers were finished would have required guessing at the pattern.

Releasing the domain papers serially would have introduced methodology drift. Each paper went through several revision cycles as the welfare-beta specification was refined, revenue-denominated rather than profit-denominated, tested against three distributional families, and anchored to a consistent Monte Carlo protocol. When a refinement was adopted, it was applied as a batch edit across the 61 studied domain papers. The same was done for the Decision Accounting seventeen-field record that appears in every paper. Papers that had already been posted under earlier conventions could not have been retrofitted cleanly, and a reader comparing a 2024 draft against a 2026 draft would have been comparing across different methodological vintages.

The consequence is a corpus in which every paper follows the same protocol, every welfare-beta is auditable against the same assumptions, and the theory papers rest on the finished empirical panel rather than a partial one. The trade-off was a longer silent interval before publication in exchange for a corpus that could be evaluated as a whole.