Revealed Preference Consistency Matrix¶
Relational consistency test — instantiates Revealed Preference Validation Against Indifference Curves
Assembles every 'chosen-over' relation from a choice history into a matrix and tests it for cycles and intransitivity that no single stable preference ordering could produce.
A choice can be perfectly reasonable on its own occasion and still be part of a contradiction. Revealed Preference Consistency Matrix looks across a chooser's whole history rather than at any single pick: it records every "A was chosen when B was affordable" relation in a matrix and then tests whether that web of relations can be reconciled with any single stable preference ordering. If the choices imply A over B, B over C, and C over A, no consistent preference exists — the chooser is cyclic. Its defining scope is relational and cross-occasional: it never asks whether one choice was dominated attribute-by-attribute; it asks whether the choices, taken together, form a self-consistent ordering.
Example¶
A company reviews three years of procurement decisions across a category of interchangeable industrial suppliers, wanting to codify a "preferred vendor" ordering. Each quarter's award, at that quarter's prices and volumes, is entered as a revealed-preference relation: awarding Vendor A over B when B's bid was also within budget means A is revealed preferred to B. Assembled into a matrix, most relations line up into a clean ranking — until the test finds a cycle: over successive quarters the firm's awards imply A ≻ B, B ≻ C, and C ≻ A, all under comparable budgets.
The cycle is the finding. It means there is no single consistent preference the procurement team was expressing — something else is driving the awards: rotating relationships, shifting internal sponsors, or negotiation gamesmanship. The matrix doesn't say which; it says the "stable preference ordering" the firm hoped to codify does not exist in the data, and any policy built on one would be fiction. That verdict comes purely from the pattern of choices against each other, with no attribute comparison at all.
How it works¶
- Build the relation set. For each choice, record which affordable alternatives it was revealed-preferred to, populating a directed "chosen-over" matrix across the whole history.
- Close and test. Take the transitive closure and check for violations — cycles, or pairs revealed preferred in both directions — that no single ordering admits.
- Localize the breakdown. Identify the specific choices and cycles responsible, so the contradiction can be traced rather than merely declared.
- Grade the severity. Distinguish a handful of near-tie reversals from a pervasively cyclic record, since the two mean very different things for downstream inference.
Tuning parameters¶
- Axiom stringency — which consistency law is imposed: the weak axiom (pairwise) or the generalized axiom (full transitivity/no cycles). Stricter axioms catch subtler contradictions but flag more borderline cases.
- Relation threshold — how clearly one option must have been affordable-but-passed-over to count as "revealed preferred," filtering marginal comparisons.
- Temporal windowing — whether the whole history is treated as one preference or split into eras, since genuine preference change is not inconsistency.
- Violation tolerance — how many minor cycles are allowed before the ordering is judged unstable.
- Aggregation unit — one matrix per individual or a pooled matrix per segment, trading noise against the risk of mixing distinct orderings.
When it helps, and when it misleads¶
Its strength is that it validates the existence of a stable preference before anyone tries to estimate its shape: if the choice history is cyclic, there is no coherent indifference map to recover, and the matrix says so cleanly, pinpointing the offending choices.[1] It catches contradictions that per-choice checks structurally cannot, because the incoherence lives between occasions, not within one.
Its failure mode is mistaking genuine preference change for inconsistency. Tastes drift, prices carry information, and a chooser who reverses over three years may simply have changed — pooling those eras into one matrix manufactures a spurious cycle. The classic misuse is declaring a chooser "irrational" from a cyclic matrix when the real cause is an unmodeled context shift or the pooling of distinct people into one ordering. The guarding discipline is to window by time and segment before reading a cycle as incoherence, and to localize violations rather than condemn the whole record.
How it implements the components¶
Revealed Preference Consistency Matrix realizes the archetype's cross-occasional coherence test:
consistency_test_suite— it contributes the transitivity and cycle checks (weak and generalized revealed-preference axioms) over the full relation set.observed_choice_record— it consumes the choice history as a body of relations, treating the record collectively rather than one choice at a time.
It does not perform the single-occasion, attribute-by-attribute dominance check (feasible_option_set, attribute_bundle_model) — that is Dominance Violation Scan; this matrix tests choices against each other for cycles, not each choice against what was on the shelf.
Related¶
- Instantiates: Revealed Preference Validation Against Indifference Curves — it establishes whether a stable preference ordering exists at all before its shape is estimated.
- Consumes: Budget Set Reconstruction supplies the choice history and the affordability of the passed-over options each relation depends on.
- Sibling mechanisms: Budget Set Reconstruction · Choice Bundle Normalization · Marginal Substitution Estimator · Indifference Region Visualization · Dominance Violation Scan · Preference Reversal Probe · Choice Architecture Confound Audit · Stated vs Revealed Gap Report · Ethical Preference Inference Review
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: Revealed Preference Consistency Matrix operates as an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution because it assembles every 'chosen-over' relation from a choice history into a matrix and tests it for cycles and intransitivity that no single stable preference ordering could produce.
Independent corroboration: The frozen evidence defines Revealed Preference Consistency Matrix as 'Assembles every 'chosen-over' relation from a choice history into a matrix and tests it for cycles and intransitivity that no single stable preference ordering could produce', so its operative form is Analysis, Modeling & Optimization.
Nearest alternative: Representation, Specification & Plan — Revealed Preference Consistency Matrix includes features of a static representation, map, specification, schema, or prospective plan that externalizes information, but its defining operation is an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution.
Review outcome: Independent reviewer agreement; medium confidence.
Origin Attribution¶
Primary origin: Economics & Finance
Origin pattern: Single lineage
Present-day reach: Specialized
Rationale: Testing chosen-over relations for rationalizability is canonical revealed-preference economics.
Related originating lineages:
- Mathematics — Order theory and graph-cycle analysis supply the formal consistency test.
- Organizational & Management Science — Organizational design, management, and operational governance supplies a parallel or contributing lineage for the mechanism's defining operation: assembles every 'chosen-over' relation from a choice history into a matrix and tests it for cycles and intransitivity that no single stable preference ordering could produce.
Review resolution: Both blind reviewers agree that economics_finance is the primary historical origin. Explicit reconciliation of alternate origin disagreement starts from reviewer_a’s mechanism-specific evidence: Testing chosen-over relations for rationalizability is canonical revealed-preference economics. Reviewer A proposed alternates=mathematics, origin_mode=single_lineage, domain_reach=specialized, and encyclopedia_synthesis=false; reviewer B proposed alternates=organizational_management, origin_mode=single_lineage, domain_reach=specialized, and encyclopedia_synthesis=false. The final record retains every independently supported alternate from either review (mathematics, organizational_management) without an arbitrary cap, selects origin_mode=single_lineage to represent the combined lineage evidence, and keeps domain_reach=specialized and encyclopedia_synthesis=false from the more mechanism-specific assessment. Present-day transfer is recorded as reach and is not treated as proof of historical origin.
Review outcome: Reconciled after independent review; high confidence.
References¶
[1] The Generalized Axiom of Revealed Preference (GARP), from Sydney Afriat (1967) and later Hal Varian (1982), states that a finite set of choices is rationalizable by a well-behaved utility function exactly when it contains no revealed-preference cycles. A cyclic matrix is a GARP violation — a proof that no single utility function fits the behavior. withdrawn registry ↩