Other-Regarding Preferences

one_liner: An agent's evaluation of outcomes depends not only on its own payoff but on the payoffs of other agents.

review_flags: DEDUP 2026-06-12T00:04:28Z: MERGE_OR_REPARENT vs preference (score 0.986, conf medium). Candidate may be the more-general parent of the existing prime; KEEP as first-class, Phase C to decide parent/child direction. Dossier: workspace/phase_b_outputs/dedup/verdicts/other_regarding_preferences.md

core_idea:
Other-regarding preferences is the structural commitment that an agent's evaluation of outcomes is indexed not only on the agent's own payoff but on the payoffs received by one or more other agents. The agent's preference function takes as input the joint outcome vector — what I get and what they get — and returns an ordering that systematically responds to both arguments, not only to the self-referential one. The dependence can run in any of several signed directions: *positive* (I prefer outcomes that benefit them — altruism, kin-directed sacrifice), *negative* (I prefer outcomes that harm them — spite, envy), *reference-comparative* (I prefer outcomes close to a fair allocation — inequity aversion), or *reciprocity-conditioned* (I prefer outcomes that reward those who cooperated and punish those who defected). The structural fact is not that any particular signed dependence holds across all agents, but that the preference function is generically not a function of own-outcome alone.

Once this commitment is named, the canonical own-payoff-maximising agent becomes the special case — the case where the cross-arguments have zero weight — and the empirical distribution of agents across substrates is not concentrated at that point. What other-regarding preferences is *not* is a specific preference content: it is not the claim that people are nice, that they care about fairness, or that they reciprocate. It is the structural meta-commitment that the preference function has cross-arguments at all, leaving open what sign and shape those arguments take in any given substrate or population. Formally it is the move from a utility function $u_i(x_i)$ of own-outcome alone to a function $u_i(x_i, x_{-i})$ of both own-outcome and others' outcomes, with the structure of the dependence — which agents enter, with what signs, under what conditions — as the empirical object of interest.

structural_signature:
*the evaluating agent* — *the joint outcome vector (own and others')* — *the preference function over that vector* — *the cross-arguments (others' outcomes as inputs)* — *the signed, conditional dependence on them* — *the own-payoff-only special case as a measure-zero point*

A setting has other-regarding preferences when each of the following holds:

- **An evaluating agent.** There is an agent with a preference ordering over outcomes — the focal agent whose evaluation is under analysis.
- **A joint outcome vector.** Outcomes are distributed across multiple recipients, so each state of the world specifies what the focal agent gets *and* what one or more other agents get.
- **A preference function over the joint vector.** The agent's evaluation is a function $u_i(x_i, x_{-i})$ taking the whole outcome vector as input, not $u_i(x_i)$ taking own-outcome alone.
- **Cross-arguments.** Others' outcomes genuinely enter the function: the ordering systematically responds to $x_{-i}$ and not only to $x_i$. This is the load-bearing meta-commitment — that the function *has* cross-arguments at all.
- **Signed, conditional dependence.** The dependence carries a sign and possibly a condition — positive (altruism), negative (spite, envy), reference-comparative (inequity aversion), or reciprocity-conditioned — and which agents enter, with what weights, under what conditions, is the empirical object, left open by the structure.
- **The own-payoff-only special case.** The canonical self-interested agent is recovered exactly when all cross-argument weights are zero — one measure-zero point in a preference-function space, not a privileged default.

The signature is structural, not psychological: it commits only to the form $u_i(x_i, x_{-i})$ with nonzero cross-arguments, leaving the sign, shape, and population distribution of those weights as parameters to be estimated per substrate.

what_it_is_not:
- **Not a sub-instance of `preference` that adds nothing.** Preference is the umbrella ordering relation over outcomes; other-regarding preferences is the specific content commitment that the ordering depends on *others'* outcomes — a function $u_i(x_i, x_{-i})$, not $u_i(x_i)$. It specialises preference rather than restating it.
- **Not `cooperation`.** Cooperation is a *behavioural* pattern that can arise without other-regarding preferences (repeated-game folk theorem, pure self-interest under the shadow of the future) and that other-regarding preferences can fail to produce (envious or spiteful agents defect).<!-- FACT-D68-151 -->[^fudenberg-maskin-1986]
- **Not `reciprocity`.** Reciprocity is *one signed, intention-contingent form* of other-regarding preference; this prime is the broader meta-commitment that the function has cross-arguments at all, of any sign.
- **Not `fairness`.** Fairness is one possible *content* (a positive weight toward equal allocations); other-regarding preferences also covers spite, envy, and norm-enforcement, which are equally other-regarding but not fair.
- **Not a `social_dilemma`.** A social dilemma is a *strategic structure* defined by the payoff matrix; this prime is about the *preference structure* over outcomes, which can be present or absent independent of the game's payoffs.
- **Common misclassification.** Reading "other-regarding" as "altruistic" and treating the prime as a niceness claim. An agent who pays to harm a rival has fully other-regarding preferences; the meta-commitment is to nonzero cross-arguments of *any* sign, not to a positive weight.

broad_use: The cross-argument structure recurs across substrates because the commitment is mathematical rather than substantively psychological. In **behavioural game theory**, its canonical home, dictator-game donations to anonymous recipients, ultimatum-game rejections of unfair offers, trust-game investments, public-goods contributions, and third-party costly punishment each surface a specific signed dependence and estimate its parameters, because the own-payoff-only special case fails systematically and predictively.<!-- FACT-D68-152 -->[^camerer-2003] In **evolutionary biology**, kin selection values relatives' reproductive success at a coefficient given by relatedness, reciprocal altruism and eusocial cooperation instantiate the same structure with fitness as the preference function and a related or grouped agent as the "other," and the cross-argument weights are biological parameters with empirical values.<!-- FACT-D68-153 -->[^hamilton-1964] In **welfare economics and social choice**, any social welfare function built from agent preferences must specify whether and how agents' orderings depend on others' outcomes, and the choice changes the aggregate and the policy recommendations. The pattern recurs in **mechanism design** (allowing other-regarding components changes truth-revelation properties, optimal bid functions, and welfare bounds), in **political philosophy** (any theory evaluating distributions across persons presupposes preferences over distributions, with the veil of ignorance a procedural way of eliciting other-regarding components<!-- FACT-D68-154 -->[^rawls-1971]), in **cooperative AI and multi-agent systems** (utility functions with non-self-only arguments to support cooperation), in **organisational behaviour** (peer-comparison effects on pay satisfaction), and in **charitable giving** (anonymous versus identified giving, warm-glow versus purely altruistic motivation). The fit holds anywhere agents are modelled with preferences and outcomes are distributed across multiple recipients.

clarity:
Other-regarding preferences clarifies by separating the question of self-interest from the question of preference content. Standard rational-choice modelling tends to conflate the two by assuming own-payoff maximisation is the default and "departures" are anomalies. Once other-regarding preferences is named as a structural option, the own-payoff-only agent is recognised as one specific point in a preference-function space, not as the natural starting point — and the empirical question becomes which point in that space a given agent or population occupies, rather than whether they have "departed" from a privileged baseline.

The clarifying force extends to a recurring source of confusion in interpreting prosocial behaviour. The same observed act — giving money to a stranger — can come from positive other-regarding preferences (I value their welfare), reciprocity-conditioned preferences (I expect they would do the same), reputation effects (I value being seen as generous), or warm-glow effects (I value the act of giving regardless of recipient outcome). Naming the underlying parameter space lets the analyst design experiments that distinguish the signed components rather than treating all prosocial behaviour as a single category. The prime also distinguishes itself carefully from neighbours. It is a content commitment about *preference*, not an alternative to it: preference is the umbrella ordering relation, and other-regarding preferences names a sub-case specifying what enters the preference function. It is distinct from *cooperation*, which is a behavioural pattern that can occur without other-regarding preferences (the folk theorem) and that other-regarding preferences can fail to produce (envious agents). It is distinct from *reciprocity* (one signed, intention-contingent form), from *fairness* (one possible content), and from a *social dilemma* (a strategic structure defined by the payoff matrix, not the preference structure). Holding these apart keeps the prime from being mistaken for niceness, for cooperation, or for any single one of its signed instances.

manages_complexity:
The prime compresses a sprawling literature of named "anomalies" — ultimatum rejections, dictator giving, public-goods contributions, third-party punishment, trust-game investments, inequity aversion, guilt aversion, intention-contingent reciprocity, identifiable-victim effects, in-group bias in helping — into a small parameter space: which other agents enter the preference function, with what signs, and under what conditions. Competing formal models each propose a specific functional form for the cross-argument weights — inequity-aversion models use two parameters for the disutility of advantageous and disadvantageous inequality, others use three, others a different two — and each can be evaluated against the same paradigm suite.<!-- FACT-D68-155 -->[^fehr-schmidt-1999] A catalogue of disconnected behavioural findings becomes a single function with a few free parameters whose values the experiments estimate.

The compression is operational because it organises the intervention catalogue as well as the explanatory one. Mechanism designers who want to elicit cooperative behaviour can target the cross-argument weights directly: framing manipulations that activate in-group membership shift in-group/out-group weights, anonymity manipulations reduce reputation-channel weights, and partner-versus-stranger matching shifts reciprocity-conditioned weights. Each intervention is recognisable as a move on a specific parameter of the prime rather than as an ad-hoc behavioural nudge. And because aggregate outcomes depend on the *distribution* of cross-argument weights across a population rather than on the modal type, the prime directs attention to sorting and matching mechanisms: a modest fraction of conditional cooperators can sustain cooperation if matched with similar types.<!-- FACT-D68-156 -->[^fischbacher-etal-2001] By naming the parameter space, the prime turns the open-ended problem of "why do people behave prosocially" into a bounded reasoning over a small set of weights and their population distribution.

abstract_reasoning:
Other-regarding preferences trains a reasoner to interrogate any multi-agent setting through the structure of the preference function. The reasoner asks: whose outcomes enter the focal agent's evaluation, with what weight, and under what conditions? Because this question references only the abstract roles — preference function, joint outcome vector, cross-arguments, signed dependence — it applies to a laboratory game, an evolving population, a welfare aggregation, or a multi-agent learning system without translation, and the kin-selection coefficient in biology and an altruism parameter in a behavioural model are recognised as structurally the same object, a weight on another agent's outcome in the focal agent's evaluation, with the substrate setting only the empirical value.

Several reusable moves follow. The parameter-identification move designs paradigms that isolate specific cross-argument components — a dictator game isolating the purely altruistic component, an ultimatum game isolating responder inequity aversion, a trust game isolating positive reciprocity expectations, third-party punishment isolating norm enforcement without own-victim status. The aggregate-prediction move treats population behaviour as a function of the distribution of cross-argument weights, so the reasoner predicts from the distribution rather than the modal type, making sorting and matching mechanisms load-bearing. The mechanism-redesign move recognises that optimal mechanisms under own-payoff agents differ systematically from those under inequity-averse or reciprocity-conditioned agents, so ignoring the cross-arguments produces predictable implementation failures. And the welfare-construction move recognises that a social welfare function can be built either by aggregating orderings over distributions or by aggregating own-payoff augmented by other-regarding terms, a choice with substantive consequences for what counts as a Pareto improvement. The same reasoning that lets an experimental economist estimate an inequity-aversion parameter lets an evolutionary biologist read a kin-selection coefficient, because both are reasoning about a weight on another agent's outcome.

knowledge_transfer:
The transferable content of the prime is that the underlying object is mathematical — a function $u_i(x_i, x_{-i})$ depending on both own-outcome and others' outcomes — so it travels cleanly across substrates that use different names for it. Experimentalists in behavioural economics, theorists in evolutionary biology, policy analysts in welfare economics, and engineers in multi-agent AI are all working with the same object, and the transferable diagnostic is identical: whose outcomes enter, with what weight, and under what conditions? Once the cross-argument structure is identified for a substrate, the existing toolkit of game-theoretic equilibrium analysis, evolutionary stability, mechanism-design implementation, and welfare aggregation applies, with the substrate-specific cross-argument weights as the new free parameters.

The transfer is deep because the design move — target the cross-argument weights, not just the own-payoff term — ports across substrates that share the structure. The dictator game makes this concrete: a proposer given an endowment unilaterally decides how much to transfer to an anonymous recipient with no power to accept, retaliate, or reciprocate, and the own-payoff-only prediction is zero<!-- FACT-D68-157 -->[^forsythe-etal-1994], while the empirical modal transfer is roughly 20–30% of the endowment.<!-- FACT-D68-158 -->[^engel-2011] Which cross-argument structure is posited determines the interpretation — positive altruistic weight predicts transfers scaling with perceived benefit, inequity aversion predicts clustering at the equal-split point, norm-following predicts insensitivity to recipient identity — and variant experiments distinguish these by manipulating the relevant parameter: transfers fall when anonymity to the experimenter is increased (implicating reputation weights), rise when the recipient is identifiable or needy (implicating recipient-specific altruistic weights), or cluster at equal split independent of recipient features (implicating norm-following). The same structural pattern recurs in eusocial-insect colonies where workers forgo reproduction for colony fitness (the cross-argument weight biologically anchored by relatedness), in workplaces where coworkers' wages enter individual job satisfaction (an inequity-aversion signature), and in multi-agent reinforcement learning where the cross-argument weight in the reward shapes whether agents converge to cooperative or competitive equilibria. Because the design move — manipulate framing, anonymity, identifiability, partner matching, or social information to shift specific cross-argument weights — is substrate-neutral, a practitioner who has elicited cooperation in one substrate can target the same parameters in another on first contact, and the strip-the-jargon form ("the preference function depends on what others get, not only on what I get") does load-bearing work across experimental economics, evolutionary biology, mechanism design, welfare economics, multi-agent AI, and charitable-giving research.

formal_abstract:
The ultimatum game with an inequity-aversion utility function is the pattern in its most explicit formal dress. The *evaluating agent* is the responder; the *joint outcome vector* is the pair $(x_i, x_j)$ — the responder's share and the proposer's share of a fixed pie. The own-payoff-only model writes the responder's utility as $u_i(x_i) = x_i$ and predicts acceptance of any positive offer, because any money beats none. The empirical fact — responders routinely reject offers below roughly 20–30% of the pie, choosing zero over a small but unfair amount — falsifies that model and forces a *cross-argument*.<!-- FACT-D68-159 -->[^guth-etal-1982] The Fehr-Schmidt inequity-aversion form makes the dependence precise: $u_i(x_i, x_j) = x_i - \alpha \max(x_j - x_i, 0) - \beta \max(x_i - x_j, 0)$, where $\alpha$ weights disadvantageous inequality (the disutility of getting less than the other) and $\beta$ weights advantageous inequality.<!-- FACT-D68-160 -->[^fehr-schmidt-1999] This is the *signed, conditional dependence* made parametric: the responder's evaluation systematically responds to $x_j$, with a kink at the equal split. The *own-payoff-only special case* is recovered exactly at $\alpha = \beta = 0$ — one point in the parameter space, not the default.<!-- FACT-D68-161 -->[^fehr-schmidt-1999] The model's predictive content is sharp and testable: a responder with $\alpha$ large enough rejects any sufficiently unfair offer because the inequality disutility exceeds the monetary gain, which locates the rejection threshold as a function of $\alpha$ and lets the parameter be estimated from the observed minimum acceptable offer.

**Mapped back:** The responder is the evaluating agent, $(x_i, x_j)$ is the joint outcome vector, the Fehr-Schmidt function is the preference function with explicit cross-arguments, $\alpha$ and $\beta$ are the signed conditional weights, and $\alpha = \beta = 0$ is the measure-zero own-payoff special case — other-regarding preferences with the cross-argument structure fully formalized.

applied_industry:
Kin selection in evolutionary biology and reward shaping in multi-agent reinforcement learning instantiate the identical cross-argument structure in unrelated substrates. In a eusocial insect colony, a sterile worker forgoes its own reproduction to raise the queen's offspring — behaviour that own-fitness maximisation cannot explain. Hamilton's rule supplies the *cross-argument* exactly: the worker's effective preference function values a relative's reproductive success at a *weight* equal to the coefficient of relatedness $r$, so an altruistic act is favoured when $rB > C$ (relatedness times benefit to the recipient exceeds cost to the actor).<!-- FACT-D68-162 -->[^hamilton-1964] The "other" whose outcome enters the function is the related individual, and the weight is biologically anchored rather than psychological — but it is structurally the same object as the economist's altruism parameter: a nonzero weight on another agent's payoff. In multi-agent reinforcement learning, a designer who wants cooperative rather than competitive convergence writes each agent's reward as its own task reward *plus a weighted term in other agents' rewards*; the sign and size of that cross-argument weight determine whether agents learn to share, ignore, or sabotage one another, and tuning it is the direct engineering analogue of the economist's "target the cross-argument weights" move.<!-- FACT-D68-163 -->[^leibo-etal-2017] The same design lever recurs in workplace compensation, where a coworker's wage entering an employee's job satisfaction (an inequity-aversion signature) means pay-transparency and relative-pay structure shift behaviour through the cross-argument rather than the own-wage term. A biologist reading a relatedness coefficient, an ML engineer setting a cooperation weight, and a compensation designer managing relative-pay effects are all reasoning about a weight on another agent's outcome.

**Mapped back:** The worker, the RL agent, and the employee are evaluating agents; relatedness $r$, the reward-sharing coefficient, and the inequity-aversion weight are the same signed cross-argument on another agent's payoff; the colony's altruism, the agents' cooperation, and the relative-pay effect are its consequences — other-regarding preferences as one mathematical object across biology, AI, and organisational behaviour.


Out Of Distribution Detection

type: prime

one_liner: Couple a scope detector to a decision system so out-of-competence cases are deferred, not answered.

status: draft

core_idea:
Out-of-distribution detection is the structural move of recognising,
*before* issuing a verdict, that the current input lies outside the regime
where the issuing system's competence has been calibrated. It separates the
question "what does my system say about this case?" from the prior question
"is this case the kind of case my system was built for?" — and routes
negative answers to the second question onto a different path (defer,
escalate, abstain, refer, demand new evidence) rather than letting the
system answer anyway.

The pattern factors into three sharable parts. There is a *competence
region* — the implicit set of cases the system was designed, trained, or
licensed to handle. There is a *scope detector* — whatever tells the system
that the current input falls outside that region. And there is a *deferral
path* — the alternative response when the detector fires. Whether the
competence region is a training distribution, a clinician's specialty, a
court's jurisdiction, a sensor's calibration range, or a contract's
coverage, the commitment is the same: judgments within competence stay
in-system, while cases outside competence are routed elsewhere, and the
system reports its own scope alongside its answers. What makes this a
distinct prime rather than a special case of "uncertainty" is the *coupled
scope-judgement architecture*: the same artefact that issues answers must
also assess whether the question is within its remit. Without the pairing,
one gets either a confident system that is silently wrong on out-of-scope
cases or a scope-only system that can answer nothing. The prime names the
move that makes these two faculties travel together.

structural_signature:
*the decision system (answerer)* — *the competence region* — *the scope detector* — *the in/out-of-scope routing decision* — *the deferral path* — *the coupled scope-judgement architecture*

A system performs out-of-distribution detection when each of the following holds:

- **A decision system.** There is an answerer that issues verdicts — a classifier, a clinician, a court, a sensor, a contract-bound procedure.
- **A competence region.** There is an implicit set of cases the system was designed, trained, or licensed to handle well — a training distribution, a specialty, a jurisdiction, a calibration range, a contract's coverage.
- **A scope detector.** A mechanism assesses whether the *current input* falls inside or outside the competence region — an OOD score, a triage gate, a standing/jurisdiction test, a range check, a precondition.
- **A routing decision.** Before (or alongside) issuing a verdict, the system asks the prior question "is this the kind of case I was built for?" and uses the detector's answer to decide whether to answer or to route away.
- **A deferral path.** The load-bearing alternative: when the detector fires, the case is routed to a different response — defer, escalate, abstain, refer, demand new evidence, enter a safe state — rather than answered anyway. The deferral path has its own failure modes (over-deferral collapses throughput; under-deferral yields silent overreach).
- **Coupled scope-judgement architecture.** The defining invariant: the same artefact that issues answers must also assess whether the question is within its remit. Without the coupling one gets either a confident system silently wrong out of scope, or a scope-only system that answers nothing. Scope detection is orthogonal to calibration — the latter tunes confidence *inside* the region and is blind to departures from it.

Composed: separating "is this in my competence?" from "what is my answer?" and binding a scope detector and deferral path to the answerer as architecture converts silent out-of-scope failure into an explicit referral — leaving in-distribution performance untouched.

what_it_is_not:
- **Not `calibration`.** Calibration tunes how *honest the confidence* is *inside* the competence region; OOD detection recognizes *departure from* the region. Calibration is computed on in-distribution cases and is blind to novel ones — a perfectly calibrated model still answers confidently and wrongly out of scope.<!-- FACT-D68-176 -->[^guo-etal-2017]
- **Not `authority_delegation_under_uncertainty`.** The nearest embedding neighbor concerns *who decides when an agent is unsure*; OOD detection concerns *recognizing the input is outside competence at all*, before any delegation. Detection is the scope check; delegation is one possible deferral path downstream of it.
- **Not `overfitting`.** Overfitting is a model fitting *noise in its training data*, degrading in-distribution generalization; OOD detection is about *recognizing inputs the training distribution never covered*. One is a within-region quality failure, the other a scope-boundary recognition.
- **Not `screening`.** Screening sorts cases by a *target property* (disease, risk, eligibility) to act on them; OOD detection sorts by *whether the case is within the system's competence* to decide whether to act at all. Screening answers a question; OOD detection decides whether the question is answerable.
- **Not `classification`.** Classification *assigns inputs to known classes*; OOD detection recognizes inputs that belong to *no* known class (open-set), routing them away rather than forcing a label. A closed-set classifier always answers; OOD detection adds the option to abstain.
- **Not a confidence threshold alone.** Low softmax confidence is not OOD detection: networks are notoriously *confidently wrong* on novel inputs.<!-- FACT-D68-177 -->[^nguyen-etal-2015] The detector must assess distance from the competence region (feature-space distance, density), a faculty orthogonal to the answerer's own confidence.
- **Common misclassification.** Hoping a well-calibrated model is therefore safe out of scope. Catch it by separating the two failure types: a *failure of the answer* (in scope, decided wrongly — fix training) versus a *failure of the scope check* (a case answered that should have been deferred — fix the gate). They live in different layers and demand different fixes.

broad_use:
- **Machine learning**: explicit detectors in classifiers (energy scores,
  Mahalanobis distance, deep ensembles), open-set recognition, selective
  prediction with reject options, abstention in conformal prediction.<!-- FACT-D68-178 -->[^yang-etal-2024]
- **Medicine**: a generalist recognising "this is outside my scope" and
  referring to a specialist; triage gates that route patients to the right
  competence band before treatment commits.
- **Law**: courts dismissing cases for lack of jurisdiction or standing —
  the matter is routed to a competent forum rather than adjudicated badly.<!-- FACT-D68-179 -->[^wright-miller-2021]
- **Engineering**: flight envelopes, reactor safe-operating regions, and
  instrument calibration ranges, where a reading outside the calibrated
  range is reported as out-of-range rather than with false precision.<!-- FACT-D68-180 -->[^leveson-2011]
- **Immunology**: self/non-self discrimination is structurally an
  in/out-of-distribution check before mounting a response.<!-- FACT-D68-181 -->[^janeway-2001]
- **Statistics and survey research**: explicit refusal to generalise beyond
  the sampled population or outside the convex hull of training data.
- **Finance**: credit models that decline to score applicants from
  populations they were not trained on, rather than producing scores that
  look like predictions.<!-- FACT-D68-182 -->[^frb-occ-sr11-7-2011]
- **Software**: precondition checks and design-by-contract systems that
  throw on out-of-contract inputs rather than producing undefined behaviour.<!-- FACT-D68-183 -->[^meyer-1992]

clarity:
Naming the move forces a system to declare its competence region
explicitly. Many disputes about failures dissolve once the conversation
moves to: *was this case in-distribution, and was the scope check armed and
working?* The diagnostic separates a *failure of the answer* — the system
was in scope and got it wrong — from a *failure of the scope check* — the
system answered a case it should have deferred. These have different
fixes — better training versus better gating — and conflating them sends
the intervention to the wrong layer.

The prime also clarifies a common false hope: that calibration alone can
rescue an out-of-distribution system. Calibration tunes confidence on the
*in-distribution* cases the calibration set saw; it says nothing about cases
the calibration set did not contain. Recognising the scope problem as
orthogonal to calibration — confidence accuracy inside the region versus
recognising departure from the region — is what unblocks deployment in
safety-critical settings, where the silent failures live precisely outside
the region and are therefore invisible to any amount of in-region
calibration.

manages_complexity:
The prime compresses a wide failure family — silent miscoverage,
hallucination on novel inputs, jurisdiction overreach, mis-triaged patients,
instrument readings outside calibration, structures loaded outside design
assumptions — into a single architectural question: *is the scope detector
coupled to the decision system, and what is its deferral path?* Once posed,
the intervention space sorts cleanly into four moves: widen the competence
region (train on more, certify the specialist more broadly); sharpen the
detector (better scope score, better triage criteria, better jurisdictional
rules); build the deferral path (referral protocol, escalation chain,
safe-state fallback); and audit detector miss rates (the unknown-unknowns
problem).

This four-way decomposition is what keeps the analysis tractable. A team
facing a deployment failure no longer has to debate the entire system at
once; it locates the failure in one of four layers and acts there. And
because the four layers are substrate-independent, the same decomposition
guides an AI deployment, an expert-hiring decision, a jurisdictional rule,
and an instrumentation design without re-derivation.

abstract_reasoning:
Recognising the pattern enables several substrate-independent moves.
*Competence-region geometry*: the detector implicitly carves the input
space into in-region and out-of-region, and the *shape* of that region —
together with the gaps where the detector fails — becomes a first-class
design object; the boundary of a training distribution, of a court's
jurisdiction, and of a sensor's calibration range are all geometries on
input spaces that admit the same diagnostic. *The unknown-unknown problem
is detector blind-spot*: failures concentrate where the detector wrongly
says "in" for inputs that are out, which isolates the cost structure into
false positives (over-deferral) and false negatives (silent out-of-scope
answers) whose consequences are asymmetric across substrates. *Coupled-
system design*: deploying an answerer without a scope detector is
structurally analogous to running a sensor without a range light — the
system gives outputs, but you cannot tell when to trust them. And *deferral
has its own failure modes*: a detector that routes everything to escalation
collapses the system's throughput, while one that routes nothing produces
silent overreach, and both are failures of the deferral path distinct from
the detector's quality.

knowledge_transfer:
The roles map cleanly across domains: the *competence region* is the
training distribution, the specialty, the jurisdiction, the calibration
range, the contract's coverage; the *scope detector* is the OOD score, the
triage gate, the standing/jurisdiction test, the range check, the
precondition; the *deferral path* is the referral, the escalation, the
abstention, the safe state, the demand for new evidence. Stripped of any
single field's vocabulary, the prime reads: *before answering, check
whether the question is the kind your competence covers, and route the
negative cases to something whose competence does — coupling the scope
check to the answerer as architecture, not afterthought.*

Concrete transfers run in several directions. The explicit "stay in lane,
refer up" architecture of emergency-medicine triage ported wholesale into
safety-critical machine learning: an answerer, plus a gate, plus a referral
path, with the carried lesson that scope detection is neither optional nor
free and must be designed explicitly. Jurisdictional doctrine — declare
scope, dismiss out-of-scope matters, document the refusal criteria —
transfers to AI governance as the practice of declaring a model's operating
envelope and refusing cases outside it. The engineering calibration-range
concept ports into conformal prediction as the set-valued prediction whose
width grows as the input drifts from the calibration set. And the
immunological self/non-self check — define normal, flag departures, defer
the response — informed the early intrusion-detection literature and recurs
in fraud detection and industrial monitoring.<!-- FACT-D68-184 -->[^denning-1987] A single worked instance
shows the move: a chest-X-ray classifier trained on adults, deployed at a
paediatric clinic, confidently mis-diagnoses paediatric anatomy until a
retrofit OOD detector flags those inputs as out-of-distribution and routes
them to a human radiologist — in-distribution performance unchanged, the
silent failure converted into an explicit referral.<!-- FACT-D68-185 -->[^zech-etal-2018] The structurally
relevant artefact is never any single component but the triple of model,
detector, and deferral path, and that triple is exactly what transfers.

formal_abstract:
Selective prediction with a reject option makes the prime's coupled architecture mathematically explicit. Take an image classifier trained on a *competence region*: a labeled distribution of, say, photographs of common objects. The *decision system* is the trained network, which outputs a class plus a confidence. Ordinary deployment answers every input. The prime's move is to bolt on a *scope detector* — a separate score that estimates whether the current input lies inside the training distribution. A standard construction uses the *Mahalanobis distance* of the input's feature representation to the nearest class-conditional Gaussian fitted on training features: in-distribution inputs land close to a training cluster (low distance), genuinely novel inputs land far (high distance).<!-- FACT-D68-186 -->[^lee-etal-2018] The *routing decision* thresholds this score: if the distance exceeds $\tau$, the input is flagged out-of-distribution and sent to the *deferral path* (abstain, or escalate to a human) rather than classified. Crucially, this is *orthogonal to calibration*: temperature-scaling the network's softmax tunes how honest its confidence is on in-distribution cases, but a perfectly calibrated network still emits a confident, wrong label on a photo from a class it never saw — calibration is computed on the training distribution and is blind to departures *from* it, which is exactly why scope detection must be a separate faculty. The design exposes the prime's asymmetric cost structure as a tunable: raising $\tau$ (defer less) increases *silent overreach* (false negatives — out-of-scope inputs answered anyway), while lowering it (defer more) increases *over-deferral* (false positives — in-scope inputs needlessly escalated, collapsing throughput). Conformal prediction formalizes the same coupling differently, emitting a *prediction set* whose size grows as the input drifts from the calibration data, so the system's own output width signals departure from competence.<!-- FACT-D68-187 -->[^vovk-etal-2005] The intervention the prime prescribes is architectural: design the detector and the deferral path as first-class components alongside the answerer, and tune the threshold against the asymmetric cost of the two error types.

**Mapped back:** Selective prediction instantiates the full signature — an answerer, a feature-distance scope detector, a thresholded routing decision, and a deferral path — with the calibration-orthogonality showing precisely why "is this in my competence?" must be a separate faculty from "what is my answer?"

applied_industry:
Emergency-medicine triage and judicial jurisdiction are the same scope-then-answer architecture in medicine and in law — and the medical case is in fact where the ML pattern was borrowed from. In an emergency department, the *decision system* is the treating clinician (or a care pathway), and the *competence region* is the band of conditions that clinician or unit is licensed and equipped to handle. Before committing to treatment, a *triage gate* assesses whether the presenting case is *the kind of case this competence covers*: a patient with symptoms outside the ED's scope (a complex cardiac case, a pediatric anatomy the unit is not set up for) is routed to the *deferral path* — referral to a specialist or transfer — rather than treated badly in place. The prime's lesson, carried wholesale into safety-critical ML, is that this scope check is *neither optional nor free*: "stay in lane, refer up" must be designed and staffed, not assumed. Jurisdiction is the identical structure in law: a *court* is the answerer, its *competence region* is its statutory jurisdiction and the standing requirements that define which disputes it may hear, and the *scope detector* is the jurisdiction-and-standing test applied *before* the merits.<!-- FACT-D68-188 -->[^wright-miller-2021] A case outside the court's remit is *dismissed for lack of jurisdiction* — routed to a competent forum — rather than adjudicated wrongly, which is exactly deferral, with the dismissal documenting the refusal criteria. The shared diagnostic the prime supplies separates two failure types that demand different fixes: a *failure of the answer* (in scope, decided wrongly — fix the training, the clinician's skill, the legal reasoning) versus a *failure of the scope check* (a case answered that should have been deferred — fix the gate, the triage criteria, the standing test). The concrete transfer is direct and documented: a chest-X-ray model trained on adults but deployed at a pediatric clinic confidently mis-reads pediatric anatomy until a retrofit OOD detector flags those inputs and routes them to a human radiologist — in-distribution performance untouched, the silent failure converted into an explicit referral, the medical triage architecture imported into the model as detector-plus-deferral.

**Mapped back:** Triage and jurisdiction are the same prime as selective prediction — an answerer coupled to a scope detector that routes out-of-competence cases to a deferral path — so the architecture and its answer-failure-versus-scope-failure diagnostic transfer across the medical, legal, and machine-learning substrates, with medical triage the documented source of the ML deployment pattern.


Outcome-Defined Adequacy

one_liner: Adequacy is specified by whether a defined outcome is produced in context, leaving the form open to any realization that achieves it.

origin_domain: philosophy

core_idea:
Outcome-defined adequacy is the meta-evaluative stance in which the adequacy of an artifact, act, or system is specified by *whether it produces a defined outcome in its context of use*, not by its internal form, surface properties, or process compliance. The form-side is deliberately left open. Success is judged *relationally* — against a real-world purpose or downstream consequence — rather than against an inventory of features, a process checklist, or a syntactic template. The essential commitment is that the spec or contract is written in *outcome terms*, not *form terms*, and that any form which reliably produces the outcome is adequate.

The arrangement has a small set of recurring roles: an artifact, act, or system being evaluated; a context of use in which adequacy is judged; a defined outcome the artifact is meant to produce in that context; an operational specification of that outcome (measurable, observable); and form-side openness, under which any form that produces the outcome counts. Verification is by outcome-measurement rather than form-inspection. The stance exploits the *many-to-one* relation between forms and outcomes — many implementations realize the same outcome, and only the outcome is load-bearing. It carries characteristic failure modes — gaming, side-effects, measurement difficulty, accountability opacity — and it sits inside a *meta-choice* among outcome-defined, form-defined, and process-defined adequacy framings, each with its own trade-offs. The prime's distinctive content is the recognition that this framing choice is itself substantive, not a neutral preliminary to evaluation.

structural_signature:
*the evaluated unit* — *the context of use* — *the defined outcome* — *the operational outcome-specification* — *the form-side openness* — *the many-to-one form→outcome relation* — *the outcome-measurement verification* — *the meta-choice among adequacy framings*

A configuration instantiates outcome-defined adequacy when each of the following holds:

- **An evaluated unit.** Some artifact, act, or system is the object whose adequacy is in question.
- **A context of use.** Adequacy is judged *relative to* a situation of use, not in the abstract; the same unit can be adequate in one context and not another.
- **A defined outcome.** A real-world purpose or downstream consequence the unit is meant to produce in that context is specified as the criterion.
- **An operational outcome-specification.** The outcome is stated measurably or observably, so adequacy can be checked. Without this the stance collapses into vague results-talk.
- **Form-side openness.** The internal form, surface properties, and process are deliberately left unconstrained: any realization that produces the outcome counts.
- **A many-to-one relation.** Many distinct forms map to the same outcome, and only the outcome is load-bearing — this is the relation the stance exploits.
- **Outcome-measurement verification.** Acceptance is by measuring the result, not inspecting the form or auditing the process.
- **A live meta-choice.** Outcome-defined adequacy sits beside form-defined and process-defined framings; selecting among them is itself a substantive, non-neutral decision with distinct failure modes (gaming, side-effects, measurement difficulty, accountability opacity).

These components compose into a stance: the spec is written on the outcome side, form is left open to absorb variety, verification is by measurement, and the framing choice is made deliberately with its characteristic failure modes in view.

what_it_is_not:
- **Not the act of checking fitness-for-purpose (see `validation`).** `validation` is the *verification procedure* that asks "does this meet the need?"; outcome-defined adequacy is the prior *framing choice* that locates the spec on the outcome side rather than the form or process side. Validation is the natural acceptance test that *follows from* an outcome framing, not the framing itself.
- **Not a results metric or its measurement (see `effect_size`).** `effect_size` quantifies *how much* of an outcome was produced; outcome-defined adequacy is the stance that *only the outcome counts*, with form left open. The prime is about where the criterion is written, not how large the measured result is.
- **Not metric-gaming (see `goodharts_law`).** `goodharts_law` is the *failure mode* in which a measured proxy decouples from the outcome under pressure; outcome-defined adequacy is the legitimate stance that *invites* that hazard. The prime names the framing; Goodhart names what goes wrong when its proxy is gamed.
- **Not a summative grade (see `summative_assessment`).** `summative_assessment` is an institutional end-of-process judgement that may itself be form-, process-, or outcome-defined; the prime is the narrower claim that adequacy is specified *by outcome with form open*, independent of whether the judgement is summative or formative.
- **Not pragmatism or "results-orientation."** Those are dispositional attitudes; the prime is a precise structural claim about *where the spec is written* — outcome side, form side, or process side — and that this choice is substantive, not a vague preference for what works.
- **Common misclassification.** Reading every results-talk evaluation as outcome-defined. Catch it by asking whether the *form is genuinely left open*: if acceptable realizations are enumerated or a procedure is mandated, the spec is actually form- or process-defined, however much "results" rhetoric surrounds it.

broad_use: The stance appears under different vocabularies across substrates. In speech-act theory, communicative success is felicity — illocutionary uptake and perlocutionary effect, not lexical form.<!-- FACT-D68-201 -->[^austin-1962] In philosophy of mind and biology, functionalism defines a mental state or biological kind by its causal role, not its material realization.<!-- FACT-D68-202 -->[^putnam-1967] In outcome-based regulation, policy specifies the outcome to be achieved — emission reduction, patient survival, a financial-stability metric — and leaves means to the regulated entity. In HCI and product design, job-to-be-done and task-success treat an artifact as adequate if it lets the user accomplish the task, regardless of feature inventory.<!-- FACT-D68-203 -->[^christensen-etal-2016] In software engineering, black-box testing and behavioural specification judge a module by whether its outputs satisfy the contract, regardless of implementation.<!-- FACT-D68-204 -->[^beizer-1995] In biology, adaptive radiation and functional morphology recognize kinds by ecological role rather than ancestry.<!-- FACT-D68-205 -->[^schluter-2000] In speech-language pathology, "functional communication" treatment is adequate if it lets the patient achieve communicative goals, regardless of grammaticality.<!-- FACT-D68-206 -->[^davis-wilcox-1985] In law, performance-based standards — the negligence reasonable-person test, the equitable outcomes of constructive trust — are outcome-defined.<!-- FACT-D68-207 -->[^keeton-prosser-1984]

clarity:
The arrangement makes visible a stance otherwise blurred under generic terms like "results-oriented" or "pragmatic." It sharpens the contrast with *form-defined adequacy* (the artifact must have these specific features) and *process-defined adequacy* (the artifact must have been produced by this procedure), making it possible to ask which adequacy framing a given evaluation regime uses and what the consequences of each are. The clarifying force is to convert a vague preference for "what works" into a precise claim about where the spec is written: on the outcome side, the form side, or the process side.

The arrangement also surfaces the recurring failure modes of each framing. Form-defined adequacy tolerates outcome failure if the form is satisfied — compliance theatre. Process-defined adequacy tolerates outcome failure if the process was followed — audit-pass with reality-fail. Outcome-defined adequacy tolerates form heterogeneity, which can be a feature (flexibility, innovation, local fit) or a bug (gaming, unmonitored side-effects). Naming the three framings side by side makes their characteristic blind spots comparable, so an evaluator can choose the framing whose failure mode is least costly in the case at hand rather than defaulting to one unreflectively.

manages_complexity:
Outcome-defined adequacy collapses the design space. Instead of writing an exhaustive feature spec or process spec — which is both under-determined (it cannot anticipate all forms that produce the outcome) and over-determined (it forecloses valid alternatives) — the evaluator specifies the outcome and accepts any form that achieves it. This factoring exploits the many-to-one relation between forms and outcomes: many implementations realize the same outcome, and only the outcome is load-bearing. The cost is harder verification (outcomes must be measured, not features inspected) and harder accountability (locating when a failure occurred is more difficult). The prime makes this trade-off explicit and names the discipline of choosing the framing intentionally.

The leverage is that the form-side openness absorbs variety the evaluator would otherwise have to enumerate. Where a form-defined spec must grow a clause for every acceptable realization, an outcome-defined spec admits all of them at once, bounded only by the outcome criterion. This is the same complexity-management move that black-box contracts and outcome-based regulation make: shift the burden from specifying the space of acceptable forms to measuring a single result.

abstract_reasoning:
Outcome-defined adequacy trains a reasoner to ask:

- What artifact, act, or system is being evaluated, and in what context of use is its adequacy judged?
- What outcome is it supposed to produce, and can that outcome be specified operationally — measurably, observably?
- Is the form side genuinely left open, so that any realization achieving the outcome counts?
- Is verification done by outcome-measurement rather than form-inspection?
- What are the characteristic failure modes here — gaming, side-effects, measurement difficulty, accountability opacity — and are they being watched?
- Is the framing choice itself — outcome-defined versus form-defined versus process-defined — being made deliberately, with its trade-offs in view?

The non-obvious inference is that the framing *choice* is substantive: the same artifact can be adequate under one framing and inadequate under another, and disputes about adequacy often turn out to be disputes about which framing is in force. The opposite framings are legitimate in some contexts — where forms are tightly coupled to outcomes, or where outcome measurement is infeasible — so the discipline is not to prefer outcome-definition universally but to recognize the choice and make it on purpose.

knowledge_transfer:
Role mappings across domains:

- **Artifact / act / system** ↔ utterance / mental state / regulated entity / product / software module / organism / legal conduct
- **Context of use** ↔ communicative situation / causal role / regulatory regime / task setting / runtime / ecological niche
- **Defined outcome** ↔ uptake and effect / causal function / emission target / task success / contract satisfaction / fitness
- **Operational outcome spec** ↔ felicity conditions / functional role / measurable threshold / success criterion / behavioural assertion
- **Form-side openness** ↔ any realization that achieves the outcome is adequate
- **Failure modes** ↔ gaming / side-effects / hard measurement / accountability opacity

A regulator choosing between prescriptive and outcome-based standards, a software architect choosing between implementation and behavioural specs, a philosopher of mind arguing functional role over material realization, and a speech-act theorist analyzing felicity are taking the same stance: adequacy specified by outcome, form left open, verification by outcome-measurement. The vocabulary — outcome-defined, form-defined, process-defined, felicity, functional role, performance-based standard — transfers across substrates. A regulator weighing outcome-based versus prescriptive standards can borrow the functionalism debate from philosophy of mind; a software architect weighing behavioural versus implementation specs can borrow from outcome-based regulation. The prime's universal failure mode — gaming, side-effects, hard verification — also transfers and serves as a check on uncritical enthusiasm for outcome-framings. What moves between fields is not a metaphor but the literal stance: the spec written in outcome terms, the form side deliberately open, the many-to-one relation exploited, and the meta-choice among framings made explicit. Recognizing the stance in one substrate lets a practitioner import both its leverage (form-side openness absorbs variety) and its discipline (watch for gaming and side-effects; verify by measuring the outcome) into another, including the recognition that validation is the natural acceptance test when adequacy is outcome-defined, just as verification is the natural test when adequacy is form-defined.

formal_abstract:
Functionalism in philosophy of mind is the clean theoretical instance. The *evaluated unit* is a mental state — say, pain. The *context of use* is the organism's causal economy: inputs (tissue damage), internal-state transitions, and outputs (withdrawal, complaint, avoidance learning). The *defined outcome* is the causal role pain plays — being typically caused by damage, typically causing aversion and protective behavior — and the *operational outcome-specification* is the input-output-transition profile that role can be written as. The decisive move is *form-side openness*: functionalism refuses to identify pain with any particular substrate. Carbon neurons, silicon circuitry, or a sufficiently organized hydraulic system all count as instantiating pain *if and only if* they realize the role.<!-- FACT-D68-208 -->[^putnam-1967] This is the *many-to-one* relation made into a thesis — multiple realizability — where many physical forms map to one functional outcome and only the functional outcome is load-bearing for being-in-pain.<!-- FACT-D68-209 -->[^putnam-1967] *Verification* is by role-occupancy, not by inspecting the wetware. The *meta-choice* is explicit and substantive: a type-identity theorist writes the spec on the form side (pain *is* C-fiber firing), and the dispute between them is precisely a dispute over which adequacy framing is in force.<!-- FACT-D68-210 -->[^smart-1959] The characteristic *failure mode* — that a system might fake the outputs without the inner organization (the absent-qualia and "China brain" worries) — is the philosophical analogue of gaming: passing the outcome test without genuinely producing the outcome.<!-- FACT-D68-211 -->[^block-1978]

**Mapped back:** Pain-as-role is adequacy specified by outcome (the causal profile) with form (the substrate) deliberately open; multiple realizability is the many-to-one relation the stance exploits, and the type-identity rival is the alternative form-defined framing the meta-choice selects against.

applied_industry:
Outcome-based regulation and black-box software testing are the same stance in two industries. In *regulation*, a prescriptive (form-defined) emissions rule names the technology — "install this scrubber, run it at this rate." An outcome-based rule instead writes the spec on the outcome side: "keep stack emissions below this measured threshold," leaving the *form* — scrubber, fuel switch, process redesign — entirely open.<!-- FACT-D68-212 -->[^coglianese-etal-2003] The *evaluated unit* is the regulated plant, the *context* its operating regime, the *defined outcome* an emissions level, the *operational specification* a metered measurement, and *verification* is by monitoring the stack, not auditing the equipment. The leverage is exactly form-side openness absorbing variety: the regulator does not have to enumerate every acceptable abatement technology, and plants innovate toward cheaper means. The named *failure modes* bite predictably — gaming (tuning the plant only during test windows), side-effects (shifting one pollutant to another the spec does not measure), and accountability opacity (a missed target is harder to pin on a specific lapse than a missing scrubber).<!-- FACT-D68-213 -->[^coglianese-etal-2003] In *software*, behavioural/black-box testing is structurally identical: the *unit* is a module, the *outcome* is a contract over outputs given inputs, the *form* (the implementation) is deliberately unconstrained, and a passing test verifies the result rather than the code. The intervention catalogue transfers directly between the two: in both, the architect's discipline is to specify the outcome operationally, leave the form open to absorb variety, and instrument against gaming and unmeasured side-effects — and to decide deliberately when a form-defined spec (a mandated algorithm, a mandated technology) is safer because outcomes are hard to measure or forms are tightly coupled to consequences.

**Mapped back:** The emissions threshold and the module contract are both the spec written on the outcome side with form left open; the regulator monitoring the stack and the test harness checking outputs are both outcome-measurement verification, and the gaming/side-effect risks are the stance's universal failure modes recurring across substrates.


Outlier Leverage

one_liner: A small number of extreme observations carry disproportionate weight in an aggregate result, so the result is more a property of those few points than of the bulk of the data — a consequence of the aggregation rule's non-resistance to extremes, not of any sampling defect.

core_idea:
Outlier leverage is the structural pattern in which a small number of
extreme observations carry disproportionate weight in shaping an
aggregate result, such that the result is more a property of those
observations than of the bulk of the data. The structural commitment is
an *asymmetry between count and influence*: one or two cases in a sample
of thousands can determine the slope of a regression, the direction of a
policy conclusion, the success of a fund, the ranking of a school, or
the safety record of a product. The leverage is a property of the
combination of the extremity of the observation in input space, the
aggregation rule (mean, slope, ratio, ranking) being applied, and the
absence of robust treatment.

The pattern is distinct from generic selection bias: even in a correctly
drawn representative sample, a tiny tail can dominate the aggregate. The
structural mechanism is the *aggregation rule's non-resistance to
extremes* — not a sampling defect. Three features make it prime-level.
The leverage is *compositional*: removing the extreme points and
refitting reveals that the inferences depended on them, often
surprisingly. The remedy family is *shared across substrates*: robust
statistics (trimming, winsorising, M-estimators, medians for means),
sensitivity analysis (leave-one-out), and contribution caps. And the
diagnostic question — *would my conclusion survive removal of the top k
cases?* — has a universal form that transfers without translation.

The arrangement names an *observation set*, the *extremity in input
space* that makes some points high-leverage, the *aggregation rule* with
its breakdown point, the *disproportionate influence* of the small
driving set, the *diagnostic* (leverage scores, Cook's distance,
leave-one-out comparisons), the *two-aggregate gap* between conclusions
with and without the extremes, and the *remedy choice* — robust
aggregation, sensitivity reporting, contribution caps, or honest
acknowledgment that the conclusion is a tail-property rather than a
population-property.

structural_signature:
*an observation set* — *an extremity in input space that confers leverage* — *an aggregation rule with a breakdown point* — *a disproportionate influence of the small driving subset* — *a diagnostic measuring per-point influence* — *a two-aggregate gap between conclusions with and without the extremes*

The pattern is present when each of the following holds:

- **An observation set.** A collection of cases combined
  into a single result — the population from which the
  aggregate is computed.
- **Extremity in input space.** Some small number of cases
  lie far from the bulk along the dimensions the
  aggregation rule weights, making them high-leverage
  rather than merely large-valued.
- **A non-resistant aggregation rule.** The rule mapping the
  set to a result has a low breakdown point — a mean,
  slope, ratio, or ranking that a single extreme case can
  move. The rule's non-resistance, not any sampling defect,
  is the mechanism.
- **Disproportionate influence.** A few cases determine the
  result, so the aggregate is more a property of the tail
  than of the bulk — an asymmetry between count and
  influence.
- **An influence diagnostic.** A per-observation measure —
  leverage score, Cook's distance, leave-one-out
  comparison — that quantifies each case's contribution.
- **A two-aggregate gap.** The difference between the result
  computed with and without the extreme cases, a single
  number measuring how much the conclusion rests on the
  tail.

The components compose so that the load-bearing question is
*the breakdown point of the aggregation against the
distribution*: the structure forces the prior choice of
whether the inquiry concerns the bulk (where robust
aggregation applies) or the tail (where the extremes are
the signal and must be kept).

what_it_is_not:
- **Not selection bias.** `selection_bias` is a *sampling*
  defect — the wrong cases entered the sample. Outlier
  leverage occurs in a *correctly drawn* sample: the data are
  representative, but the aggregation rule is non-resistant to
  extremes.
- **Not heavy-tailed distributions per se.** `heavy_tailed_distributions`
  is a property of the data; outlier leverage is what happens
  when a low-breakdown *rule* (mean, OLS slope) is applied to
  such data. The same heavy tail is harmless under a median.
- **Not antifragility.** `antifragility` is a system that
  *gains* from volatility; outlier leverage is a measurement
  pathology where a few extremes *distort* an aggregate. The
  extremes here are an inference hazard, not a benefit.
- **Not the Pareto effect.** `pareto_effect_80_20_rule`
  observes that a few inputs produce most output; outlier
  leverage adds the *aggregation-rule sensitivity* — whether
  that concentration corrupts a conclusion depends on the
  rule's breakdown point.
- **Not risk pooling.** `risk_pooling` aggregates to *cancel*
  idiosyncratic variation; outlier leverage is the case where
  aggregation fails to cancel because a few points dominate
  the rule.
- **Common misclassification.** Diagnosing a fragile result
  as "biased data" and chasing a sampling fix. Catch it by
  asking whether the conclusion survives removal of the top-k
  cases under a robust re-aggregation; if the sample is fine
  but the slope flips, the rule, not the sample, is the
  problem.

broad_use:
The pattern recurs wherever an aggregation rule is applied to a
distribution with non-trivial tails. In **statistics and regression** —
the classical case — high-leverage points pull the fit line toward
themselves, and Cook's distance, hat values, and influence diagnostics
were developed because ordinary least squares has zero breakdown point
against a single bad point.<!-- FACT-D68-226 -->[^cook-weisberg-1982] In **education research**, a single
charismatic teacher's classroom or one underperforming school can drive
program-evaluation results in samples too small to absorb the extreme.
In **medical trials**, a handful of strong responders or non-responders
can determine the trial-mean effect even when the median patient is
unaffected. In **finance**, a single trader, fund, or position can
dominate firm-level performance or risk — one trader collapsed Barings,
a handful of trades concentrated the largest losses at LTCM, and
long-tail returns make hedge-fund alpha dominated by a few vintages.<!-- FACT-D68-227 -->[^lowenstein-2000] In
**policy evaluation**, a single failed program or unrepresentative
jurisdiction can drive national policy from a sample whose mean is
unrepresentative of the median. In **product analytics**, whale users
generate the bulk of revenue, so mean revenue per user is dominated by
the tail and A/B wins on means can entirely reflect tail shifts with no
median effect.<!-- FACT-D68-228 -->[^swrve-2016] In **sports analytics**, single-game performances drive
season-level statistics for small-sample positions.

clarity:
Naming outlier leverage separates two diagnoses that are routinely
conflated: "the data are biased" and "the data are unbiased but the
aggregation is sensitive to extremes." The two call for different
responses — bias calls for better sampling, while leverage calls for
either robust aggregation or honest acknowledgment that the conclusion
depends on the tail. Without the distinction, an analyst confronting a
fragile result is liable to chase a sampling fix that cannot help,
because the sample was fine and the aggregation rule was the problem.

The frame also clarifies the recurrent rhetorical move of attacking or
defending a conclusion by pointing to a single extreme case. That move
can be valid (the case genuinely has high leverage and the conclusion
turns on it) or invalid (the case is one of many and has little
leverage), and the leverage framing makes the distinction explicit and
testable rather than rhetorical. By converting "everyone knows about
case X" into the checkable question "what is case X's leverage, and does
the conclusion survive its removal?", the frame defuses anecdote-driven
argument and replaces it with a computation that either supports or
refutes the case's claimed importance.

manages_complexity:
The diagnostic compresses a wide class of inference problems to two
checks: compute leverage scores or influence measures for each
observation, then refit the model with the high-leverage observations
removed and compare. If the conclusion changes, the bulk of the data did
not support it and the conclusion is a property of the tail. This
two-check protocol is identical in regression, in trial analysis, in
risk management, and in A/B testing — only the software changes — so a
sprawling family of "is this result real?" questions reduces to one
reusable procedure.

The compression's power is that it makes the dependence visible and
quantifiable rather than leaving it as a worry. The *two-aggregate gap* —
what the conclusion looks like with versus without the extreme points —
is a single number that measures how much the result rests on the tail,
and it can be reported alongside the result so that a reader sees the
dependence directly. That single quantity turns an open-ended robustness
concern into a definite measurement, and it tells the analyst which
remedy fits: a large gap with a population-level question calls for
robust aggregation, while a large gap with a tail-level question (where
the extremes *are* the signal) calls for keeping them and reporting the
dependence honestly.

abstract_reasoning:
The pattern licenses inferences of a precise form: if top-k removal flips
the sign or significantly changes the magnitude of an estimate, the
estimate is not a property of the population but of those k observations.
It also predicts that aggregation rules with breakdown point near zero —
the mean, the variance, the OLS slope — become increasingly
leverage-vulnerable as distributions grow more heavy-tailed, while rules
with breakdown point near one-half — the median, the MAD, the Theil–Sen
slope — trade some efficiency on Gaussian data for robustness to leverage
on real-world data.<!-- FACT-D68-229 -->[^rousseeuw-leroy-1987] These inferences are domain-free, depending only on
the aggregation rule and the distribution rather than on any substrate.

The frame also supports a subtler inference: in some domains *the
leverage is the signal*. In risk management, the few extreme losses
determine the actuarial reality and discarding them is precisely the
wrong move; in safety engineering and fraud detection, the tail is the
object of interest. So the diagnostic does not say "remove the outliers";
it says "decide whether the question you are asking is about the bulk or
about the tail, and use an aggregation that matches." The pattern is
purely structural: its vocabulary travels unmodified, it carries no
normative load, and it depends on no institution — the load-bearing
question "what is the breakdown point of my aggregation against my
distribution?" is a mathematical question asked at the aggregation step,
which is why the prime sits among the high-abstraction structural cases.

knowledge_transfer:
The robust-statistics catalogue — trim, winsorise, M-estimate, use the
median, use rank-based methods, bound individual contribution — was
developed in regression and transfers because the roles map cleanly
across substrates<!-- FACT-D68-230 -->[^huber-1981]: the *observation set* maps to data points, students,
patients, trades, jurisdictions, users, or games; the *aggregation rule*
maps to the mean, slope, ratio, or ranking in each; the *high-leverage
points* map to extreme states, strong responders, dominant traders, or
whale users; and the *diagnostic* maps to leverage scores, Cook's
distance, or leave-one-out comparison everywhere. Because the roles
correspond, each remedy is a recognisable application of the same
intervention family: winsorise extreme responders before computing a
mean treatment effect, cap each trader's contribution to firm P&L, run
leave-one-out sensitivity over jurisdictions, cap revenue per user in
A/B computations, and weight career projections toward median
performance.

The transfer also runs the other direction. Position limits from finance
transfer into A/B-test design as per-user contribution caps and into
reviewer-influence design in peer-review and hiring panels, where no
single reviewer's score should determine the outcome.<!-- FACT-D68-231 -->[^pier-etal-2018] The two-check
protocol — refit without the extremes; report the dependence — applies
identically whether the result is a fifty-state funding-outcomes
regression whose slope collapses when two states are removed, a hedge
fund whose track record is one trader's single year, a trial whose
positive result is three super-responders, or a revenue forecast
dominated by a hundred whales out of millions. The transfer is
structural rather than metaphorical, and unusually clean, because the
remedy catalogue moves across substrate unchanged: the load-bearing
quantity is the breakdown point of the aggregation against the
distribution, which is a property of the rule and the data and not of
the domain, so the diagnostic and its remedies carry without any
translation at all. The candidate's contribution is naming the
configuration so the question — bulk or tail? — can be asked, not
prescribing the answer, since the correct response is sometimes to
discount the outliers and sometimes to amplify attention to them.

formal_abstract:
Consider ordinary least squares fit to a scatter of $n = 500$ points
whose bulk lies in a tight cloud near the origin, plus a single point
placed far out along the $x$-axis at $(x_0, y_0)$ with large $x_0$.<!-- FACT-D68-232 -->[^belsley-etal-1980] The
observation set is the 500 points; the extremity in input space is
$x_0$'s distance from the bulk, which gives that point a hat-value (its
diagonal entry in the projection matrix) approaching 1 — near-maximal
leverage.<!-- FACT-D68-233 -->[^belsley-etal-1980] The aggregation rule is OLS, whose breakdown point is exactly
$1/n$: a single point can move the slope arbitrarily, because the slope
is a weighted sum in which the far point's weight dominates.<!-- FACT-D68-234 -->[^rousseeuw-leroy-1987] The
disproportionate influence shows up in Cook's distance for that point,
which dwarfs every other observation's. The two-aggregate gap is
computed by leave-one-out: refit without the far point and the slope can
flip sign entirely, revealing that the fit was a property of one
observation, not of the 500. The remedy the structure dictates depends
on the question: if the inquiry is about the bulk relationship, replace
OLS with a high-breakdown estimator (Theil–Sen, breakdown point ~0.29,
or an M-estimator) so no single point can dominate<!-- FACT-D68-235 -->[^rousseeuw-leroy-1987]; if the far point is
a genuine signal — a real but rare regime — keep it and report the
dependence explicitly. The diagnostic is the same either way: *would the
conclusion survive removal of the top $k$ points?*

**Mapped back:** The regression instance carries every role —
observation set, extremity (hat-value), non-resistant rule (OLS,
breakdown $1/n$), disproportionate influence (Cook's distance), and
two-aggregate gap (leave-one-out slope flip) — and shows the failure is
the breakdown point of the rule, not a sampling defect.

applied_industry:
In **quantitative finance risk aggregation**, a trading firm computes
mean P&L and firm-level risk across hundreds of traders. The
observation set is the traders; the extreme cases are one or two who run
outsized concentrated positions; the aggregation rule is the sum (or
mean) of P&L, with breakdown point near zero. A single trader can
determine firm-level performance and risk — the structure that let one
trader's positions collapse Barings, and that concentrated the largest
losses at LTCM in a handful of trades.<!-- FACT-D68-236 -->[^lowenstein-2000] The leave-one-out two-aggregate
gap — firm P&L with versus without the top trader — quantifies the
dependence, and the remedy is a contribution cap: position limits that
bound any single trader's influence on the aggregate, the finance
analogue of winsorizing. The identical structure governs **product
revenue analytics**: "whale" users generate the bulk of revenue, so mean
revenue per user is dominated by the tail, and an A/B test that wins on
mean revenue may reflect a shift in a few whales with no median effect;
the remedy is to cap per-user contribution in the test computation or to
report median alongside mean. And in **multi-site clinical trials**, a
handful of strong responders can drive a positive mean treatment effect
even when the median patient is unaffected<!-- FACT-D68-237 -->[^kent-hayward-2010]; leave-one-out sensitivity
over patients and a robust or median-based summary reveal whether the
effect is a population property or a tail property.

**Mapped back:** Across finance, product analytics, and clinical trials
the same roles recur — an observation set, a few high-leverage extremes,
a non-resistant aggregation rule, and a measurable two-aggregate gap —
and the same intervention family transports unchanged: cap individual
contribution, run leave-one-out, and choose an aggregation whose
breakdown point matches whether the question is about the bulk or the
tail.


Overfitting

slug: overfitting

one_liner: Poor generalization.

core_idea: Overfitting is the structural condition in which a model or learned procedure captures patterns in its training or reference data that do not correspond to generalizable structure — including noise, idiosyncratic coincidences, or features specific to the training distribution — such that its performance on training data is disproportionately good relative to its performance on new cases drawn from the target population<!-- FACT-D25-046 -->[^hawkins-2004]. The essential commitment is relational: overfitting is not a property of the model alone or the data alone, but of the model-data-target relationship, diagnosed by the gap between in-sample and out-of-sample performance<!-- FACT-D25-047 -->[^geman-bienenstock-doursat-1992]. The core tension is between flexibility (enough capacity to capture real structure) and restraint (enough regularity to avoid fitting noise); navigating this tension is the central problem of empirical modeling. Every overfitting claim specifies (1) the model and its capacity, (2) the training sample and its relationship to the target distribution, (3) the measurable gap between in-sample and out-of-sample performance, and (4) the mechanism by which training-specific patterns were absorbed.

structural_signature:
- *The model-flexibility hyperparameter and its magnitude relative to training signal*
- *The bias-variance trade-off curve governing in-sample-versus-out-of-sample performance divergence*
- *The noise-fitting versus signal-fitting distinction as the mechanism of overfitting*
- *The regularization and capacity-reduction mechanisms constraining model flexibility*
- *The cross-validation and held-out-test diagnostic revealing train-test generalization gap*
- *The training-sample-to-target-distribution relationship determining transferability of learned patterns*

what_it_is_not:
- **Not mere error on new data.** A model may err on new data for many reasons (distribution shift, bias, insufficient capacity); overfitting specifically names the case where the in-sample fit is much better than the out-of-sample fit<!-- FACT-D25-048 -->[^hastie-tibshirani-friedman-2009]. See also `regression_to_the_mean` — extreme test-set performance in one study selected on being significant will regress in replication.
- **Not underfitting.** Underfitting is the opposite failure — the model is too inflexible to capture real structure, with poor performance both in- and out-of-sample<!-- FACT-D25-049 -->[^james-witten-hastie-tibshirani-2013]. Overfitting and underfitting bracket the capacity problem; this is the bias-variance trade-off in its canonical form.
- **Not the same as overgeneralization.** Overgeneralization in cognition is applying a rule beyond its domain (a child saying "goed" instead of "went"); overfitting is under-generalization caused by fitting noise. The relationship is subtle — overfitting produces specific-to-training predictions that fail on new data.
- **Not a purely ML concept.** Overfitting describes a failure mode in any inductive process — scientific modeling, expert judgment calibrated to narrow case sets, organizational learning, stereotype formation — and predates ML as a diagnostic<!-- FACT-D25-050 -->[^hawkins-2004]. The phenomenon is endemic to empirical reasoning.
- **Not always the model's "fault."** When training data is small, sampling noise is high, or features are many, even well-designed procedures can overfit; the cure is often structural (more data, regularization) rather than correcting the model.
- **Common misclassification.** Confusing overfitting with high variance in the predictor without checking training-test gap; attributing generalization failure to overfitting when distribution shift is the operative cause; treating overfitting as a specifically ML problem when it is a generic inductive-inference failure mode.

broad_use:
- **Statistics and machine learning**
    - Bias-variance trade-off; cross-validation;
      regularization (L1, L2, dropout);
      structural risk minimization; PAC-learning
      theory; early stopping; ensemble methods.
- **Scientific modeling**
    - Curve-fitting overfit to data points;
      model selection via information criteria
      (AIC, BIC); the replication crisis partly
      as a population-level overfitting of the
      research literature; garden of forking
      paths and researcher-degrees-of-freedom
      problems.
- **Finance and quantitative investing**
    - Backtest overfitting; curve-fitting trading
      strategies to historical data that fail
      live; the cost of data snooping in
      strategy development.
- **Cognitive psychology and learning**
    - Overlearning of specific examples without
      principle extraction; rigid cognitive
      schemas that fail on new cases; stereotype
      formation as overfitting to limited
      category exposure.
- **Economics and policy modeling**
    - Over-calibration of macroeconomic models to
      historical periods; policies designed for
      past patterns that fail under regime
      change; optimization against historical
      metrics producing fragile policy
      architectures.
- **Organizational learning**
    - Procedures calibrated to past conditions
      that fail under change; lessons-learned
      systems that encode idiosyncratic details;
      hiring systems that over-fit to
      characteristics of past successful
      candidates.

clarity: Overfitting clarifies by forcing distinction between "performs well here" and "generalizes well." A claim like "the model works" resolves into "the model was trained on sample S from distribution D; evaluated on S, performance is P1; evaluated on held-out sample from D (or on deployment data), performance is P2; the gap P1 − P2 is [negligible / moderate / large]; where the gap is large, the model has captured training-specific patterns [noise, rare cases, sampling artifacts] that don't transfer; the remedy is [more data, regularization, simpler hypothesis class, feature selection, validation-based early stopping] chosen for the specific overfitting mechanism<!-- FACT-D25-051 -->[^domingos-2012]." The clarifying force is to separate in-sample success from deployment success and to diagnose the structural cause. This discipline has transformed empirical ML and statistics practice: out-of-sample testing is now standard, not exceptional, precisely because overfitting is recognized as the central challenge.

manages_complexity:
- Supports disciplined modeling: out-of-sample testing, cross-validation, and regularization are deliberate responses to overfitting risk<!-- FACT-D25-052 -->[^stone-1974] and have become standard practice in statistics and ML because they work. The discipline replaces ad-hoc judgment with systematic validation.
- Frames the capacity-regularity trade-off: choosing model capacity, feature count, and regularization strength is a principled navigation between overfitting and underfitting informed by bias-variance analysis and empirical validation. Model-selection criteria (AIC, BIC, cross-validation error) operationalize this trade-off.
- Structures scientific practice: pre-registration, holdout test sets, replication requirements, and theory-driven constraints on hypotheses are responses to population-level overfitting in the research ecosystem<!-- FACT-D25-053 -->[^hawkins-2004]. The replication crisis is partly understood as literature-wide overfitting to publishable findings.
- Frames organizational design: periodic review of calibrated procedures, explicit distinction between principle and instance in training, and scenario-based testing guard against organizational-scale overfitting to past conditions. Procedures that generalize survive regime change; those calibrated to specific periods fail.
- Informs human cognition: people overfit too — over-inferring from small samples, treating coincidences as patterns, rigidifying around specific experiences. Explicit de-biasing practices (considering base rates, sampling more cases, checking alternative explanations) act as regularization for human inference<!-- FACT-D25-054 -->[^hawkins-2004].

abstract_reasoning: Overfitting trains a reasoner to ask: What is the model (or rule, or procedure), and what is its capacity to fit patterns<!-- FACT-D25-055 -->[^vapnik-1998]? What training data was used, and how representative is it of the target? Has out-of-sample performance been measured, and how does it compare to in-sample performance? Where does the gap come from — fitted noise, fitted idiosyncrasies, fitted distributional features? What structural interventions (more data, simpler model, regularization, feature selection, inductive biases) are appropriate? Where in non-ML contexts (scientific finding, organizational procedure, human judgment) might the same failure mode be operating? How is overfitting distinguished from distribution shift in the observed failure? What is the bias-variance decomposition of the learned model — is high error from bias (underfitting) or variance (overfitting)<!-- FACT-D25-056 -->[^geman-bienenstock-doursat-1992]? The mature reasoner holds overfitting and generalization as central diagnostic frames, recognizing that most claims about learned-system effectiveness rest on out-of-sample validation.

knowledge_transfer:
Role mappings across domains:

- **Model / learner** ↔ ML model / statistical
  estimator / scientific theory / organizational
  procedure / human rule
- **Training data / experience** ↔ training set /
  sample / historical cases / personal history
- **Target distribution** ↔ test set / population /
  future cases / deployment conditions
- **Capacity** ↔ parameters / degrees of freedom /
  flexibility / rule specificity
- **In-sample performance** ↔ training accuracy /
  fit / historical backtest / self-reported
  success
- **Out-of-sample performance** ↔ test accuracy /
  generalization / live trading / future
  deployment / new-case performance
- **Regularization** ↔ L1/L2 / prior / simplicity
  preference / general-principle training /
  robustness check

A data scientist evaluating a classifier, a
quantitative investor backtesting a strategy, a
research methodologist evaluating a finding's
replicability, and an organizational consultant
examining whether procedures will survive a market
shift are all doing the same structural work: specify
the training data and target, measure the in-sample
vs out-of-sample gap, identify the overfitting
mechanism, and apply capacity or regularization
remedies. The same diagnostic — "model, training,
target, gap, mechanism, remedy?" — applies across
their contexts, with the same failure modes (mistaking
in-sample fit for success, skipping out-of-sample
testing, choosing complexity without regularization)
in each.

formal_abstract:
A decision tree grown to arbitrary depth on a training set of 1000 labeled examples of iris flowers<!-- FACT-D25-057 -->[^hastie-tibshirani-friedman-2009] exemplifies the canonical overfitting pattern. Model capacity: essentially unlimited — the tree can memorize every training example through many splits. Training performance: 100% accuracy (every example classified correctly). Test performance on held-out iris examples: drops substantially — the deepest branches captured specific training examples' quirks (small measurement noise, rare combinations) that don't generalize. Pruning the tree to limited depth (say, 3 or 4), or using random-forest averaging, reduces training accuracy modestly but improves test accuracy substantially — the capacity reduction regularizes against overfitting. This is the textbook demonstration and the standard intuition pump in ML courses, showing that high in-sample performance combined with poor out-of-sample performance is the overfitting signature.

**Mapped back:** The decision tree / iris example isolates the mechanism (capacity fits noise), the diagnosis (train-test gap), and the remedy (regularization via depth limitation) in a single transparent case.

applied_industry:
A hedge fund developing an equity long-short strategy using 20 years of historical data illustrates overfitting at institutional scale<!-- FACT-D25-058 -->[^domingos-2012]. Strategy: elaborate rule combining dozens of signals (fundamentals, technicals, macro, sector effects). In-sample backtest: strong performance across the historical period with high risk-adjusted returns. Out-of-sample (the future) performance after deployment: much weaker, often negative. Mechanism: parameters were tuned to patterns specific to the 2000s financial cycle, idiosyncratic sector rotations, and particular crises that do not repeat identically; the many degrees of freedom in the rule combined with implicit data snooping (iterative refinement against history) produced in-sample fit to noise and period-specific patterns. Industry practice — walk-forward validation, parameter stability tests, stress testing against alternative periods, preference for simpler rules with fewer parameters, out-of-sample trading periods before deployment — are direct responses to this failure mode<!-- FACT-D25-059 -->[^murphy-2012]. The structural kinship with the decision-tree case is precise — capacity, training, target, gap, mechanism, remedy — despite the shift from classroom ML to institutional finance.

**Mapped back:** The hedge-fund strategy case shows that overfitting is not ML-specific but a general failure of empirical optimization when facing noisy data with many degrees of freedom and implicit data snooping during development.

prose:
_(Pass B — pending; see `tracker/v2_upgrade.md`.)_

### 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 (8):** `core_model_first`, `false_convergence_prevention`, `iterative_refinement_loop`, `layered_model_validation`, `objective_function_alignment`, `overoptimization_guardrail`, `parsimony_filter`, `system_archetype_diagnosis`

notes: Overfitting is foundational to statistical learning theory, the bias-variance decomposition, and the entire inferential discipline of empirical science and machine learning. The concept originated in the statistical literature (Fisher's distinction between fitting and prediction) but found its sharpest formulation in the ML and computational-learning literature through the work of Geman et al. (1992), Vapnik's structural-risk-minimization framework, and contemporary cross-validation and regularization practice. The phenomenon is both mathematically clear (imperfect correlation produces regression; finite sample sizes produce noise-fitting) and practically slippery (the intuition to credit causes for observed changes is strong; out-of-sample testing requires discipline). Modern deep learning has complicated the narrative — neural networks with many more parameters than training samples can still generalize well, suggesting that capacity alone does not determine overfitting (the "double descent" phenomenon, Belkin et al. 2019). Still, the overfitting frame remains central: practitioners still validate on held-out data, use regularization, and understand generalization as the core challenge of empirical modeling.