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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 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 the same event into named sub-events, violating the probability axioms. Formalised by Tversky and Koehler's support theory, the mechanism is that judgments respond to the description, not the event: each named sub-event recruits its own cognitive support, and unpacking forces retrieval of instances the coarse description failed to activate. So P(A) < P(A1) + ... + P(An), with a known upward sign.

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.

  • Medical risk assessment — "any complication" estimated below the summed named complications.
  • Expert forecasting and elicitation — decomposed scenarios over-counting unless corrected.
  • Insurance valuation — cover for "any cause" priced below the summed specific causes.
  • Jury and legal-evidence reasoning — listed alternatives outrunning "some other explanation."
  • Survey and market research — buying reasons listed versus bundled shifting the total.

Clarity

Naming the effect makes a tacit elicitation assumption visible and refutes it: that one event earns one probability, that granularity of description is inert. It exposes granularity as a hidden parameter under every probability judgment. A forecaster facing an irreconcilable packed and unpacked total no longer reaches for the wrong fix ("inconsistent expert," "can't add") but asks which description recruited more support and at which grain the answer is wanted — separating genuine disagreement from a solicitation artifact, with the corrective falling straight out.

Manages Complexity

Probability elicitation throws off a sprawl of puzzling discrepancies, each looking case by case like its own pathology. The effect collapses that sprawl into one regularity with a definite sign: unpacking inflates the total, never deflates it. The reconciliation problem reduces to a single tracked quantity — the grain of description — and one mechanism. The analyst reads off the direction of the gap without re-deriving the case, sizes it from two parameters, and follows a tight branch: packed-versus-unpacked mismatch is the effect, not an error to chase.

Abstract Reasoning

The effect licenses a grain-of-description diagnostic reasoning from a mismatch to its source, carrying a known sign. A boundary move sorts which mismatches are the effect and which are real disagreement. A predictive move sizes the gap from the number and salience of sub-events. An interventionist corollary solicits at the grain of aggregation wanted. An attribution move reframes many domains as one regularity, and boundary-drawing scopes it to a judging agent facing a description contrast.

Knowledge Transfer

Within judgment-and-decision-making the effect transfers as a working diagnostic, cleanly because the substrate is constant: medical risk, forecasting, insurance, juries, and surveys are one mechanism in different content, and the whole apparatus and vocabulary carry. Beyond elicited judgment, two kinds: instrument-reach (any procedure eliciting a judged probability over two descriptions inherits it literally, but not computed quantities — that over-reading is a category error), and looser "parts swell the whole" uses that are analogy. Those belong to the parent framing / description-dependence, not the named effect.

Relationships to Other Abstractions

Local relationship map for Subadditivity EffectParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Subadditivity EffectDOMAINPrime abstraction: Partition — is part ofPartitionPRIMEPrime abstraction: Probability — presupposesProbabilityPRIMEPrime abstraction: Framing — is a decomposition ofFramingPRIME

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

Neighborhood in Abstraction Space

Subadditivity Effect sits in a sparse region of the domain-specific corpus (72nd 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