Petrie multiplier¶
A composition model in which equal individual rates of cross-group remarks yield unequal expected recipient exposure, amplified by the squared size ratio under its basic random-targeting assumptions.
Core Idea¶
The Petrie multiplier separates behavior rates from exposure rates. Each member of two groups is assigned the same propensity to direct a remark at the other group. When one group is much larger, its many potential sources concentrate events among fewer opposite-group recipients, while the minority group's events are diluted among many recipients.
The square-law comparison follows from the basic counting assumptions, not from a universal law of social behavior. Heterogeneous rates, repeated contacts, network structure, nonbinary grouping, and nonrandom targeting require extensions. The model is a thought experiment until its variables and assumptions are empirically measured.
Structural Signature¶
Sig role-phrases:
- Two groups — Partition the population into target-source categories with sizes m and w. It is population. Counterfactual: More groups or within-group targeting require a different exposure matrix.
- Equal propensity — Assigns the same per-person rate or probability of making cross-group remarks. It is assumption. Counterfactual: Different behavioral rates can dominate the composition effect.
- Cross-group targeting — Directs each event from one group to a member of the other. It is channel. Counterfactual: Within-group events do not follow the basic multiplier.
- Random target allocation — Spreads each source group's events uniformly across opposite-group recipients. It is distribution. Counterfactual: Network clustering or repeated targeting changes individual exposure.
- Group-size ratio — Creates more sources per available target in one direction than the other. It is imbalance. Counterfactual: With equal group sizes the composition multiplier disappears.
- Expected per-member exposure — Produces the modeled outcome for each target group. It is output. Counterfactual: An expectation does not predict every individual's experience or prove causation in observed data.
What It Is Not¶
- It is not evidence that actual groups offend at equal rates.
- It is not an empirical estimate of experienced sexism.
- It is not a generic multiplier effect.
- It is not valid unchanged for networked or within-group targeting.
- Closest near-miss. The model explains a composition-induced exposure asymmetry under equal propensity; it does not claim equal actual behavior or measure discrimination in a real setting without data.
Scope of Application¶
- Workplace composition. Illustrates why minority experience can differ from majority impressions.
- Exposure modeling. Distinguishes event production from per-recipient burden.
- Diversity analysis. Generates testable hypotheses about composition and reported experience.
- Simulation. Explores departures from equal rates and random targeting.
- Statistical communication. Demonstrates denominator effects without inferring individual intent.
Clarity¶
State group definitions and sizes, event type, per-person source-rate assumption, target-selection rule, observation period, and whether results are expectations, simulations, or measured data. Avoid binary-gender generalization and causal conclusions not supported by the model.
Manages Complexity¶
The multiplier compresses a directional interaction system into sources, targets, rates, and group sizes. It exposes how identical actor propensities can generate unequal recipient burdens and identifies exactly which structural and behavioral assumptions must be tested rather than argued from intuition.
Abstract Reasoning¶
- Define the two groups and count members.
- Specify the cross-group event and equal or unequal source rates.
- Declare how targets are selected.
- Compute total events from each source group.
- Divide by the number of recipients in the opposite group and compare expectations.
- Stress-test heterogeneity, networks, uncertainty, and empirical fit.
Knowledge Transfer¶
The transferable cargo is directional exposure accounting in an imbalanced bipartite population. It transfers to other interaction harms or benefits only with equivalent source, target, and allocation rules; it stops at rhetorical use of square law without a model.
Examples¶
Canonical¶
In a room with nine members of group A and one of group B, equal per-person cross-group remark rates generate many A-to-B sources concentrated on one recipient and few B-to-A events spread across nine recipients.
Mapped back: ratio → 9:1; propensity → equal; targeting → cross-group random; exposure → minority amplified.
Applied / In Practice¶
With equal group sizes and the same assumptions, expected per-person exposure is symmetric and the composition multiplier is one.
Mapped back: ratio → 1:1; exposure ratio → 1.
Applied / In Practice¶
Remarks travel mainly along a friendship network and one person is repeatedly targeted; the uniform-random Petrie calculation no longer describes individual exposure.
Mapped back: target allocation → clustered; basic model → violated.
Structural Tensions¶
T1 — Behavioral Equality versus Experiential Inequality. Identical source rates can coexist with unequal received rates because denominators differ.
Diagnostic: Which rate is being compared: acts made or acts received?
T2 — Explanatory Simplicity versus Social-Network Realism. Random targeting isolates composition but omits hierarchy, repeated interaction, and selection.
Diagnostic: How sensitive is the result to an explicit contact matrix?
T3 — Thought Experiment versus Empirical Claim. The algebra demonstrates possibility while real prevalence and effects require measurement.
Diagnostic: What data test each assumption and prediction?
Structural–Framed Character¶
Petrie Multiplier is hybrid: structurally a source–recipient denominator effect and framed by the social interpretation and assumptions of cross-group remarks.
Structural Core vs. Domain Accent¶
The core is a two-sided event process whose expected recipient load depends on both source and target population sizes. The domain accent supplies sexism, gender composition, questionable remarks, random targeting, Poisson variants, simulation, and empirical limits.
Instantiates / Related Primes¶
This entry is a kind of Formal Model.
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Approved root. Retrieved multiplier nodes concern unrelated mechanisms, so the frozen unparented placement is retained.
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Related — exposure rate, bipartite graph, base-rate effect, Lanchester square law, contact matrix, and Monte Carlo simulation. These provide mathematical analogues and extensions.
Relationships to Other Abstractions¶
Current abstraction Petrie multiplier Domain-specific
Parents (1) — more general patterns this builds on
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Petrie multiplier is a kind of Formal Model Domain-specific
The Petrie multiplier is a formal probabilistic composition model relating group proportions, equal individual remark rates, and unequal expected recipient exposure.The Petrie multiplier is a formal probabilistic composition model relating group proportions, equal individual remark rates, and unequal expected recipient exposure.
Hierarchy path (1) — routes to 1 parentless root
- Petrie multiplier → Formal Model → Representation → Abstraction
Neighborhood in Abstraction Space¶
Petrie multiplier sits in a moderately populated region (45th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Social Structure & Group Identity (12 abstractions)
Nearest neighbors
- Precision marketing — 0.87
- Kruskal–Wallis Test — 0.87
- N-of-1 Trial — 0.87
- Lincoln Index — 0.86
- Optimal Distinctiveness Theory — 0.86
Computed from structural-signature embeddings · 2026-10-08
Not to Be Confused With¶
- Lanchester Square Law. Tell: Lanchester models combat attrition; the Petrie model uses analogous square scaling for directional exposure under different assumptions.
- Risk Ratio. Tell: A risk ratio compares observed probabilities, whereas the multiplier derives expected exposure from a stylized mechanism.
- Ecological Fallacy. Tell: The model operates on group expectations and cannot determine any individual's behavior or experience.
- Multiplier Effect. Tell: Generic amplification mechanisms do not specify this two-group source–target denominator structure.
References¶
- Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Petrie_multiplier (revision 1359636571).
- Preserved source candidate: http://www.scotsman.com/news/attack-on-sexism-not-an-attack-on-men-1-3209552
- Preserved source candidate: https://www.theguardian.com/science/life-and-physics/2015/mar/08/the-petrie-multiplier
- Preserved source candidate: https://blog.ian.gent/2013/10/the-petrie-multiplier-why-attack-on.html
- Preserved source candidate: http://fob.po8.org/node/622
- Preserved source candidate: https://web.archive.org/web/20160701200939/http://fob.po8.org/node/622
- Preserved source candidate: https://www.davidchart.com/2013/10/20/the-petrie-multiplier/
The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.