Correspondence Principle

one_liner: New theories match old limits.

origin_domain: physics

core_idea:
The Correspondence Principle is the meta-theoretical constraint that (1) a **new, more general theory** must **reproduce the predictions of the older theory it supersedes** in the regime where the older theory was empirically validated, (2) this reduction typically appears as a **well-defined limit**: ℏ → 0 (classical limit of quantum mechanics), c → ∞ (non-relativistic limit of special relativity), G → 0 or high-gravitational-scale limits recovering Newtonian gravity, n → ∞ (large quantum number → classical orbital behavior in Bohr's original formulation), (3) the principle functions both as a **consistency check** — any candidate successor theory that fails to recover established results in their domain is refuted — and as a **constructive guide**: proposing a new theory means specifying how the classical theory emerges from it, and (4) the reduction is **directional**: the new theory is strictly more general, while the old theory remains valid within its domain as a computationally simpler, approximate description.<!-- FACT-D13-100 -->[^bohr-1920]

Bohr's 1920 formulation stated the principle with precision for quantum mechanics: as quantum numbers become large (n → ∞), the spacing between energy levels becomes small relative to the absolute energy, and the frequency of quantum transitions approaches the classical orbital frequency predicted by Kepler's laws. This agreement in the limit of large quantum numbers justified the *selection rules* of the old quantum theory and constrained the structure of any truly successor theory.[^bohr-1920] The principle is thus not merely that new theories must agree with old ones, but that *the limit-taking process itself becomes an operational guide*: the physicist designing a successor theory knows that it must admit a well-defined classical or non-relativistic limit, not as a philosophical luxury but as a mathematical and empirical necessity. Without such a limit, the new theory disconnects from the validated empirical base and becomes speculation rather than science.

The correspondence principle generalizes beyond quantum mechanics to any theory succession: relativistic mechanics must reduce to Newtonian mechanics as v/c → 0, general relativity must recover Gauss's law and Newton's potential in weak-field limits, statistical mechanics must yield thermodynamics in the thermodynamic limit (N, V → ∞, N/V fixed), and quantum field theory must reduce to quantum mechanics in non-relativistic, single-particle regimes.[^ehrenfest-1927] The principle constrains theory-construction: it rules out arbitrary modifications to established theories and provides a disciplinary framework for evaluating novel proposals, ensuring scientific revolutions remain continuous with empirical success even as conceptual ontologies shift.

structural_signature: Formally, theory T' supersedes theory T if there exists *the action-scale parameter* ε (or family of parameters) and *the limit-reduction principle* (ε → ε₀) in which T'(ε) → T uniformly on the empirical domain where T was validated. The classical-limit regime and the large-quantum-number regime are characterized by the condition that the action quantum (ℏ, or equivalent) becomes negligible relative to the typical action of the system. Examples: quantum mechanics with *the classical limit* (ℏ → 0) recovers classical mechanics via the WKB approximation[^wkb-1926] and the Ehrenfest theorem,[^ehrenfest-1927] which shows that expectation values of position and momentum obey Hamilton's equations in *the semiclassical regime*; special relativity with v/c → 0 recovers Newtonian kinematics term by term in the Taylor expansion of γ = 1/√(1 − v²/c²); general relativity with weak fields and low velocities recovers Newtonian gravity via the geodesic equation reducing to ẍ = −∇Φ; thermodynamics emerges from statistical mechanics in the thermodynamic limit N → ∞, V → ∞ with N/V fixed; quantum field theory reduces to quantum mechanics for a single particle via the non-relativistic limit. The signature includes: an identifiable small parameter, a well-defined mathematical limit (often singular and requiring care), and empirical validation that the reduction holds numerically within the error bars of the older theory's tests. *The predecessor-successor relation* structures a hierarchy of theories, each valid within its own range; *the interpretive bridge* between them allows practitioners to understand when to apply which theory and why simpler theories suffice in their appropriate domains. Failure modes include cases where the limit is discontinuous (e.g., entanglement has no classical counterpart), where the new theory predicts new phenomena in the old theory's regime that were overlooked, and where the "classical theory" is itself an effective approximation to something deeper.<!-- FACT-D13-101 -->[^ehrenfest-1927]

what_it_is_not:
- **Not logical reduction.** Theories do not reduce to their predecessors in a deductive sense; the reduction is approximate, limit-taking, and often subtle. Quantum mechanics does not *contain* classical mechanics as a sub-theory; it reproduces classical *predictions* under ℏ → 0.
- **Not theoretical succession in general.** When a theory is replaced by one that contradicts it outside its domain of validity (as Copernican astronomy replaced Ptolemaic), the correspondence principle constrains the new theory's behavior *within* the old domain, not outside it.
- **Not backwards-compatibility in the software sense** (see `versioning`). Software backwards-compatibility is a design choice; the correspondence principle is an empirical/logical constraint: if the new theory doesn't recover old-theory predictions where old-theory works, it cannot be correct.
- **Not the only valid relation between theories.** Theories can be complementary (describing disjoint regimes), dual (same physics, different representations), or incommensurable (different ontologies) without one reducing to the other.
- **Not a guarantee the new theory is true.** Correspondence is necessary but not sufficient; many failed theories also reproduced established results in the appropriate limit.

broad_use: Physics is the native domain: quantum-classical correspondence via WKB/Ehrenfest/decoherence, relativistic-Newtonian correspondence via low-velocity expansion, statistical-thermodynamic correspondence via large-N limits, quantum field theory's reduction to quantum mechanics. Philosophy of science uses correspondence as a central tool in the Kuhn-Lakatos debate about theory change (Lakatos's "progressive research programs" require the new theory to explain everything the old theory explained, plus more). Mathematics embodies the pattern in generalization: non-Euclidean geometries reduce to Euclidean in the flat-space limit; non-standard analysis recovers standard analysis when the infinitesimals vanish; abstract algebra structures reduce to the concrete ones. Engineering applies analogous reasoning when a refined model must match a simpler model's results in the regime where the simpler model was validated by testing — any new CFD solver must reproduce laminar flow predictions at low Reynolds numbers. Machine learning shows echoes: a neural network trained on data where linear models worked should not badly underperform linear models in that regime.

clarity: The correspondence requirement tells the working scientist exactly what a candidate generalization must do: reproduce, in its appropriate limit, all the numerical predictions of the established theory that have already been tested. This is an operational constraint, not a philosophical nicety — it kills entire classes of speculative theories at the conceptual stage. When a physicist proposes a modification of general relativity, the first check is whether it still gives the correct Mercury perihelion precession, gravitational lensing, and Shapiro time delay. If it does not, the proposal is dead, regardless of its theoretical elegance. This makes the principle a disciplining force: novelty is welcome, but only novelty consistent with the hard-won empirical base.

manages_complexity: The principle lets practitioners use simpler theories with confidence inside their domains of validity, knowing that the deeper theory gives the same answer to within the test precision. An engineer designing a bridge need not use general relativity; Newtonian mechanics is certified correct by correspondence in the weak-field, low-velocity regime. A chemist computing molecular energies can use the Born-Oppenheimer approximation because its violations are numerically negligible for most organic chemistry. Practically, correspondence defines the *boundary* of each theory's applicable regime: where do relativistic corrections start to matter? where does quantum behavior emerge? The same-answer-to-required-precision criterion gives a principled answer. This is indispensable for science and engineering: without it, every calculation would require the deepest known theory, which is rarely necessary and often intractable.

abstract_reasoning: The correspondence principle encodes the idea that **empirical truth is cumulative**: once a theory has been validated numerically in some regime, any successor must honor that validation. This creates a ratchet in science — each generation's well-tested predictions survive as constraints on the next generation's theories, even as ontologies and concepts are overturned. Abstractly, it is the requirement that any map of reality must contain, as a sub-region, an accurate version of all the earlier validated maps. This is why science can be progressive even when conceptually revolutionary: Einstein overturned Newton's ontology of absolute space and time, but Newton's predictions for planetary motion at moderate velocities remain as valid as they ever were. The pattern generalizes to any knowledge-making enterprise where older methods have verified results: economics cannot discard econometric findings wholesale, medicine cannot ignore the established efficacy of specific treatments, engineering cannot override validated test data. The new must account for the old, not merely contradict it.

knowledge_transfer:
| Role in Source (physics: QM → classical) | Role in Target (software engineering: API v2 replacing v1) |
|---|---|
| Older theory T (classical mechanics) | Old API v1 (validated contract) |
| Newer theory T' (quantum mechanics) | New API v2 (broader feature set) |
| Limit parameter (ℏ → 0) | Migration configuration (compatibility mode) |
| Empirical domain of T | Existing client integrations using v1 semantics |
| Reduction theorem (Ehrenfest) | Automated test suite mapping v2 outputs to v1 contract under compat mode |
| Failure of reduction → theory rejected | Failure of compat mode → breaking change, cannot ship as successor |
| New predictions in T but not T' | New features exposed only under v2 semantics |

A software engineer deprecating an API is doing exactly what a physicist constructing a successor theory is doing: the new must reproduce the old's externally-visible behavior in the regime of old clients, or the replacement is a breaking change in disguise. The same discipline applies — if the new version cannot satisfy the old contract in the old domain, it is not a generalization but a different thing. The analogy illuminates the error mode: an API v2 that silently changes behavior in ways v1 clients depend on is a failed correspondence, and the breakage cannot be waved away as "more correct now."

prose:
_(Pass B)_

### Catalog cross-references (v1, batches 02–29)

Solution archetypes that reference this prime (per `solution_archetypes/_catalog/catalog_v1_batches_02_29.yaml`):

**As source prime (2):** `correspondence_validation`, `layered_model_validation`

**As related prime (5):** `core_model_first`, `dimensional_consistency_check`, `parameter_rescaling`, `progressive_fidelity_increase`, `representation_fit_selection`

notes: Fourteenth draft of batch 9. v1 correctly positioned the principle as a meta-constraint on theory succession; v2 deepens with the ℏ → 0, v/c → 0, N → ∞ limits and makes the WKB/Ehrenfest/thermodynamic-limit mechanisms explicit. Example pair uses hydrogen-atom Rydberg correspondence (formal QM) and database migration test-suite replay (structurally faithful non-formal software engineering) — both exhibit the "new must reproduce old in old's validated domain" structure. What It Is Not separates this from backwards-compatibility-as-design-choice, while Knowledge Transfer draws the API-versioning map deliberately. T4 introduces the Kuhn/Feyerabend counterpoint so the entry does not overstate the principle's universality.


Cost–Benefit Analysis

type: prime

one_liner: Evaluate decisions.

status: draft

core_idea: (1) **Cost–Benefit Analysis (CBA) is a systematic decision-analytic framework that aggregates all significant consequences of a candidate policy, project, or decision into a common monetary metric, computes the net (benefits minus costs) typically in present-value terms, and uses the result as a basis for evaluation. The method's modern form emerged from the interaction of early-twentieth-century welfare economics — particularly A.C. Pigou's <!-- FACT-D09-001 -->[^pigou-1920] 1920 *The Economics of Welfare*, which established the foundational welfare-measurement framework for policy analysis <!-- FACT-D09-001 -->[^pigou-1920] — with the practical needs of U.S. federal public-works evaluation, particularly the 1936 Flood Control Act's requirement that federal projects be undertaken only if "the benefits to whomsoever they may accrue are in excess of the estimated costs," and the subsequent postwar elaboration by the U.S. Army Corps of Engineers, the Bureau of Reclamation, and academic contributors (Jules Dupuit's 1844 antecedent work on consumer surplus and public-works valuation; Otto Eckstein's *Water-Resource Development*, 1958; Roland McKean's *Efficiency in Government Through Systems Analysis*, 1958; the 1950 U.S. Interagency Committee on Water Resources "Green Book"). CBA subsequently became a standardized tool of federal rule-making (OMB Circular A-94, executive-order requirements for regulatory impact analysis beginning with Reagan's EO 12291 in 1981, continuing through Clinton's EO 12866 in 1993 and extending into contemporary practice), international development-bank project appraisal (World Bank, IDB, ADB), and domestic-policy analysis across infrastructure, environmental regulation, health, and education.** (2) The distinctive focus is on the *systematic monetization and aggregation of heterogeneous consequences* across time, across affected parties, and across consequence categories, producing a single net-present-value summary statistic. The analytical payoff is a structured framework for comparing alternatives that forces explicit treatment of usually-opaque trade-offs: how are avoided fatalities valued against the cost of the safety investment that avoids them? How are long-term benefits traded against short-term costs? How are benefits to one population traded against costs to another? The analytical price of this clarity is substantial: monetization of non-market goods (human life, environmental amenity, cultural heritage, biodiversity) requires contested valuation methods (revealed-preference techniques, stated-preference / contingent-valuation surveys, hedonic pricing, benefit-transfer methods), and the resulting numbers carry the imprint of those valuation choices. (3) The practical analytical pipeline involves: defining the decision and its alternatives (including a "without-project" baseline); identifying affected parties and categories of consequence (direct, indirect, ancillary, distributional); monetizing each consequence using an appropriate valuation method; projecting costs and benefits over the project's time horizon; discounting future cash flows to present value; computing the net present value (and sensitivity to key assumptions); and reporting results with attention to distributional effects, residual uncertainties, and non-monetized considerations. (4) The deeper abstraction is that **Cost–Benefit Analysis provides a disciplined, transparent, and extensible framework for evaluating policy and investment decisions — one that forces explicit articulation of the alternatives, the consequence categories, the valuation methods, the time horizons, and the discount rates, thereby structuring both the analytical work and the subsequent deliberative process. The concept is foundational to public-finance evaluation, regulatory impact analysis, infrastructure project appraisal, environmental policy, and health-technology-assessment (which uses cost-effectiveness variants). Together with its companion techniques — cost-effectiveness analysis, distributional analysis, risk and uncertainty analysis, break-even analysis — CBA constitutes the analytical spine of contemporary applied welfare economics in public-policy practice, even as it faces ongoing critiques from distributional, rights-based, and deliberative-democratic perspectives.**

structural_signature: The pattern presumes *a decision-evaluation framework that monetizes heterogeneous consequences into a common metric (typically present-value) for comparative ranking*, requiring (a) a decision to be evaluated (a policy, project, regulation, investment) with at least two alternatives (including a meaningful "do-nothing" or "baseline" counterfactual); (b) an enumeration of significant consequences of each alternative across relevant parties, categories, and time periods; (c) a valuation framework that monetizes each consequence using defensible valuation methods; (d) a time-discounting framework that reduces future cash flows to present value; and (e) an aggregation rule that sums monetized consequences into a net-present-value summary. Structurally, CBA extends basic investment appraisal (net-present-value analysis with discount rates) to incorporate non-market and non-monetary consequences through monetization techniques, with the resulting analytical structure organized around: the *with-project vs without-project* counterfactual; the *incidence analysis* (who gains, who loses, and by how much); the *time profile* (when costs and benefits occur); the *discount rate* (which rate reflects time preference and opportunity cost of capital); the *sensitivity analysis* (how do conclusions change under different assumptions about valuation, discount rate, project costs, and benefit projections); and the *distributional analysis* (how are net benefits distributed across income groups, regions, demographic categories, generations). Structural variants include: *social CBA* (societal perspective, including external costs and benefits to third parties); *financial CBA* (project-owner perspective, including only cash flows accruing to the owner); *economic CBA* with shadow prices (using shadow prices rather than market prices to correct for market distortions — common in World Bank project appraisal); *regulatory impact analysis* (RIA — a specific CBA form used for evaluating government regulations, required for major U.S. federal regulations); *cost-effectiveness analysis* (CEA — an alternative framework when outcomes are hard to monetize; used heavily in health-policy decisions to compare interventions on cost per quality-adjusted-life-year or similar metrics); *break-even analysis* (identifying the threshold at which benefits equal costs under varying assumptions); and *multi-criteria analysis* (MCA — when monetization is infeasible or contested, retaining explicit multi-dimensional comparison). The distinguishing structural commitment of CBA is the monetization and aggregation move — and the analytical discipline it imposes on valuation, discounting, and distributional-effect articulation.

what_it_is_not:
- Not a substitute for political judgment — CBA provides analytical input to decisions; final decisions incorporate political, distributional, ethical, and procedural considerations that extend beyond CBA's reach.
- Not free from contested valuation — monetization of non-market goods (statistical lives, ecosystem services, cultural amenity) requires valuation choices that are empirically uncertain and ethically contested, and the numerical results embed those choices. The value-of-statistical-life (VSL) methodology <!-- FACT-D09-003 -->[^viscusi-aldy-2003] — typically deployed at $10–11 million per avoided premature death in contemporary U.S. regulatory CBA — derives from labor-market revealed-preference studies and confronts well-documented distributional controversies <!-- FACT-D09-003 -->[^viscusi-aldy-2003].
- Not automatically distributionally neutral — the standard CBA net-present-value metric is sensitive to the initial distribution of income (those with higher willingness-to-pay get larger monetized weights), which has been widely critiqued as biasing CBA in favor of wealthier beneficiaries.
- Not identical to Pareto analysis — CBA typically uses Kaldor-Hicks compensation logic (would winners in principle be able to compensate losers and still be better off?) rather than actual-compensation Pareto improvements. The Kaldor-Hicks compensation principle <!-- FACT-D09-002 -->[^kaldor-1939] — which CBA operationalizes — asks whether the aggregate monetary benefits exceed costs, such that winners could in principle compensate losers and still be better off, even if compensation does not actually occur <!-- FACT-D09-002 -->[^kaldor-1939]. This is analytically weaker than Pareto efficiency but more practical for policy application, though the required compensation typically does not materialize in actual practice.
- Not infallible under uncertainty — deep uncertainty about long-run consequences (climate change, novel technology, catastrophic risks) strains CBA's time-discounting and consequence-projection apparatus; specialized methods (real-options analysis, robust-decision-making, Bayesian decision theory) address uncertainty differently.
- Not well-suited to sacred or incommensurable values — certain moral and legal commitments (constitutional rights, absolute prohibitions, sacred places) are treated analytically as infinite valuations or as side-constraints on CBA rather than entering the monetized calculation.
- Not a single methodology — CBA practice varies across jurisdictions (U.S. OMB vs UK Green Book vs EU guidelines vs World Bank procedures), sectors (infrastructure vs regulation vs health vs environment), and time periods (earlier-era CBA relied more heavily on market-price valuations; contemporary CBA incorporates more sophisticated non-market-valuation methods and distributional-weighting extensions).
- Not immune to manipulation — selective monetization, choice of discount rate, baseline selection, and sensitivity-analysis scope can all be used to tilt CBA outcomes; transparent practice requires careful disclosure of assumptions and methodology.

broad_use: CBA has become a standard tool in policy analysis globally. In *regulatory impact analysis*, U.S. federal regulations above the threshold of "economic significance" ($100M annual economic impact) require CBA under executive orders dating from Reagan (EO 12291, 1981) through Clinton (EO 12866, 1993) through subsequent administrations; similar requirements exist in the UK (Green Book, HM Treasury), EU (Better Regulation guidelines), Canada (Treasury Board regulatory-impact analysis), and many other jurisdictions. In *infrastructure project appraisal*, CBA structures federal evaluation of transportation projects (FHWA, FTA, FAA project-evaluation procedures), water-resources projects (USACE Principles and Guidelines, subsequently Principles and Requirements), and energy projects (FERC environmental impact statements). In *international development*, the World Bank, Inter-American Development Bank, Asian Development Bank, African Development Bank, and bilateral agencies (USAID, DFID, AFD, KfW, JICA) use CBA as a core project-appraisal tool, typically with shadow-pricing corrections for market distortions in developing-country contexts. In *environmental regulation*, CBA is used to evaluate rules under the Clean Air Act, Clean Water Act, Endangered Species Act, and other major environmental statutes — with particular attention to valuation of health benefits (avoided mortality, avoided morbidity), ecosystem services, and climate-related consequences. In *health policy*, cost-effectiveness analysis (a CBA variant expressing results in cost-per-QALY terms rather than net-present-value) is used for drug formulary decisions (UK NICE, Canadian CADTH, U.S. ICER assessments for many health plans, international HTA bodies), public-health intervention prioritization (CDC, WHO), and healthcare-investment decisions (hospital capital-budgeting, medical-technology assessment). In *transportation planning*, CBA is standard for project prioritization, highway-capacity decisions, transit-investment evaluation, and congestion-pricing design. In *energy and climate policy*, CBA (or its social-cost-of-carbon extensions) enters federal climate rules, greenhouse-gas-emissions regulations, and clean-electricity investment decisions. In *food and drug regulation*, FDA has used CBA-informed approaches for some regulatory decisions, though its use in safety-critical contexts is frequently contested. In *education policy*, evaluation of education reforms, early-childhood-intervention programs (Heckman's work on the high returns to early-childhood investment), and higher-education-subsidy policy incorporates cost-benefit reasoning. In *criminal-justice policy*, CBA is used to evaluate sentencing alternatives, incarceration decisions, and criminal-justice-system reforms. Beyond specific applications, CBA has been institutionalized in government analytical practice — the U.S. OMB's Office of Information and Regulatory Affairs (OIRA) reviews CBA analyses for major federal regulations, and most federal agencies maintain significant in-house CBA expertise. International bodies (OECD, IMF, World Bank, UN agencies) have published extensive CBA-methodology guidance.

clarity: CBA offers a clear articulation of the analytical work required to evaluate a policy or project: explicit alternatives, explicit consequences, explicit valuation, explicit time profile, explicit distributional effects, and explicit uncertainty. The framework clarifies *how different considerations should be compared* (by translation to a common monetary metric), *why time horizons matter* (through discounting), *who gains and who loses* (through incidence analysis), and *how sensitive conclusions are to specific assumptions* (through sensitivity analysis). The framework also clarifies *where analytical work is contested* by surfacing the contested valuation choices — the value of statistical life, the social cost of carbon, ecosystem-service values, cultural-heritage values — so that disagreement focuses on specifically where disagreement lies rather than being diffuse. The discipline of explicit articulation is itself a clarification benefit, even when the monetary aggregation is partial or contested — CBA forces "showing your work" in a way that other evaluation frameworks may not. The companion techniques — cost-effectiveness analysis, multi-criteria analysis, distributional analysis — extend the clarification toolkit when pure CBA is inadequate for the specific decision context.

manages_complexity: CBA manages the complexity of policy evaluation by providing a unified analytical framework within which the many dimensions of a policy choice can be systematically considered. Without CBA or similar structured methods, policy evaluation often devolves to ad hoc comparison of salient features, with substantial vulnerability to framing effects, political pressures, and analytical inattention. With CBA, the analytical work decomposes into manageable subtasks: identify alternatives, project each alternative's consequences, value consequences, discount, aggregate, and report. Complex decisions — evaluating a major infrastructure project, a new environmental regulation, a health-technology adoption decision — become analytically tractable through decomposition into these components. CBA also manages the multi-stakeholder complexity of policy deliberation: by expressing results in a common metric, CBA facilitates structured comparison across stakeholders with different interests and values, even though the final decision-making typically incorporates considerations beyond the CBA calculation. Extensions like distributional-weighted CBA (giving explicit weight to distributional-equity considerations), risk-and-uncertainty analysis (handling deep uncertainty about consequences), and ex-post CBA (evaluating actual outcomes against ex-ante projections to improve future analysis) further extend the framework's capability to manage policy-analytic complexity.

abstract_reasoning: CBA embodies a deep analytical commitment: *the claim that systematic consequence-based evaluation with common-metric aggregation is a useful organizing framework for comparing alternatives*. This is a particular instance of consequentialist reasoning — what matters about a policy is its consequences, aggregated across affected parties in a principled way — and inherits both the strengths and the limitations of consequentialism. The analytical discipline imposed by CBA — explicit valuation, explicit discounting, explicit distributional accounting, explicit uncertainty treatment — is valuable even when the specific valuation or aggregation choices are contested. The broader analytical lesson is that *making valuations explicit is typically better than leaving them implicit*: implicit valuations in public decision-making (what is the implicit value of statistical life revealed by a safety regulation's stringency? what is the implicit social cost of carbon revealed by emissions-regulation choices?) are often inconsistent across decisions, inconsistent with stated policy objectives, and resistant to deliberative improvement. CBA makes valuations explicit and thus subject to debate, improvement, and refinement over time. The framework also exemplifies the productive interaction of welfare economics with practical decision-making: formal welfare-theoretic foundations (Kaldor-Hicks compensation, consumer-surplus measurement, Hicksian vs Marshallian valuation) are translated into operational analytical procedures that working analysts can apply. Critics from multiple directions — rights-based ethics (Sen and others on the incompleteness of welfarist aggregation), deliberative democracy (Habermas, Sunstein on the limits of monetization), distributional-justice frameworks (Rawls, capability approach) — have extended and qualified CBA rather than displacing it; contemporary CBA practice increasingly incorporates distributional weighting, sensitivity-analysis against value uncertainty, and complementary methods (multi-criteria analysis, deliberative-polling on key valuation parameters).

knowledge_transfer:
| Domain                             | Manifestation                                                                                |
|------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Regulatory Impact Analysis         | U.S. federal CBA requirements (EO 12866), UK Green Book, EU Better Regulation, Canadian and Australian regulatory-impact analysis.                                          |
| Infrastructure Appraisal           | FHWA/FTA/FAA transportation CBA, USACE water-resources Principles and Requirements, FERC energy project evaluation.                                                          |
| International Development          | World Bank project-appraisal, IDB/ADB/AfDB project evaluation, USAID/DFID/AFD evaluation procedures.                                                                        |
| Environmental Regulation           | EPA Clean Air Act CBA, Clean Water Act CBA, endangered-species-act analysis, social cost of carbon.                                                                          |
| Health Technology Assessment       | NICE (UK), CADTH (Canada), ICER (U.S.), HTA bodies globally — cost-per-QALY analysis and variants.                                                                           |
| Transportation Planning            | Project prioritization, highway-capacity decisions, transit investment evaluation, congestion-pricing design.                                                                |
| Energy & Climate                   | Federal energy-efficiency rules, GHG-emissions regulations, IRA clean-electricity investment evaluation.                                                                    |
| Criminal Justice                   | Sentencing-alternative evaluation, incarceration-policy analysis, criminal-justice-system reforms.                                                                           |
| Education Policy                   | Early-childhood-intervention evaluation (Heckman), education-reform evaluation, higher-education-subsidy analysis.                                                          |
| Corporate Capital Budgeting        | NPV analysis with incorporation of externalities and intangible benefits, environmental-social-governance CBA extensions.                                                     |

prose:
### Catalog cross-references (v1, batches 02–29)

Solution archetypes that reference this prime (per `solution_archetypes/_catalog/catalog_v1_batches_02_29.yaml`):

**As related prime (14):** `diminishing_returns_detection`, `elastic_capacity_scaling`, `elasticity_based_leverage`, `externality_internalization`, `leverage_point_intervention`, `marginal_stop_rule`, `opportunity_cost_surfacing`, `overoptimization_guardrail`, `pareto_focus`, `parsimony_filter`, `payoff_restructuring`, `probabilistic_risk_weighting`, `public_goods_provision`, `safety_margin_design`

notes: The development of CBA in modern form traces through Jules Dupuit's 1844 "On the Measurement of the Utility of Public Works" (an early French formulation of consumer-surplus-based public-works valuation); Marshall's 1890 *Principles of Economics* (consumer-surplus formalization); Pigou's 1920 *The Economics of Welfare* <!-- FACT-D09-001 -->[^pigou-1920] (welfare-measurement framework); the U.S. 1936 Flood Control Act's benefit-cost requirement; the 1950 U.S. Interagency Committee on Water Resources "Green Book" (the first formal federal CBA methodology); Otto Eckstein's 1958 *Water-Resource Development*; the Kaldor-Hicks compensation-criterion foundation (Kaldor 1939 <!-- FACT-D09-002 -->[^kaldor-1939], Hicks 1939 <!-- FACT-D09-006 -->[^hicks-1939]); the Harberger-triangle analysis of deadweight loss (Harberger 1954); U.S. regulatory-CBA institutionalization beginning with Reagan's EO 12291 (1981) and extended through subsequent administrations; Mishan's 1971 *Cost-Benefit Analysis* <!-- FACT-D09-007 -->[^mishan-1971] (systematic CBA textbook); the modern canonical textbook by Boardman-Greenberg-Vining-Weimer 2018 <!-- FACT-D09-008 -->[^boardman-2018]; Stern's 2007 application of CBA to climate policy at societal scale <!-- FACT-D09-004 -->[^stern-2007]; and the ongoing refinement of non-market valuation methods. Arrow's work on learning-by-doing externalities and capital externalities <!-- FACT-D09-009 -->[^arrow-1962] provides CBA-relevant frameworks for valuing external benefits in project appraisal. Arrow et al.'s 1996 work on intergenerational equity and discounting <!-- FACT-D09-010 -->[^arrow-et-al-1996] directly addresses discount-rate methodology for long-horizon CBA. Sen's 2000 critique and defense of CBA <!-- FACT-D09-011 -->[^sen-2000] articulates both the framework's disciplinary power and its limitations relative to capability-approach reasoning. Viscusi-Aldy's 2003 comprehensive treatment of VSL methodology <!-- FACT-D09-003 -->[^viscusi-aldy-2003] provides the canonical modern reference for statistical-life valuation. Adler-Posner 2006 <!-- FACT-D09-012 -->[^adler-posner-2006] provides foundational welfare-theoretic critique and reformulation of CBA. Sunstein 2002 <!-- FACT-D09-013 -->[^sunstein-2002] applies CBA to regulatory-analysis contexts with attention to risk perception and behavioral departures from expected-utility logic. Friedman 1953 <!-- FACT-D09-014 -->[^friedman-1953] on positive economics provides methodological framing for how CBA's empirical apparatus can be separated from its normative commitments. Ongoing critiques: *distributional-justice critiques* (standard CBA weights willingness-to-pay equally across income levels, which implicitly favors wealthier beneficiaries); *rights-based critiques* (Sen on capabilities and the limits of welfarist aggregation); *deliberative-democratic critiques* (Habermas, Sunstein on the limits of consumer-preference valuations for civic decisions); *environmental-ethics critiques* (intrinsic vs instrumental values); *uncertainty-focused critiques* (Weitzman on climate CBA under catastrophic-risk uncertainty); and *behavioral-economics critiques* (preference-reversal problems for stated-preference valuation methods). Despite these critiques, CBA remains a central analytical tool in policy analysis, with contemporary practice generally incorporating supplementary distributional analysis, uncertainty analysis, and acknowledgment of non-monetized considerations rather than relying on a single net-present-value number in isolation.


Counter-Current Exchange

one_liner: Two streams flowing in opposite directions along a shared interface preserve a near-constant driving gradient along the whole contact, lifting extraction efficiency toward unity.

core_idea:
Counter-current exchange is the structural pattern in which two streams flow in *opposite directions* along a shared interface, exchanging some quantity — heat, mass, momentum, information — across that interface, such that the *opposing flow geometry* maintains a near-constant driving gradient along the entire length of contact. The defining feature is a contrast with co-current geometry. When the two streams run in the same direction, they approach equilibrium at the contact line and the driving gradient collapses to zero; the exchange chokes itself off as it proceeds. When they run in opposition, each stream meets a partner with a freshly different state at every position, so a finite gradient persists at every point along the contact. The structural consequence is sharp and quantitative: the *extraction efficiency* asymptotes toward one as contact length grows, where the co-current limit is one-half.<!-- FACT-D60-876 -->[^kays-london-1984] The geometry, not the substrate, sets the achievable regime.

The pattern carries a small set of structural commitments: two streams carrying an exchangeable quantity; a shared interface along which they run parallel but in opposite directions; a local exchange mechanism whose rate depends on the instantaneous difference between the two streams' states; and the geometric consequence that the difference is preserved along the contact axis rather than annihilated at a point. The mathematics is invariant across substrates. Writing the local exchange rate as a linear function of the local difference in stream states, co-current flow drives that difference exponentially toward zero as the streams equilibrate (asymptotic extraction one-half), while counter-current flow holds the difference roughly constant along the axis when flow capacities match (asymptotic extraction approaching unity as contact length grows).<!-- FACT-D60-877 -->[^kays-london-1984] The same differential equation governs heat, mass, momentum, and bidirectional-channel information exchange, which is why the pattern carries a precise signature — asymptotic efficiency, characteristic gradient profile, dependence on flow ratio and contact length — that travels unchanged.

structural_signature:
*two streams carrying an exchangeable quantity* — *a shared interface along which they run parallel but opposed* — *a local exchange rate proportional to the instantaneous between-stream difference* — *the opposing-flow geometry that preserves the gradient along the axis* — *the matched-capacity and contact-length conditions* — *the efficiency invariant (extraction → unity vs. the co-current cap of one-half)*

The pattern is present when each of the following holds:

- **Two streams.** Two flows each carry an exchangeable quantity — heat, mass, momentum, information — and have a definable direction.
- **A shared interface.** The streams run alongside a common boundary across which the quantity transfers.
- **Opposed directions.** The streams flow in opposition along that interface, so each meets a partner of freshly different state at every position.
- **A difference-proportional exchange.** The local transfer rate is a function of the instantaneous difference between the two streams' states.
- **Gradient preservation.** The opposing geometry holds a finite driving difference along the whole contact, rather than letting it collapse to zero at a point as co-current flow does.
- **The capacity and length conditions.** When flow capacities match and contact length grows, the difference stays roughly constant along the axis and the geometric limit is approached.
- **The efficiency invariant.** Extraction efficiency asymptotes toward unity, where the co-current geometry caps at one-half; the geometry, not the substrate or interface material, sets the achievable regime.

The components compose so that "which way do the streams run?" becomes a first-order design question that changes the achievable bound rather than nudging performance within a fixed one. The portable interventions — flip a stream, lengthen contact, match capacities, suppress lateral mixing — recover the gap wherever flow direction is well-defined.

what_it_is_not:
- **Not environmental coupling strength.** `environmental_coupling_strength` measures how tightly a system is tied to its surroundings; counter-current exchange is a *geometric arrangement* of two opposing streams that preserves the driving gradient along the contact, lifting extraction toward unity. Coupling strength sets how strongly the interface transfers per unit gradient; the prime is about how much gradient the geometry leaves available.
- **Not impedance mismatch.** `impedance_mismatch_and_coupling_efficiency` concerns lost transfer at a boundary between mismatched media; counter-current exchange is about flow *direction* setting the achievable efficiency bound, independent of interface material.
- **Not escape and leakage.** `escape_and_leakage` is unwanted loss of a quantity through imperfect containment; counter-current exchange is the *deliberate, efficient transfer* of a quantity across a shared interface via opposing flow.
- **Not phase alignment.** `temporal_synchronization_and_phase_alignment` aligns oscillations in time; counter-current exchange aligns two streams in *opposite spatial directions* along an interface, a geometric not a temporal arrangement.
- **Not an allometric scaling law.** `allometry_and_scaling_law` relates size to function by power laws; counter-current exchange is a flow-geometry efficiency result, not a size-scaling relation.
- **Common misclassification.** Exporting the unity-versus-one-half efficiency invariant to social systems that share *directional opposition* (rotation programmes, counter-flowing trades) without *gradient-preservation geometry*. Catch it by checking whether a literal exchangeable quantity transfers at a rate set by an instantaneous between-stream difference; absent that mechanism, only the loose metaphor travels, not the quantitative signature.

broad_use:
- **Vertebrate physiology**: fish gill water flows opposite to capillary blood, supporting near-complete oxygen extraction where co-current flow would cap near one-half; the kidney's loop of Henle uses counter-current geometry to build the medullary osmotic gradient that concentrates urine.<!-- FACT-D60-878 -->[^schmidt-nielsen-1997]
- **Animal thermoregulation**: arterial-venous counter-current heat exchange in giraffe legs, tuna red muscle, and penguin feet preserves core temperature while permitting peripheral heat dump or cold-blood return.<!-- FACT-D60-879 -->[^schmidt-nielsen-1997]
- **Heat-exchanger engineering**: counter-flow shell-and-tube exchangers achieve higher effectiveness than parallel-flow designs of the same size; the choice is structural, not empirical.<!-- FACT-D60-880 -->[^incropera-etal-2007]
- **Chemical separation**: distillation columns, absorption columns, leaching cascades, and stripping operations exploit counter-current contact between a heavy and a light stream to push separation toward thermodynamic limits.<!-- FACT-D60-881 -->[^treybal-1980]
- **Building HVAC**: heat-recovery ventilators run incoming and outgoing air in opposition across a thin exchanger to recover sensible and latent heat from exhaust.
- **Oceanography**: in stratified estuaries, rivers and saltier ocean water flow in opposite directions, and the geometry sets the mixing efficiency that shapes salinity, nutrient, and sediment profiles.<!-- FACT-D60-882 -->[^geyer-maccready-2014]

clarity: The label distinguishes a *geometric design choice* from the substrate-level mechanism. Naive accounts of "heat exchangers" or "gas exchange" describe surface area and flow rates as if they jointly determined performance, leaving the dominant variable implicit. Counter-current exchange names that variable: the *relative direction* of the two streams. Once a student or designer can name it, the performance gap between co-current and counter-current designs of identical area stops being a surprising empirical fact and becomes an intuitive consequence of whether the gradient is preserved or annihilated. The clarifying separation is between the rate of the local exchange mechanism — how strongly the interface couples per unit gradient — and the geometry that determines how much gradient is available to be coupled. Two designs can share the same coupling rate and the same area and yet differ enormously in effectiveness purely because one collapses its gradient and the other preserves it. Naming the geometry makes that difference visible and predictable rather than mysterious.

manages_complexity: The pattern reduces a complex transport-engineering question to a small set of parameters that travel across substrates: *contact length* (how far the streams run alongside each other), *cross-sectional coupling rate* (heat-transfer coefficient, mass-transfer coefficient, membrane permeability), *residence time and flow ratio* (the relative velocities and capacities of the two streams), and *asymptotic extraction efficiency* (the upper bound the geometry allows). A designer who has internalised the pattern asks four parametric questions rather than re-deriving the transport equations from scratch for each new substrate. The intervention catalogue is correspondingly small and portable: *flip one stream's direction*, *increase contact length*, *match flow capacities*, and *suppress lateral mixing within streams that would short-circuit the gradient*. These four moves recover most of the performance gap whatever the medium. The compression is that a heat-transfer engineer, a separations chemist, and a physiologist studying renal concentration are all manipulating the same four parameters under the same effectiveness relationship; the substrate changes the units but not the structure, so expertise in one transfers as parametric intuition in the others.

abstract_reasoning: The reasoning core is that an exchange process's efficiency is bounded not only by how strongly the interface couples but by how much driving gradient the flow geometry leaves available along the contact. Co-current geometry spends its gradient early and runs the rest of the contact at near-zero difference; counter-current geometry rations the gradient across the whole length, so each increment of contact does comparable work. The prime trains a reasoner to ask, of any exchange across an interface: is this co-current or counter-current? Is the driving difference collapsing at a point or preserved along the axis? Are the flow capacities matched, and is the contact long enough to approach the geometric limit? The structural prediction is universal and substrate-free: any system that *can* be configured for opposing flow along a shared interface unlocks an efficiency regime — extraction toward unity — that co-current geometry cannot reach, and the gap is recoverable by reorientation alone. The deeper move is to treat "which way do the streams run?" as a first-order design question rather than an incidental detail, because it changes the achievable bound rather than merely nudging performance within a fixed bound.

knowledge_transfer: Once recognised, the pattern ports directly across substrates. A biologist who has learned the gill case correctly predicts that the kidney's loop of Henle, the giraffe-leg arterial-venous bundle, and the bluefin-tuna red-muscle exchanger share the same geometric trick; a chemical engineer designing a leaching cascade reuses the effectiveness-NTU formalism a heat-transfer engineer applies to a counter-flow exchanger, because the substrate changes while the geometry does not. The role mappings transfer cleanly — *two streams* ↔ blood and water / hot and cold fluid / vapour and liquid / incoming and outgoing air; *shared interface* ↔ gill lamella / tube wall / column packing / membrane; *driving difference* ↔ oxygen partial-pressure gap / temperature gap / concentration gap; *asymptotic efficiency* ↔ oxygen extraction fraction / exchanger effectiveness / separation factor. The diagnostic move — "is this exchange happening co-current or counter-current?" — is a generic audit that reliably finds underperforming exchanges across substrates, and the four-move intervention catalogue (flip a stream, lengthen contact, match capacities, suppress lateral mixing) recovers most of the gap wherever it applies. The transferred prediction is non-obvious to anyone reasoning only about surface area and coupling strength: a design can be made dramatically more effective without improving the interface material or enlarging it at all, purely by reorienting one stream so the gradient is preserved rather than annihilated. The substrate-independence is sharpest where flow direction is well-defined — physical and biological systems — and the prime is most reliably applied there; loose social analogies (rotation programmes, trade counter-flows) share the directional opposition but not the gradient-preservation geometry that does the work, so the quantitative signature should be confined, in the first instance, to substrates where it genuinely holds.

formal_abstract:
The counter-flow heat exchanger is the prime's cleanest formal instance, because the efficiency invariant can be derived exactly and contrasted term-for-term with the co-current case. The *two streams* are a hot fluid and a cold fluid; the *shared interface* is the wall separating them; the *difference-proportional exchange* is the local heat flux, proportional to the instantaneous temperature difference across the wall. Consider first *co-current* geometry, both streams entering the same end. At the inlet the temperature difference is large, so heat transfers rapidly, but the hot stream cools and the cold stream warms toward each other, so the difference *decays exponentially along the length* toward a common intermediate temperature; the back half of the exchanger runs at near-zero gradient and does almost no work. Even with infinite length and area, neither stream can pass the other's exit temperature, capping the *extraction efficiency at one-half* of the thermodynamic maximum.<!-- FACT-D60-883 -->[^incropera-etal-2007] Now *flip one stream* — counter-current geometry, the streams entering opposite ends. Now the hot fluid's *hottest* point meets the cold fluid's *warmest* exit, and the hot fluid's *coolest* exit meets the cold fluid's *coldest* inlet, so at *every* position along the contact each stream meets a partner of freshly different state and a finite driving difference *persists along the whole axis*. When the flow capacities are matched, that difference becomes nearly constant, every increment of length does comparable work, and the *extraction efficiency asymptotes toward unity* as contact length grows.<!-- FACT-D60-884 -->[^incropera-etal-2007] The same first-order differential equation — local rate proportional to local difference — governs both cases; only the boundary conditions (same-end versus opposite-end) differ, and that single geometric choice moves the achievable bound from one-half to one. The design lesson is sharp: a co-current exchanger can be made dramatically more effective *without enlarging it or improving the wall material at all*, purely by reversing one stream so the gradient is rationed rather than spent early.

**Mapped back:** The heat exchanger instantiates every role of the signature — two streams, a shared wall, a flux proportional to the local temperature difference, opposing-flow geometry that preserves the gradient along the axis, the matched-capacity and contact-length conditions, and the efficiency invariant (unity versus the co-current cap of one-half) — and shows the prime's central claim that flow *direction*, not interface area or material, sets the achievable regime.

applied_industry:
The fish gill and the building heat-recovery ventilator are the same counter-current-exchange object on a biological and an HVAC substrate, and recognising the shared geometry lets prediction and design carry directly between them. In the gill the *two streams* are water flowing over the lamellae and blood flowing through the capillaries beneath them; the *shared interface* is the thin lamellar surface; the *exchangeable quantity* is dissolved oxygen, transferring at a rate set by the local partial-pressure difference. Critically, water and blood flow in *opposition*, so deoxygenated blood entering the lamella meets already-oxygen-depleted water at its exit, while blood about to leave (nearly saturated) meets fresh, oxygen-rich incoming water — a finite oxygen gradient persists along the entire contact, and the fish extracts a large fraction of the water's oxygen, far beyond the one-half ceiling a co-current gill would impose.<!-- FACT-D60-885 -->[^schmidt-nielsen-1997] A biologist who has internalised this correctly predicts that the kidney's loop of Henle, the giraffe-leg arterial-venous bundle, and tuna red-muscle exchangers share the identical geometric trick.<!-- FACT-D60-886 -->[^schmidt-nielsen-1997] In the HVAC case the *two streams* are warm exhaust air leaving a building and cold fresh air entering it; the *shared interface* is a thin counter-flow exchanger core; the *quantity* is sensible (and latent) heat. Running the incoming and outgoing air in opposition recovers a large fraction of the heat that would otherwise be lost with the exhaust, where a parallel-flow core of identical size would recover far less. The engineer's *effectiveness* relationship and the physiologist's *oxygen-extraction fraction* are the same parametric formalism: a chemical engineer designing a distillation column, the gill, and the heat-recovery ventilator all manipulate the same four parameters — contact length, coupling rate, flow ratio, and the asymptotic efficiency the geometry allows. The diagnostic audit — "is this exchange co-current or counter-current?" — reliably finds underperforming exchangers across all of them, and the same four interventions (flip a stream, lengthen contact, match capacities, suppress lateral mixing) recover most of the gap.

**Mapped back:** The gill and the heat-recovery ventilator are the same opposing-flow geometry as the formal heat exchanger — two streams along a shared interface whose counter-current arrangement preserves the driving gradient and lifts extraction toward unity — so expertise in one transfers to the others as parametric intuition over contact length, coupling rate, flow ratio, and the geometric efficiency bound.


Counterfactual Proximity Weighting

one_liner: An internal signal is graded not by the outcome alone but by its distance to a nearby counterfactual outcome of different value, so near misses carry near-reward signals.

core_idea:
Counterfactual proximity weighting is the structural pattern in which the *internal signal* an agent or system assigns to an outcome is not a function of the outcome alone but of the *distance* from that outcome to a *nearby counterfactual outcome of different value*. A near miss carries a near-reward signal even though no reward was delivered; a near-catastrophe carries a near-loss signal even though no harm occurred. The pattern concerns *signal generation*, not interpretation: the internal update — to behaviour, attention, a risk register, an investment posture — is graded by proximity to a counterfactual rather than by the outcome's realised value alone. When the actual outcome was a clean miss but a catastrophe lay close by in the relevant state space, the system updates as if the catastrophe partially happened.

The pattern carries a small set of structural commitments. There is an agent or system generating an internal signal in response to an outcome; a nearby counterfactual outcome of meaningfully different value; a proximity measure in the relevant state space — causal distance, perceptual similarity, temporal nearness; a decreasing function of that distance that weights the counterfactual's value into the signal; and a downstream effect calibrated to the signal rather than to the realised outcome alone. The structure admits a compact model: with `r(o)` the realised value of outcome `o` and `c(o)` the value of the nearest counterfactual at distance `d`, the internal signal is well-fit by `s(o) = α·r(o) + (1 − α)·w(d)·c(o)`, where `w` decreases in distance. The classical assumption `α = 1` — signal depends only on the realised outcome — is the limiting case; the prime is everything to its left. Critically, the signal is *not* irrational when outcomes are noisy: a near miss genuinely carries information about how close to a failure boundary the agent was operating. The pattern becomes maladaptive only when the proximity weight is miscalibrated relative to the true counterfactual probability, which is the substrate-specific question.

structural_signature:
*an agent or system generating an internal signal* — *a realised outcome of some value* — *a nearby counterfactual outcome of meaningfully different value* — *a proximity measure in the relevant state space* — *a distance-decreasing weight folding the counterfactual into the signal* — *a downstream effect calibrated to the signal rather than the realised outcome*

The pattern is present when each of the following holds:

- **A signal-generating agent.** Something produces an internal update — to behaviour, attention, a risk register, an investment posture — in response to an outcome.
- **A realised outcome.** An actual result occurs with its own value `r(o)`; under the classical outcome-only view, only this would matter.
- **A nearby counterfactual.** A different outcome of meaningfully different value `c(o)` — a jackpot just missed, a catastrophe just avoided — lies close by in the relevant state space.
- **A proximity measure.** A distance metric exists in that space: causal-chain branching, perceptual similarity, score margin, temporal nearness.
- **A distance-decreasing weight.** A function `w(d)` that falls with distance folds the counterfactual's value into the signal: `s(o) = α·r(o) + (1 − α)·w(d)·c(o)`, with the outcome-only case recovered at `α = 1`.
- **A signal-calibrated downstream effect.** The behavioural update tracks `s`, not `r` — the system updates as if the nearby counterfactual partially happened.

The components compose so that signal *generation* separates from outcome *interpretation*: a near miss carries genuine information about operating margin when outcomes are noisy, so the weighting is normatively appropriate up to the accuracy of `w(d)`. The pathology is not the response but a single auditable parameter — whether the proximity weight tracks true counterfactual probability or mere perceptual vividness.

what_it_is_not:
- **Not counterfactual reasoning.** `counterfactual_reasoning` is the cognitive operation of considering what would have happened under different conditions; counterfactual proximity weighting is the *signal-generation* mechanism in which an internal update is graded by *distance* to a nearby counterfactual of different value. Reasoning constructs the alternative; proximity weighting weights it into a reward/loss signal.
- **Not anchoring.** `anchoring` is the pull of an initial reference value on a judgement; counterfactual proximity weighting grades a signal by how *near* an alternative outcome was, not by adjustment from a starting anchor.
- **Not attention.** `attention` is the selective allocation of processing; counterfactual proximity weighting is about how an outcome's *internal signal* is computed (weighting a nearby counterfactual), though it may drive attention downstream.
- **Not conformity.** `conformity` is alignment of behaviour to a group; counterfactual proximity weighting is an individual signal-generation pattern keyed to a counterfactual's proximity, with no social reference required.
- **Not regret as such.** Regret and relief are *instances* of the pattern (signals scaling with counterfactual proximity), not the structure itself, which is substrate-general across reward, loss, and engineered systems.
- **Common misclassification.** Reading a response disproportionate to the realised outcome as irrational. Catch it by asking what counterfactual lay nearby and how its value is weighted in; when outcomes are noisy a near miss carries genuine information, so the question is whether the proximity weight tracks true counterfactual probability or mere perceptual vividness.

broad_use:
- **Operant learning and gambling**: the near-miss effect — a slot machine showing "two cherries and a lemon" produces approach behaviour and dopaminergic response resembling a partial win, even though nothing was paid; the graded counterfactual proximity drives re-engagement.<!-- FACT-D60-901 -->[^clark-etal-2009]
- **Decision theory and emotion**: counterfactual regret (how much better could it have gone?) and relief (how much worse?) scale with the proximity of the alternative, not its mere existence; regret-driven choice models formalise the weighting.<!-- FACT-D60-902 -->[^loomes-sugden-1982]
- **Safety engineering**: leading-indicator weighting of near-misses (the Heinrich pyramid, state-safety programmes) enters near-catastrophes into the risk register at a fraction of the catastrophe's cost, proportional to their proximity in the causal chain.<!-- FACT-D60-903 -->[^heinrich-1931]
- **Sports and competition**: almost-victory drives re-engagement more than clear defeat; the near-counterfactual win carries a partial-reward signal that powers subsequent practice and investment.<!-- FACT-D60-904 -->[^cote-etal-2003]
- **Negotiation**: an offer "just barely" rejected anchors the next round more than one wildly off-base; the narrow gap to acceptance functions as a partial-acceptance signal.<!-- FACT-D60-905 -->[^unverified-905]
- **Driving and piloting**: a near-collision recalibrates risk perception disproportionate to the objective hazard density, because the proximity-weighted near-loss signal drives attention recalibration.<!-- FACT-D60-906 -->[^dillon-tinsley-2008]

clarity: The label distinguishes the *generation* of an internal signal from its *interpretation*. The naive lens treats outcomes as binary — won or lost, harmed or unharmed — and reads an agent's subsequent behaviour as a response to that outcome; behaviour that does not match the realised outcome then looks irrational. The proximity-weighted lens reveals an entire layer of pre-outcome signal: how close was the counterfactual? This is what makes near-miss data informative about risk and what makes near-victory motivating about engagement, and it reframes a class of apparently irrational responses as correct responses to a counterfactual-proximity signal the outcome record does not capture. The clarifying force is to separate the realised value of an outcome from the proximity-weighted signal the system actually acts on, and to make the proximity weight itself the auditable object — is it calibrated to the true counterfactual probability, or to perceptual vividness? Once named, the gambler chasing near-misses, the over-corrector driven by regret, and the post-near-miss safety hyper-vigilance are visibly the same mechanism rather than separate quirks.

manages_complexity: The pattern reduces a confused mix of "irrational" behaviours to a single mechanism — the system is responding to a counterfactual-proximity signal the outcome record does not contain — and compresses the intervention space into three families keyed to the direction of the desired change. *To dampen the response*, suppress the salience of the counterfactual neighbour: regulators removing near-miss displays from gaming machines, debriefings that focus on the actual outcome rather than the avoided one, techniques for interrupting regret rumination. *To amplify the response*, surface the counterfactual neighbour: safety programmes that publicise close-call statistics, leadership debriefs that walk through "what could have happened." *To weight it correctly*, ground the proximity weight in an explicit causal model rather than perceptual proximity: fault-tree analysis weights near-misses by failure-mode branching, not by emotional vividness.<!-- FACT-D60-907 -->[^vesely-etal-1981] The compression is that a single parameter — the proximity weight and how it is set — captures near-miss reinforcement, regret and relief, leading-indicator safety weighting, and motivational asymmetry, so an intervention designer reasons about that one lever rather than about a catalogue of unrelated phenomena. The same move (suppress or surface the counterfactual neighbour) reliably shifts the response across substrates.

abstract_reasoning: The prime trains a reasoner to ask, of any update that seems disproportionate to the realised outcome: what counterfactual lay nearby, how close was it, and how is its value being weighted into the internal signal? The compact model `s(o) = α·r(o) + (1 − α)·w(d)·c(o)` makes the reasoning explicit — the behaviour is driven by `s`, not by `r`, and the classical outcome-only view is recovered only at `α = 1`. The non-obvious move the prime licenses is to treat a "near miss" as carrying genuine information rather than as a non-event: when outcomes are noisy, proximity to a failure boundary is real evidence about operating margin, so the proximity-weighted signal is normatively appropriate up to the accuracy of its weight. This reframes the diagnostic question from "is this response rational?" to "is the proximity weight calibrated to the true counterfactual probability, or to perceptual vividness?" — relocating the pathology from the response itself to a single, auditable parameter. The reasoning generalises across reward and loss, across stochastic and non-stochastic counterfactuals, and across agents and engineered systems, because all that the structure requires is an internal signal, a nearby counterfactual of different value, and a distance metric that weights one into the other.

knowledge_transfer: The structure ports across substrates that share nothing else. A gambling regulator who understands the prime predicts that reducing near-miss displays will dampen play, and predicts the same effect across every reward-uncertainty substrate — loot boxes, retention loops, prediction-error-driven engagement systems — because the mechanism, not the surface, is what transfers. A safety officer who understands it extracts one intervention catalogue across aviation, medicine, nuclear, and industrial process safety: surface close-call data, weight it by causal proximity rather than vividness, and audit organisational responses to the graded signal. A negotiator who understands it can both predict and shape the anchoring effect of a narrowly rejected offer on the next round. The role mappings transfer directly — *realised outcome* ↔ no payout / actual loss / non-event / clear defeat; *nearby counterfactual* ↔ the jackpot just missed / the catastrophe just avoided / the win just lost; *proximity measure* ↔ symbol distance / causal-chain branching / score margin / temporal nearness; *internal signal* ↔ dopaminergic response / regret intensity / risk-register weight / motivation. The intervention vocabulary — suppress or surface the counterfactual neighbour, ground the weight in an explicit causal model — is invariant; the only substrate-specific work is identifying the relevant state space and the true counterfactual probability against which the weight should be calibrated. The transferred and non-obvious prediction is that the *same* intervention, suppressing counterfactual salience, reliably reduces the response wherever the structure holds — which is the prime's strongest cross-substrate evidence, since a gaming regulator, a safety officer, and a clinician arrive at the identical lever from unrelated literatures. The complement is equally portable: where the response is too weak, surfacing the counterfactual neighbour amplifies it, and where it is merely miscalibrated, replacing perceptual proximity with a causal model corrects it without abolishing the informative signal.

formal_abstract:
The compact signal model the prime supplies can be worked as a decision-theoretic instance, making every role explicit and the calibration question precise. Let an *agent* face an outcome `o` whose *realised value* is `r(o)` — say a clean loss, `r(o) = 0`. A *nearby counterfactual* outcome of meaningfully different value exists: a large win, `c(o)`, that lay close by in the relevant state space. The *proximity measure* `d` quantifies that closeness — how few state transitions, or how small a margin, separated the realised loss from the counterfactual win. A *distance-decreasing weight* `w(d)`, large when the counterfactual was near and falling toward zero as it recedes, folds the counterfactual's value into the *internal signal*: `s(o) = α·r(o) + (1 − α)·w(d)·c(o)`. The classical outcome-only view is the limiting case `α = 1`, under which the agent updates only on `r(o)` and a clean loss produces no reinforcement. The prime is everything to the *left* of that limit: with `α < 1` and a near counterfactual (`w(d)` large), the signal `s(o)` is substantially positive *even though nothing was won*, and the *downstream effect* — the behavioural update, the propensity to re-engage — tracks `s`, not `r`. The decisive analytical point is that this is *not* irrational when outcomes are noisy: proximity to a high-value boundary is genuine evidence about the agent's operating margin, so weighting `c(o)` into the signal is normatively appropriate *up to the accuracy of `w(d)`*. The pathology is therefore relocated from the response to a single auditable parameter: does `w(d)` track the *true counterfactual probability* (the actual chance the win would have occurred), or merely *perceptual vividness* (how salient the near-win looked)? When `w(d)` is anchored to vividness rather than probability, the same model that explains adaptive risk-sensitivity also explains maladaptive chasing — the difference is one calibration term, not two mechanisms.

**Mapped back:** The signal model instantiates every role of the signature — a signal-generating agent, a realised outcome `r(o)`, a nearby counterfactual `c(o)`, a proximity measure `d`, a distance-decreasing weight `w(d)` folding the counterfactual into `s(o)`, and a downstream effect calibrated to `s` rather than `r` — and shows the prime's central separation of signal generation from outcome interpretation, with the pathology isolated to whether the weight tracks probability or vividness.

applied_industry:
Slot-machine near-miss design and aviation near-miss safety reporting are the same counterfactual-proximity-weighting object on a gambling-behaviour and a safety-engineering substrate, and they run the prime's lever in *opposite* directions, which is itself the strongest cross-substrate evidence. In the gambling case the *agent* is the player; the *realised outcome* is no payout (`r = 0`); the *nearby counterfactual* is the jackpot just missed; the *proximity measure* is symbol distance — "two cherries and a lemon" on the payline; and the *internal signal* is a dopaminergic, approach-driving response resembling a partial win.<!-- FACT-D60-908 -->[^clark-etal-2009] The machine is engineered to *maximise* `w(d)`'s perceptual vividness — displaying near-misses far more often than chance would produce — so the proximity weight is deliberately decoupled from the true (near-zero) counterfactual probability, driving re-engagement.<!-- FACT-D60-909 -->[^harrigan-dixon-2009] The prime's diagnosis names this exactly: the response is not the player's irrationality but a proximity-weighted signal the outcome record does not contain, miscalibrated by design. The intervention follows from the *suppress the counterfactual neighbour* family — regulators removing or limiting near-miss displays reliably dampens play. In the aviation case the *agent* is the safety organisation; the *realised outcome* is a non-event (no crash); the *nearby counterfactual* is the catastrophe just avoided (a runway incursion that came within seconds of collision); the *proximity measure* is causal-chain branching — how few failures separated the non-event from disaster; and the *internal signal* is the weight that incident enters in the risk register.<!-- FACT-D60-910 -->[^reason-1997] Here the desired move is the *opposite* — *surface and amplify* the counterfactual neighbour by publicising close-call data — and *weight it correctly* by grounding `w(d)` in fault-tree causal proximity rather than how frightening the event felt.<!-- FACT-D60-911 -->[^vesely-etal-1981] A gambling regulator and a safety officer, arriving from unrelated literatures, reach the *identical lever* — manipulate the salience and calibration of the counterfactual neighbour — which is the prime's clearest demonstration that the mechanism, not the surface, is what transfers.<!-- FACT-D60-912 -->[^dillon-tinsley-2008]

**Mapped back:** Near-miss slot design and aviation near-miss reporting are the same proximity-weighting mechanism as the formal model — an internal signal graded by distance to a nearby counterfactual of different value — run in opposite directions: gambling miscalibrates `w(d)` toward vividness to amplify engagement, while safety engineering re-grounds `w(d)` in causal probability to amplify a genuinely informative signal, both acting on the prime's single auditable parameter.


Counterfactual Reasoning

one_liner: Hypothetical alternatives.

origin_domain: psychology

aliases:
what-if reasoning
mental simulation
counterfactual thinking
alternative scenario cognition

core_idea: Counterfactual reasoning is the COGNITIVE PROCESS by which a reasoner mentally simulates one or more alternative states-of-affairs contrary to the actual situation, holds that simulation as a variant scenario, performs a mental-comparison operation between the actual situation and the counterfactual variant, and uses the output of that comparison to guide judgments about causation, blame, regret, learning, and decision-making. The process comprises four essential components: (1) *the actual situation S* as the baseline reference state, the state that actually obtained or was actually observed; (2) *the counterfactual variant S'* generated by mental simulation — a mentally constructed alternative past or future created by altering one or more antecedent conditions in S while holding other factors mentally fixed; (3) *the mental-comparison operation* between S and S' that highlights what would have been different, what consequences would have followed, and how far S diverges from S'; (4) *the cognitive/affective/judgmental output* — the regret, blame attribution, causal inference, learning signal, or decision adjustment that flows from the comparison. This is fundamentally a process of mental simulation and imagination constrained by background knowledge of regularities, laws, and typical causal pathways; it is distinct from the metaphysical or semantic analysis of counterfactual conditionals (see `counterfactuals.md`, which treats the logical structure of "if A had been true, then B would have been true" as a truth-conditional claim). The cognitive process is empirically tractable — Kahneman and Tversky (1981) documented that mental simulation distance, norm violations, and ease of imagining alternatives predict regret intensity and learning effectiveness. The process operates across regret psychology (ruminating on roads not taken), blame and responsibility attribution (considering alternative actions the agent could have taken), educational learning (productive failure and deliberate reflection on counterfactual solution paths), medical decision-making (mental simulation of alternative treatment scenarios), legal reasoning (but-for counterfactuals grounded in cognitive narrative construction), and AI/ML fairness (generating minimal counterfactual input perturbations that flip model decisions). <!-- FACT-D20-031 -->[^kahneman-tversky-1981]

structural_signature:
A reasoning pattern qualifies as counterfactual reasoning when each of the following italicized six structural roles holds:

- *The actual-situation reference* — The reasoner anchors on an actual state of affairs S (past outcome, present decision, observed behavior, or current decision point) taken as the baseline fact from which the counterfactual is constructed.
- *The counterfactual variant generation* — The reasoner mentally constructs an alternative scenario S' by modifying one or more antecedent conditions in S — changing what the agent did, what external circumstances were, or what decisions were made — while leaving the background regularities and other contextual factors mentally fixed (the "ceteris paribus" or "all else equal" constraint).
- *The mental-comparison operation* — The reasoner performs an imaginative comparison between S and S', tracing the divergent consequences, noting what would have been different, and extracting the implications for causation (would altering X have changed Y?), blame (could the agent have prevented the outcome by acting differently?), regret (how much worse/better was the actual outcome relative to the counterfactual?), or learning (what does this comparison teach about how the world works?).
- *The upward-vs-downward direction* — Counterfactual simulations can be upward-directed (simulating a better, more favorable S') or downward-directed (simulating a worse, less favorable S'); upward counterfactuals typically trigger regret and self-focused motivation ("I could have done better"), while downward counterfactuals trigger relief and comparison-focused reflection ("it could have been worse").
- *The regret-blame attribution output* — The comparison yields affective (regret, relief, sympathy, anger) and attributional (blame, responsibility, credit, luck) judgments that depend on whether the actual outcome could have been avoided by the agent's alternative action, whether norms were violated, and how easy it is to imagine the alternative scenario.
- *The causal-inference and learning signal* — The counterfactual comparison supports causal inference (identifying which antecedent changes would have altered the outcome), learning signals (encoding lessons about action-consequence contingencies), and decision adjustment (revising future choices based on mental simulation of past counterfactuals or anticipated future counterfactuals).

what_it_is_not:
- **Not the metaphysical/semantic analysis of counterfactual conditionals.** The prime `counterfactuals.md` treats counterfactual conditionals as truth-conditional claims ("if A had been true, C would have been true") analyzed via possible-worlds semantics, nearest-world similarity metrics, or structural causal models. This prime focuses on the COGNITIVE PROCESS of mental simulation, not the metaphysics of truth-conditions or the formal semantics of counterfactual propositions. The two primes are distinct and complementary: one is about the logical structure and truth-value of counterfactual claims; this one is about how reasoners actually mentally generate, compare, and use simulated alternatives.

- **Not all hypothetical reasoning.** Hypothetical reasoning includes forward-looking conditional planning ("if it rains tomorrow, I will bring an umbrella"), probabilistic reasoning about uncertain futures ("if the stock market crashes, my portfolio will decline"), and open-ended possibility exploration ("what if we tried a different business model?"). Counterfactual reasoning specifically involves simulation of CONTRARY-TO-FACT alternatives (what did not happen or would not happen) used for regret, blame, or causal inference about the actual situation — not open-ended hypotheticals about the future.

- **Not future planning alone.** Planning involves simulating future scenarios to guide present action ("if I start studying now, I will pass the exam; therefore I will study"). Counterfactual reasoning is past-oriented or retrospective, focusing on mental simulation of alternatives to what actually happened ("if I had studied, I would have passed"; "I didn't study, and I failed") to support attributions of responsibility and regret. Though the two processes share simulation machinery, their function and temporal direction differ.

- **Not the simulation heuristic alone.** Kahneman-Tversky's simulation heuristic (1981) is a specific SUBSET of counterfactual reasoning in which reasoners assess the ease or availability of mentally simulating a scenario to judge its likelihood or emotional intensity. Counterfactual reasoning is broader: it includes all mental-simulation-based cognition serving regret, blame, causal inference, and learning, not only those judgments based on simulation ease.

- **Not regret alone.** Regret is one output of counterfactual reasoning — the affective-evaluative result of comparing an actual outcome unfavorably to a counterfactual alternative. But counterfactual reasoning also produces blame attribution (is the agent causally responsible for the bad outcome?), learning signals (what does this comparison teach about action-consequence links?), and causal inference (would changing X have changed Y?), which extend beyond the emotional experience of regret.

- **Not blame attribution alone.** Blame is another output of counterfactual reasoning — attributing responsibility to an agent for failing to act in a way that would have prevented an unfavorable outcome. But counterfactual reasoning also supports causal judgment (X caused Y), learning (understanding which actions lead to which consequences), and emotional responses (regret, relief, sympathy) that do not reduce to blame.

broad_use:
- **Psychology of regret and loss aversion.** Kahneman-Tversky (1981) and Roese (1994)<!-- FACT-D20-032 -->[^roese-1994] documented that regret intensity depends on counterfactual simulation distance and norm violations; near counterfactuals (missing a flight by 5 minutes) produce stronger regret than far counterfactuals (missing by 30 minutes) because the alternative is easier to imagine. This pattern predicts emotional and behavioral responses to negative outcomes across contexts (consumer purchases, relationship decisions, career changes). Roese-Olson (1995) Functions of Counterfactual Thinking framework identified adaptive and maladaptive patterns: upward counterfactuals can drive self-improvement or rumination; downward counterfactuals can stabilize affect or induce complacency.

- **Blame attribution and moral responsibility.** Legal reasoning (but-for causation: "but for the defendant's action, harm would not have occurred") relies on mental simulation of counterfactual scenarios — would the victim have been harmed if the agent had acted differently? Psychological research (Miller-McFarland 1986, Markman-McMullen 2003)<!-- FACT-D20-033 -->[^markman-mcmullen-2003] shows that attributions of blame and responsibility depend on how easy it is to imagine the agent acting otherwise and on whether the agent violated a norm. Counterfactual reasoning grounds causal attributions in cognitive simulation, making legal and moral responsibility cognitively tractable and empirically testable.

- **Educational learning and productive failure.** Kapur's (2008)<!-- FACT-D20-034 -->[^kapur-2008] productive failure paradigm demonstrates that learners who struggle with a problem, generate their own failed solution strategies, and then receive instruction in the correct approach learn more deeply than those who receive direct instruction. The mechanism involves mental simulation: students imagine counterfactual solution paths ("what if I had tried this approach?"), compare them to the correct solution, and extract conceptual lessons about why alternatives failed. Counterfactual reasoning is the cognitive engine of learning from mistakes and deliberate reflection.

- **Medical decision-making and regret.** Patients and clinicians mentally simulate alternative treatment pathways to evaluate decisions and understand outcomes. A patient given treatment A might experience regret by imagining the counterfactual: "what if I had chosen treatment B?" This mental simulation depends on the availability of the counterfactual (how easy is it to imagine?) and on whether the outcome was norm-violating or surprising.<!-- FACT-D20-035 -->[^kahneman-miller-1986] Understanding counterfactual-reasoning psychology informs shared decision-making, managing patient regret, and post-treatment adjustment.

- **Legal reasoning and causal responsibility.** Beyond blame, counterfactual reasoning supports causal inferences in legal contexts (proximate cause, foreseeability, alternative causation). Courts and juries mentally simulate whether an omitted action or prevented harm would have altered the outcome, treating counterfactual reasoning as a tool for establishing causal dependence grounded in cognitive simulation<!-- FACT-D20-036 -->[^miller-mcfarland-1986] rather than metaphysical truth-conditions.

- **Economics of post-decision regret and choice.** Regret theory in economics (Bell 1985, Loomes-Sugden 1982)<!-- FACT-D20-037 -->[^loomes-sugden-1982] models choice behavior as minimizing anticipated regret by simulating counterfactual outcomes of alternatives. Consumer behavior, risky choice, and brand switching all show regret-driven patterns: people anticipate regret about paths not taken and adjust choices to minimize it.

- **Historical-counterfactual cognition and narrative understanding.** Historians and readers of history engage counterfactual reasoning to understand causal chains and contingency. Mental simulation of alternative histories ("what if Napoleon had won at Waterloo?")<!-- FACT-D20-038 -->[^byrne-2005] supports understanding of actual historical causation — by imagining what would have been different, we isolate the causal importance of actual events. This reasoning is constrained by historical knowledge of regularities, background conditions, and plausibility (see `counterfactuals.md` for metaphysical debates about tractability).

- **AI/ML fairness audits and counterfactual explanations.** Wachter-Mittelstadt-Russell (2018)<!-- FACT-D20-039 -->[^wachter-mittelstadt-russell-2018] and related work in algorithmic fairness generate counterfactual explanations for opaque model decisions: "your loan was denied; if your income had been $5K higher, it would have been approved." This generates the minimal perturbation to the input that flips the decision, providing recourse, interpretability, and fairness audits. The cognitive process of generating and evaluating such counterfactuals mirrors human counterfactual reasoning and has become a standard tool in ML interpretability and regulatory compliance (GDPR, fairness-impact assessments).

clarity: Counterfactual reasoning clarifies by forcing articulation of which antecedent factors could have been changed, what the outcome would have been under that change, and whether the agent could have acted differently. A statement like "I should have studied harder" resolves into: **actual state S** (studied moderately, failed); **counterfactual variant S'** (studied harder — how much? in which subjects? with what support?); **comparison** (would have passed in S'); **responsibility** (the agent could have studied harder, studying is under the agent's control, so the failure is attributable to the agent). Clarifying force: exposes what is actually being claimed (that studying more would have changed the outcome), what evidence would support it (correlations between study effort and exam performance in prior contexts), and what remains uncertain (did the agent have sufficient motivation or knowledge of what to study?). Distinguishing actual from counterfactual, and comparing them explicitly, prevents conflation of luck (what the agent could not have controlled) with responsibility (what the agent could have controlled).

manages_complexity:
- **Isolates causal pathways via mental simulation.** Counterfactual reasoning reduces high-dimensional outcome spaces (all the factors that might have contributed to an outcome) to a manageable sequence of focused questions: would changing X have changed Y? The comparison between S and S' highlights which factors made a difference, collapsing combinatorial complexity into a causal narrative.

- **Frames learning from mistakes.** Productive failure and deliberate reflection use counterfactual reasoning to extract lessons: students imagine where they went wrong ("if I had considered this alternative approach") and extract principles about problem-solving. This turns experience (a failed attempt) into learning signal (a principle about what works) via counterfactual comparison.

- **Supports decision adjustment.** By simulating alternative decisions and their counterfactual outcomes, a reasoner can adjust future choices without re-experiencing all alternatives: "I chose X, experienced outcome O₁, but if I had chosen Y, I would have experienced O₂ (worse); therefore I will stick with X for future similar decisions." This compresses experience-driven learning into a compact causal rule.

- **Structures legal and ethical reasoning.** In responsibility attribution and blame, counterfactual reasoning isolates what an agent could have done differently and whether doing so would have prevented harm. This discipline clarifies whether responsibility attaches to the agent (could have acted otherwise) or to circumstance (agent could not have acted otherwise).

abstract_reasoning:
Counterfactual reasoning trains a reasoner to ask:

- What is the actual state S (the actual outcome, decision, or circumstance)?
- What counterfactual variant S' is most diagnostic or most relevant to the question at hand?
- What antecedent conditions differ between S and S'?
- Would changing those antecedents have changed the outcome, and by how much?
- How easy is it to mentally simulate S'? (Simulation ease predicts emotional intensity and belief in causal dependence.)
- Was the actual outcome norm-violating or exceptional, making the counterfactual more salient?
- What causal lessons does the S-vs-S' comparison teach about how the world works?
- What decision adjustments follow from this counterfactual reasoning?

These questions abstract across psychology, education, law, medicine, and AI, revealing the common cognitive work that counterfactual reasoning performs across domains.

knowledge_transfer:
| Role in Regret Psychology | Role in Medical Decision-Making | Role in ML Fairness Audits |
|---|---|---|
| Actual situation S (outcome achieved) | Actual treatment chosen and outcome experienced | Actual loan decision (denied) and actual applicant input |
| Counterfactual variant S' (alternative outcome imagined) | Alternative treatment simulated and hypothetical outcome | Minimal counterfactual input (income $5K higher) and hypothetical approval |
| Simulation distance / ease | Norm violation, surprise, recency | Input perturbation magnitude, realism, actionability |
| Emotional output | Regret, relief, disappointment, satisfaction | Not applicable in technical context; regret expressed by denied applicant |
| Causal inference | "Career choice caused my regret because I could have chosen differently" | "Income caused the decision because modifying it would flip the approval" |
| Learning signal | Adjust future choices to avoid regret scenarios | Inform applicant of the causal factor in the decision; support fairness audit |
| Blame / responsibility | Blame self for not choosing the better path | Responsibility assignment (is the factor a legitimate proxy or unfair discrimination?) |

A psychologist studying regret, a physician navigating shared decision-making with a patient, and a fairness auditor explaining a denied loan are all performing the same structural work: constructing counterfactual scenarios S', comparing to S, extracting causal and affective implications, and using the comparison to guide subsequent judgment or action. The same diagnostic applies: what is S, what is S', how do they differ, what does the difference teach? The difference in context (emotion vs. decision vs. algorithm) shapes the output but not the underlying cognitive machinery.

prose:
_(deferred to Pass B)_

### Catalog cross-references (v1, batches 02–29)

Solution archetypes that reference this prime (per `solution_archetypes/_catalog/catalog_v1_batches_02_29.yaml`):

**As related prime (2):** `hidden_path_discovery`, `opportunity_cost_surfacing`

notes: Second-pass densification (DP-20) targeting cognitive-process variant of counterfactual reasoning, distinguished from `counterfactuals.md` (metaphysical-semantic analysis, DP-19 G2). This prime treats the COGNITIVE PROCESS: how reasoners mentally simulate alternatives, the regret-and-blame psychology, the educational and clinical use of counterfactual thinking. Core contributions of this density pass: (1) explicit four-component structure (actual situation, counterfactual variant, mental-comparison operation, cognitive/affective output); (2) six italicized role-phrases (the actual-situation reference, the counterfactual variant generation, the mental-comparison operation, the upward-vs-downward direction, the regret-blame attribution output, the causal-inference and learning signal); (3) clear demarcation from `counterfactuals.md` (this is process, not metaphysics); (4) densified Clarity, Manages Complexity, Abstract Reasoning, Knowledge Transfer sections with domain-specific examples (psychology, medicine, ML fairness); (5) dual-example structure (Kahneman-Tversky simulation heuristic and Roese upward-downward formally; Wachter-Mittelstadt-Russell counterfactual explanations in ML fairness applied); (6) six full Tensions addressing upward-vs-downward divergence, adaptive vs ruminative loops, process-vs-metaphysics divide, cultural variation, causal-inference integration, and productive-failure pedagogical tensions. All fifteen FACT-D20 IDs (031–045) embedded inline and in reference footnotes, with dual-placement verification and distribution across ≥4 prose sections (Core Idea, Broad Use, Examples, Tensions, References). Line count: 624 lines. Status: draft; pending Pass B for solution archetypes and full verification.