Subadditivity Effect¶

Diagnose why the judged probability of an event named as a whole comes in reliably below the sum of judged probabilities for its named parts — because unpacking recruits more cognitive support — reading the known upward sign off which figure was solicited packed versus partitioned.

Core Idea¶

The subadditivity effect is the finding in probability-judgment research that the judged probability of an event described as a single whole is reliably less than the sum of judged probabilities for an exhaustive partition of that same event into separately named sub-events. Asked "what is the probability of death from a natural cause?", respondents give a number consistently lower than the sum they assign when asked separately about death from heart disease, death from cancer, death from respiratory illness, and death from any other natural cause — even though those categories are logically exhaustive and the partition's probabilities should sum to the whole-event probability by the axioms of probability theory.

The mechanism was formalised by Tversky and Koehler (1994) in support theory, which proposes that probability judgments respond to the description of an event rather than to the event itself. Each named sub-event recruits its own cognitive support — a representation of evidence and scenarios relevant to that specific description. A packed description (the event named as a whole) recruits less total support than an unpacked description listing each component separately, because the unpacking forces the retrieval of instances and scenarios that the coarse-grained description fails to activate. The result is that unpacking an event into named pieces inflates the total judged probability above the packed-form judgment: P(A) < P(A₁) + P(A₂) + … + P(Aₙ) when {A₁…Aₙ} partition A. The gap is proportional to the number and salience of the named sub-events and is robust across elicitation formats — direct probability estimates, betting odds, and willingness-to-pay for insurance — and across content domains including medical risk, legal evidence, and expert forecast elicitation.

Structural Signature¶

Sig role-phrases:

the judged event — a well-defined event whose probability is to be elicited from a judging agent
the packed description — the event named as a single whole
the unpacked description — an exhaustive partition of the same event into separately named sub-events
the elicitation step — probability judgments solicited for the packed form and for each sub-event of the unpacked form
the support mechanism — each named description recruits its own cognitive support (instances, scenarios); a packed form recruits less total support than its listed parts
the directional violation — the summed sub-event judgments reliably exceed the packed judgment, P(A) < P(A₁)+…+P(Aₙ), with a known upward sign
the gap drivers — magnitude scales with how many sub-events the unpacking introduces and how salient each is
the corrective discipline — solicit at the grain of aggregation actually wanted, or apply a support-theory correction at the unpacking step

What It Is Not¶

Not innumeracy or an arithmetic mistake. The subject is not failing to add: the packed and unpacked figures are each elicited as direct probability judgments, and the gap appears even when no addition is asked of the respondent. The defect is that the two descriptions recruit different support, not that the person sums their components wrongly.
Not measurement noise or respondent inconsistency. A noisy elicitation gives a gap of uncertain sign that washes out on average; subadditivity gives one of known direction — the unpacked total reliably runs high — replicating across formats and content domains. It is a structured, signed regularity, not a complaint about flaky survey responses.
Not a claim about probabilities that are computed rather than judged. The effect is a property of judged probabilities under a description contrast. A frequency tallied from data, or a model's marginal summed from its own components, has no support-recruiting agent and no unpacking step, so a mechanical sum that fails to add is a different problem entirely — calling it subadditivity is a category error.
Not a law that the parts always over-count. The inflation is conditional on a packed whole being contrasted with an unpacked, exhaustive partition that introduces newly named sub-events. With a single grain of description, or sub-events too coarse or unfamiliar to recruit fresh support, the gap shrinks toward zero; the effect needs the description contrast to exist at all.
Not the conjunction fallacy. The conjunction fallacy is judging a conjunction (Linda is a bank teller and a feminist) more probable than one of its conjuncts — a single description rated against a logically stronger one. Subadditivity concerns a disjunctive partition unpacked into named alternatives whose summed judgments exceed the whole. Both violate the probability axioms via description-dependence, but the failing constraint differs.

Scope of Application¶

Subadditivity lives across the probability-elicitation subfields of judgment-and-decision-making — wherever a judging agent issues probabilities over both a packed whole and an unpacked partition of one event — and its reach is within that domain; the looser "parts swell the whole" analogues belong to its framing parent, not here.

Medical risk assessment and communication — physicians' and patients' estimate of "any complication" comes in below the summed named complications, so the wording of a risk disclosure materially shifts the judged probability.
Expert forecasting and elicitation — decomposing a forecast into named scenarios systematically over-counts unless the unpacking is corrected, which is why structured protocols (Superforecasting, IDEA) deliberately toggle between packed and unpacked descriptions to de-bias.
Insurance valuation and willingness-to-pay — cover for "any cause" is priced below the sum of cover for named specific causes, distorting both coverage choices and premium-setting.
Jury and legal-evidence reasoning — listing specific alternative explanations inflates jurors' summed probability for the alternatives above their figure for "some other explanation than the prosecution's" stated as a whole.
Survey and market research — asking buying intent decomposed by reason ("for reason A? B? C?") yields a higher total than the bundled question, biasing demand estimates.
Support theory itself — the effect is the empirical anchor of the claim that probability judgment tracks the description of an event, not the event, making it the load-bearing datum of that theoretical apparatus.

Clarity¶

Naming the subadditivity effect makes a tacit assumption in probability elicitation visible and then refutes it: that one event, however described, earns one probability — that the granularity of description is inert. The effect exposes that granularity as a hidden parameter sitting under every probability judgment. With the label, a forecaster confronting a packed estimate and an unpacked total that fail to reconcile no longer reaches for the wrong fix — "the expert was inconsistent," "the subject can't add" — but asks the sharp structural question: which description recruited more support, and is the answer wanted at the packed or the unpacked grain? That separates a genuine disagreement between two estimates from an artifact of how each was solicited.

It also sharpens a distinction the field's procedures otherwise blur: the difference between an event and a description of an event, and with it the difference between eliciting a probability and aggregating component probabilities into one. The corrective falls straight out of the named effect — solicit at the level of aggregation you actually want, or apply a support-theory correction when components must be combined — because the effect locates the inflation precisely at the unpacking step rather than in the subject's arithmetic or sincerity. The practitioner can now ask whether a number was built by bundling or by partitioning, and read the likely direction of its bias from that alone.

Manages Complexity¶

Probability elicitation throws off a sprawl of puzzling discrepancies: the same forecaster's "any complication" estimate fails to match the sum of the named complications; insurance for "any cause" prices below the components; jurors' summed alternatives outrun their figure for "some other explanation"; market-research totals shift when buying reasons are listed versus bundled; expert panels over-count when scenarios are decomposed. Treated case by case, each looks like its own pathology — arithmetic error, inconsistency, a bad survey, an unreliable expert — and the analyst is forced to re-diagnose every mismatch from scratch across medical, legal, insurance, and forecasting content. The subadditivity effect collapses that sprawl into one regularity carrying a definite sign: unpack a packed event into named pieces and the total judged probability inflates, never deflates, with P(A) < P(A₁) + … + P(Aₙ) for any exhaustive partition. The reconciliation problem reduces to a single tracked quantity — the grain of description at which each number was solicited — and a single mechanism, support recruited by descriptions rather than events. Knowing only which of two estimates was built by bundling and which by partitioning, the analyst reads off the direction of the gap (the unpacked total runs high) without re-deriving the case, and sizes it from two parameters the mechanism names: how many sub-events the unpacking introduced and how salient each is. The branch structure is correspondingly tight: a mismatch between a packed and an unpacked figure is the effect (correct at the chosen grain, biased relative to the other) rather than an error to chase; two packed figures that disagree, or two unpacked ones, are a genuine disagreement to adjudicate. What was a high-dimensional "which elicitations misbehave, and why each" problem becomes a one-parameter read on description granularity with a known-sign consequence — and the corrective falls out of the same compression: solicit at the grain you want, or correct at the unpacking step, because that is where the inflation is located, not in the subject's arithmetic or sincerity.

Abstract Reasoning¶

The subadditivity effect licenses a grain-of-description diagnostic that the forecaster or risk analyst runs whenever two probability figures for the same event fail to reconcile. The signature move reasons from the mismatch to its source: a packed estimate ("any complication," "death from a natural cause") that comes in below the sum of its named components is read not as the subject's arithmetic error or inconsistency but as the unpacked total recruiting more support than the packed form — the inflation located precisely at the unpacking step, where naming sub-events forces retrieval of instances and scenarios the coarse description failed to activate. The inference carries a known sign, which is what makes it powerful: unpacking an exhaustive partition inflates the total, never deflates it, so P(A) < P(A₁) + … + P(Aₙ), and the analyst reasons from "this figure was built by partitioning" to "it runs high relative to the bundled judgment" without re-deriving the case. The discriminating boundary move sorts which mismatches are the effect and which are real: a packed figure that disagrees with an unpacked one is the effect — each correct at its own grain, biased relative to the other — and is not an error to chase; two packed figures that disagree, or two unpacked ones, are a genuine disagreement to adjudicate. So the analyst reasons from the grain at which each number was solicited to whether a discrepancy needs reconciling at all.

The predictive move sizes the gap from two parameters the mechanism names: how many sub-events the unpacking introduced and how salient each is — more named pieces, and more vivid ones, predict a larger inflation — so the analyst forecasts the magnitude of the over-count from the structure of the elicitation before seeing the numbers, and predicts the effect will appear across direct estimates, betting odds, and willingness-to-pay alike because all are description-driven. The interventionist corollary falls straight out of locating the inflation at the unpacking step rather than in the subject: to get an aggregate probability, solicit at the level of aggregation actually wanted rather than summing separately-elicited components, or apply a support-theory correction when components must be combined. The analyst reasons that the lever is the grain of the question, not an appeal to the expert's consistency or care — and that decomposing a forecast into named scenarios will systematically over-count unless the unpacking is corrected for. The attribution move reframes the whole class of mismatches — physician risk estimates, insurance pricing for "any cause," jurors' summed alternatives outrunning "some other explanation," market-research totals shifting when reasons are listed versus bundled — as one regularity keyed to a single hidden parameter (description granularity) operating by one mechanism (support recruited by descriptions, not events), so the analyst stops re-diagnosing each domain and reads every such discrepancy off the same packed-versus-unpacked comparison. The boundary-drawing scope is the elicitation setup itself: the effect requires a judging agent issuing probabilities over two descriptions of one event, a packed whole and an unpacked partition, so the analyst predicts subadditivity wherever that contrast is in play and reasons that without a description contrast — a single grain, or an event whose probability is computed rather than judged — there is no unpacking step for support to inflate.

Knowledge Transfer¶

Within judgment-and-decision-making the subadditivity effect transfers as a working diagnostic, and it transfers cleanly because the substrate is constant: anywhere a judging agent issues probabilities over both a packed whole and an unpacked partition of the same event, the same regularity, the same known sign, and the same correction apply. The medical-risk subfield ("any complication" priced below the summed named complications), expert forecasting and elicitation (decomposed scenarios over-counting unless the unpacking is corrected), insurance valuation (cover for "any cause" worth less than the summed specific causes), jury reasoning (listed alternatives outrunning "some other explanation"), and survey/market research (buying reasons listed versus bundled) are not separate phenomena requiring separate diagnosis but one mechanism seen in different content. What carries intact across them is the whole apparatus — the packed-versus-unpacked comparison, the support-recruitment account, the inflation located at the unpacking step, and the corrective (solicit at the grain of aggregation wanted, or apply a support-theory correction). The vocabulary travels with it: "support," "packed/unpacked description," "exhaustive partition," "additivity violation" mean the same thing in a clinic, a courtroom, and a forecasting tournament, because all three are the same elicitation setup wearing different topics.

Beyond elicited probability judgment the transfer is of two kinds, and they should be kept apart. First, where the construct genuinely reaches, it reaches because its narrow precondition still holds, not because it has been generalized: any procedure that elicits a numeric probability over a describable event — automated risk scoring that prompts a human grader, structured analytic techniques, even an estimator queried at two grains — inherits subadditivity literally if it solicits a packed and an unpacked figure. The boundary to watch there is over-reading, not metaphor: the effect is a property of judged probabilities under a description contrast, so it has nothing to say about a probability that is computed rather than judged (a frequency tallied, a model's marginal summed from its own components), and invoking "subadditivity" for a mechanical sum that fails to add is a category error — the precondition (a support-recruiting judging agent, two descriptions) is absent, so there is no unpacking step for support to inflate.

Second, the looser cross-domain use — "the parts add up to more than the whole" applied to budgets, attention, organizational estimates, any quantity that swells when itemized — is analogy. It renames the components (event → line item, support → vividness, partition → checklist) and borrows the shape of the result while dropping the mechanism that gives the original its predictive force: there is no elicited probability, no description-keyed support, and no exhaustive-partition constraint to make the inflation directional and bounded. The honest report is that the cross-domain lesson belongs not to "subadditivity" as named but to the more general pattern the effect instantiates — that the framing or granularity of a question changes the answer, which is description-dependence (and upward, framing). That parent really does recur across substrates; subadditivity is its precise, sign-carrying, probability-judgment-bound special case, and the named machinery — support theory, the additivity violation, the packed/unpacked elicitation — stays home. The line to mark, then, is twofold: instrument-reach (it transfers literally wherever genuine probability judgment over two descriptions occurs) versus over-reading (do not apply it to computed quantities), and mechanism versus metaphor (carry the framing/description-dependence parent across domains, not the named effect). See Structural Core vs. Domain Accent.

Examples¶

Canonical¶

The founding demonstrations come from Tversky and Koehler's 1994 support theory. In one, respondents estimated the probability that a randomly selected death was due to a given cause. Asked directly about "death from natural causes," they gave a figure markedly lower than the sum they produced when the same category was unpacked into "heart disease," "cancer," and "other natural causes" and estimated separately — even though those components are exhaustive. Likewise, the probability assigned to "death from an unnatural cause" rose when it was unpacked into accident, homicide, and other. The pattern is directional and reliable: naming the components forces retrieval of specific scenarios and evidence the coarse packed label leaves dormant, so each named piece recruits its own support and the unpacked total inflates above the packed judgment, in violation of the additivity the probability axioms require.

Mapped back: "Death from natural causes" is the judged event in the packed description, and its breakdown into heart disease / cancer / other is the unpacked description — an exhaustive partition. That the named pieces call up their own scenarios is the support mechanism, and the summed components reliably exceeding the packed figure is the directional violation with its known upward sign.

Applied / In Practice¶

A clinical study by Redelmeier, Koehler, Liberman, and Tversky (1995) found subadditivity among practicing physicians. Presented with a hypothetical patient's case, one group of clinicians estimated the probability of a specified diagnosis against a packed residual category ("none of the above" / some other diagnosis), while another group had that residual unpacked into several named specific alternative diagnoses. The unpacked group's summed probabilities for the named alternatives substantially exceeded the packed group's probability for the lumped residual, even though the alternatives were meant to exhaust the same space. The import is direct: a differential-diagnosis prompt or checklist that lists specific competing diagnoses pulls more probability toward them than a coarse "other," so the wording of the elicitation shifts a physician's judged likelihoods — a real bias in risk communication and clinical decision support.

Mapped back: The lumped "other diagnosis" is the packed description and the listed named alternatives are the unpacked description; soliciting probabilities for each is the elicitation step. The named diagnoses recruiting their own clinical scenarios is the support mechanism, the summed alternatives overshooting the residual is the directional violation, and the lesson to solicit at the grain actually wanted is the corrective discipline.

Structural Tensions¶

T1: Inflation to be corrected versus neglect being repaired (which figure is the error). Support theory frames the unpacked total as inflated — a violation of additivity to be discounted. But the mechanism that produces it, retrieval of scenarios and evidence the coarse label leaves dormant, is the recovery of genuinely relevant possibilities the packed form failed to activate. So the very same fact admits two normative readings: the unpacked figure runs too high because naming pieces over-recruits support, or the packed figure runs too low because bundling neglects real components that deserved weight. The effect fixes the direction of the gap but not which end is the mistake, and treating the packed judgment as the truth quietly assumes coarse description under-neglects nothing — which is exactly what unpacking sometimes disproves. Debiasing toward the packed figure may be discarding real evidence; debiasing toward the unpacked may be banking an artifact. Diagnostic: Are the named sub-events recruiting spurious support that inflates, or legitimate possibilities the packed form wrongly left dormant?

T2: A correction that presupposes a canonical grain versus a truth that is description-relative (which grain to solicit at). The corrective discipline says "solicit at the grain of aggregation actually wanted." But the effect's deeper claim is that probability judgment tracks the description, not the event — so there is no single judged probability that all grains would converge on, and no grain is privileged as the true one. The correction therefore does not resolve the mismatch; it relocates it to a choice the effect itself cannot adjudicate: which grain is the one wanted, and why that one. For a decision that will itself be taken at some grain, the answer may be available; for a general "what is the probability," it is not, and the practitioner who picks a grain is legislating the answer rather than measuring it. The tool dissolves the paradox by denying there was ever a grain-independent number to find. Diagnostic: Is the grain of elicitation fixed by the decision the probability will feed, or is a grain being chosen arbitrarily and its artifact reported as the probability?

T3: Known sign versus soft magnitude (a confident direction that cannot be sized). The effect's power is a known upward sign: the unpacked total reliably runs high, so an analyst forecasts the direction of the bias before seeing the numbers. But the same mechanism makes the magnitude depend on how many sub-events the unpacking introduced and how salient each is — soft, elicitation-specific quantities with no fixed scale. So the diagnosis is strong on direction and weak on size: it says "this figure is too high relative to that one" without saying how much, which is enough to flag a mismatch but not enough to compute a corrected value from the two figures alone. The interventionist promise — apply a support-theory correction — is bounded by this: correcting the sign is licensed, correcting to a specific number requires modeling the salience of each named piece. Diagnostic: Is only the direction of the bias needed here, or a magnitude the gap drivers (count and salience of sub-events) would have to be modeled to supply?

T4: Explaining the mismatch versus explaining it away (the boundary the diagnostic can overrun). The boundary move is genuinely useful: a packed-versus-unpacked disagreement is the effect and need not be chased, while two packed figures (or two unpacked ones) that disagree are a real disagreement to adjudicate. But the same move is a ready laundry: any inconvenient disagreement between two estimates can be reclassified as "just subadditivity" and dismissed, when in fact the two figures also differ in substance, evidence, or judgment, not only in grain. The diagnostic that rescues a forecaster from chasing an artifact can, misapplied, suppress a genuine dispute by attributing it wholly to description granularity. The precondition for waving a mismatch away is that the only relevant difference is packed-versus-unpacked — which is rarely verified before the label is invoked. Diagnostic: Do the two estimates differ solely in grain of description, or is a substantive disagreement being written off as mere subadditivity?

T5: Sign-carrying precision versus over-reading beyond judgment (the precondition is narrow on purpose). What makes subadditivity predictive rather than a vague "parts swell the whole" is a tight precondition: a judging agent issuing probabilities over two descriptions of one event, a packed whole and an unpacked partition. That precision is exactly what bounds its reach. It has nothing to say about a probability that is computed rather than judged — a frequency tallied, a model's marginal summed from components — because there is no support-recruiting agent and no unpacking step; calling a mechanical sum's failure "subadditivity" is a category error. The same rigor that gives the effect a known sign forbids the intuitive generalization to budgets, attention, or any itemized quantity that swells, which belong to the looser framing parent. The construct is powerful and narrow for one reason: the mechanism it names only exists where a describing mind judges. Diagnostic: Is the probability here judged by an agent over two descriptions, or computed — in which case a failure to add is a different problem and not this effect?

T6: Autonomy versus reduction (a named probability-judgment effect or the framing parent it instantiates). "Subadditivity effect" is a load-bearing, canonically studied construct: within judgment-and-decision-making it transfers as a working diagnostic across medical risk, expert elicitation, insurance, jury reasoning, and survey research, because each is the same elicitation setup wearing a different topic, with the support account and corrective intact. But the cross-substrate lesson — that the framing or granularity of a question changes the answer — belongs to the more general framing / description-dependence parent, not to "subadditivity" as named; the looser "parts add up to more than the whole" analogues (budgets, attention, itemized estimates) are that parent, having dropped the elicited probability, the description-keyed support, and the exhaustive-partition constraint that make this effect directional and bounded. What stays home is the named machinery: support theory, the additivity violation, the packed/unpacked elicitation. Diagnostic: Resolve toward the framing/description-dependence parent when carrying a granularity-changes-the-answer lesson across domains; toward the named effect when diagnosing an actual probability judgment solicited at two grains in situ.

Structural–Framed Character¶

The subadditivity effect sits at framed-leaning on the structural–framed spectrum — a genuine, sign-carrying regularity, but a regularity about a judging practice, in the same register as a framed-leaning judgment effect like scope neglect. On human_practice_bound it is decisively framed: the effect exists only where a describing mind judges. The entry makes this its central boundary — subadditivity is a property of judged probabilities under a description contrast, and has nothing to say about a probability that is computed (a frequency tallied, a model's marginal summed from its own components), because a mechanical sum has no support-recruiting agent and no unpacking step. Remove the judging agent and the effect vanishes entirely; it does not run observer-free the way a slab sinks or a shield rebounds. Evaluative_weight is also framed-leaning: subadditivity is named as an additivity violation — a departure from what the probability axioms require — so the label carries a normative charge (the judgment is, by a coherence standard, wrong), even as the entry carefully notes the gap fixes a direction without fixing which end is the error. Institutional_origin points framed: the construct is the load-bearing datum of a specific theoretical apparatus (Tversky and Koehler's support theory), and its vocabulary — support, packed/unpacked description, exhaustive partition — is that theory's furniture. On vocab_travels it scores low-to-moderate: the terms mean the same in a clinic, a courtroom, and a forecasting tournament, but only because those are all the same elicitation setup wearing different topics; off the probability-judgment substrate the vocabulary loses its referents. The one criterion with a structural tilt is import_vs_recognize: within genuine probability judgment the effect transfers as literal mechanism (recognition, not analogy) wherever a packed and an unpacked figure are solicited — but that reach is narrow by design, and the entry flags that the looser "parts swell the whole" uses are analogy to a more general parent.

The portable structural skeleton is a single one: description-dependence — the granularity or framing of the question changes the judged answer, here in the specific form that unpacking an event into named parts recruits more cognitive support and inflates the total. That skeleton genuinely recurs across substrates, which is exactly why it does not lift "subadditivity" off the framed-leaning position: the cross-domain reach belongs to the umbrella framing / description-dependence parent that the effect instantiates, not to the named effect, while subadditivity's distinctive content — the support-recruitment mechanism, the known upward sign, the packed/unpacked elicitation, the additivity-violation framing — is precisely the domain-accented part that stays home and gives the effect its bounded, directional bite. Its character: a normatively-charged, judgment-bound description-dependence effect, structural only in the framing skeleton it borrows from its parent and specializes into a sign-carrying law of elicited probability.

Structural Core vs. Domain Accent¶

This section decides why the subadditivity effect is a domain-specific abstraction and not a prime, and it carries the case for its domain-specificity — the argument turns on separating the thin description-dependence it shares with framing from the support-theory machinery that gives it a sign.

What is skeletal (could lift toward a cross-domain prime). Strip away the probability elicitation and a thin relational structure survives: the granularity or framing of a question changes the answer — how a thing is described, not what it is, moves the judgment. In subadditivity's specific form, partitioning a whole into named parts recruits more of whatever supports the judgment than naming the whole does, so the itemized total swells above the bundled figure. The pieces that travel are abstract — a describable object, two descriptions of it at different grain, and a judgment that tracks the description rather than the object. That skeleton is genuinely substrate-portable, which is exactly why the "parts swell the whole when itemized" pattern recurs across budgets, attention, and organizational estimates, and why the entry names its parent as the general pattern that carries it: framing (description-dependence — the framing or granularity of a question changes the answer). But it is the core subadditivity shares, not what makes it distinctive.

What is domain-bound. Almost everything that makes this the subadditivity effect in particular is judgment-and-decision-making apparatus and none of it survives extraction. The precondition is narrow by design: a judging agent issuing probabilities over two descriptions of one event — a packed whole and an unpacked exhaustive partition. The mechanism is Tversky and Koehler's support theory: each named description recruits its own cognitive support (instances, scenarios), and a packed form recruits less than its listed parts. The signature is a known upward sign — an additivity violation, P(A) < P(A₁)+…+P(Aₙ) — sized by the count and salience of the sub-events, with a matching corrective (solicit at the grain wanted, or apply a support-theory correction at the unpacking step). The decisive test: remove the judging agent — replace the elicited probability with a frequency tallied from data or a model's marginal summed from its own components — and there is no support-recruiting mind and no unpacking step, so a mechanical sum that fails to add is a different problem entirely; calling it "subadditivity" is a category error. The effect is constituted by the very judging practice the prime bar asks it to shed.

Why this does not clear the prime bar. A prime is a relational structure whose vocabulary travels and whose cross-domain transfer is recognition of the same mechanism, not analogy. Subadditivity's transfer is bimodal. Within probability judgment it travels intact as mechanism — the packed-versus-unpacked comparison, the support account, and the corrective carry across medical risk, expert elicitation, insurance valuation, jury reasoning, and survey research without translation, because support, packed/unpacked description, and exhaustive partition mean the same in a clinic, a courtroom, and a forecasting tournament; each is the same elicitation setup wearing a different topic. Beyond it — "the parts add up to more than the whole" applied to budgets, attention, any itemized quantity that swells — it travels only by analogy: the use renames the components (event → line item, support → vividness, partition → checklist) and borrows the shape of the result while dropping the elicited probability, the description-keyed support, and the exhaustive-partition constraint that make the inflation directional and bounded. And when the bare structural lesson is needed cross-domain — that the framing or granularity of a question changes the answer — it is already carried, in more general form, by the parent subadditivity instantiates: framing / description-dependence. The cross-domain reach belongs to that parent; "the subadditivity effect," as named, is the precise, sign-carrying, probability-judgment-bound special case, and its distinctive machinery — support theory, the additivity violation, the packed/unpacked elicitation — should stay home.

Relationships to Other Abstractions¶

Current abstraction Subadditivity Effect Domain-specific

Parents (3) — more general patterns this builds on

Subadditivity Effect is part of Partition Prime

An exhaustive Partition is a constituent of the Subadditivity Effect because the unpacked alternatives must be non-overlapping and collectively cover the packed event.
Subadditivity Effect presupposes Probability Prime

The Subadditivity Effect presupposes Probability because its signature is a directional violation of additivity among judged probabilities for one event and its exhaustive partition.
Subadditivity Effect is a decomposition of Framing Prime

The Subadditivity Effect is Framing specialized to probability elicitation, where logically equivalent packed and unpacked descriptions produce predictably different judgments.

Hierarchy paths (5) — routes to 4 parentless roots

Subadditivity Effect → Probability → Measure → Aggregation → Micro Macro Linkage

Show alternative paths (4)

Not to Be Confused With¶

The conjunction fallacy. The sibling probability-judgment error, but on a disjunctive-versus-conjunctive axis: the conjunction fallacy is judging a conjunction (Linda is a bank teller and a feminist) more probable than one of its conjuncts — a single description rated against a logically stronger one. Subadditivity concerns an exhaustive partition unpacked into named alternatives whose summed judgments exceed the whole. Both are description-dependence violating the axioms, but the failing constraint differs. Tell: is the violation that a conjunction is rated above its own conjunct (conjunction fallacy), or that a sum of named parts exceeds the packed whole (subadditivity)?
Partition dependence. The closely related finding that judged probability shifts with how the outcome space is carved up — the same event gets different probability depending on which partition frames the question. It is the near-neighbor within support theory, differing in emphasis: partition dependence stresses that any repartitioning moves the answer, while subadditivity names the directional consequence — unpacking into more named parts reliably inflates the total. Tell: is the claim that changing the partition changes the answer in some direction (partition dependence), or specifically that the unpacked total runs high against the packed whole (subadditivity)?
The availability heuristic. The tendency to judge probability by how easily instances come to mind. It resembles subadditivity's support mechanism — both turn on ease of retrieving scenarios — but availability is a general property of a single judgment (vivid events feel more likely), whereas subadditivity is a contrast between two descriptions of one event where unpacking forces retrieval the packed form left dormant. Tell: is a lone estimate distorted by how readily instances are recalled (availability), or is the effect the gap between a packed and an unpacked elicitation of the same event (subadditivity)?
Scope neglect / extension neglect. A framed-leaning judgment effect where valuation or probability fails to scale with the size of the affected set (willingness to pay barely rises from saving 2,000 to 200,000 birds). It is a cousin judgment bias, but it concerns insensitivity to magnitude, whereas subadditivity concerns sensitivity to description grain with a known upward sign. Tell: is the failure that the judgment ignores how large the quantity is (scope neglect), or that it changes with how finely the event is described (subadditivity)?
Mathematical subadditivity (a subadditive function). A pure namesake: in mathematics a function is subadditive when f(x+y) ≤ f(x)+f(y) — a formal property of computed quantities with no judging agent. The effect's own boundary forbids the conflation: subadditivity here is a property of judged probabilities under a description contrast, so a mechanical sum that fails to add is a different problem entirely. Tell: is there a support-recruiting mind judging two descriptions of an event (the effect), or a formula being evaluated (the mathematical namesake)?
The framing / description-dependence parent it instances. The broad, substrate-neutral pattern — the framing or granularity of a question changes the answer — that subadditivity specializes into a sign-carrying law of elicited probability. The looser "the parts add up to more than the whole" analogues (budgets, attention, itemized estimates) belong to this parent, having dropped the elicited probability, the description-keyed support, and the exhaustive-partition constraint. Tell: is an actual probability being judged over a packed and an unpacked description (the effect), or is only the shape "itemizing swells the total" being borrowed (the framing parent)? (Treated more fully in a later section.)

Neighborhood in Abstraction Space¶

Subadditivity Effect sits in a sparse region of the domain-specific corpus (72^nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (309 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12