PRIE — Design rationale and provenance

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What PRIE computes

score(c) = propensity(c)^Wp × relevance(c)^Wr × impact(c)^Wi × emphasis(c)^We

• propensity(c) ∈ [0, 1] is the predicted probability that the customer responds positively to candidate c. Computed from one or more learned models (Bayesian, logistic-regression, or gradient-boosted, depending on the active scoring strategy).
• relevance(c) ∈ [0, 1] is the contextual fit of c to the current request — channel match, recency match, segment match. Computed from request-time signals.
• impact(c) ∈ [0, 1] is the normalized business value of c — revenue, margin, or operator-defined value mapped into the unit interval.
• emphasis(c) ∈ [0, 1] is a manual priority lever that lets operators boost or suppress specific candidates without retraining models.
• Wp + Wr + Wi + We = 1 are the per-factor weights, configurable per RankingProfile (see Ranking Profiles API).

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Optional exponent terms: uplift and CLV

score(c) = ⟨base PRIE⟩ × upliftMultiplier(c)^Wu × impact(c)^(Wclv × clvNorm)

• Uplift (Wu) — when Wu > 0, persuadable offers (positive CATE τ) are pulled up the ranking and sleeping-dog offers (negative τ) are pushed down. See How scoring works and Uplift modeling for the CATE derivation.
• CLV (Wclv) — when Wclv > 0, the per-offer impact factor gets an extra exponent of Wclv × clvNorm, where clvNorm = clvScore / 100 from the customer’s CLV row. A per-customer constant alone cannot reorder candidates inside one arbitration (it scales every candidate equally in the geometric mean), so the CLV weight deliberately rides on the per-offer impact component: high-CLV customers see high-impact offers ranked higher. No CLV row → term skipped (never penalizes).

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Why four factors

1. Same-customer-same-time context shifts. A customer’s response probability for a given offer depends on the channel, time of day, current campaign, recent interaction history, and other contextual signals that the offline-trained propensity model does not always see at request time. Giving these their own factor lets the runtime apply contextual nudges without retraining the model.
2. Operator-set business value. Two offers with the same predicted response rate can have very different unit economics (margin, lifetime value, strategic priority). A scoring system that doesn’t surface a business-value axis forces operators to bake economic preferences into propensity model training data, which is brittle and slow to adjust.
3. Manual operator override. Real campaigns have moments when an operator needs to immediately boost or suppress a specific candidate — for legal compliance, regulatory blackout, supply chain shock, or campaign launch. Without an explicit lever factor, operators have to deploy code or retrain models to make these adjustments; the lever factor lets them do it through configuration.

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Public-source citations per factor

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Propensity

• Hosmer, Lemeshow, Sturdivant (2013), Applied Logistic Regression, 3rd edition, Wiley — for logistic-regression propensity.
• Friedman (2001), “Greedy Function Approximation: A Gradient Boosting Machine”, Annals of Statistics — for gradient-boosted propensity.
• Wikipedia: Propensity score, Naive Bayes classifier.

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Relevance (contextual fit)

• Adomavicius & Tuzhilin (2011), “Context-Aware Recommender Systems”, in Recommender Systems Handbook, Springer.
• Russo, Van Roy, Kazerouni, Osband, Wen (2018), “A Tutorial on Thompson Sampling”, FnT Machine Learning (arXiv:1707.02038) — discusses contextual bandits where context modifies the action-value function.

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Impact (business value)

• Standard utility-theory literature; see Gilbert & Mosteller (1966), “Recognizing the Maximum of a Sequence”, JASA — early multi-criteria utility decomposition.
• The principle that recommendation systems must surface a separate “business value” axis is documented across recommender-systems industry literature (e.g. Salesforce Einstein NBA docs, AWS Personalize Next-Best-Action recipe).

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Emphasis (manual lever)

• Sutton & Barto (2018), Reinforcement Learning: An Introduction, 2nd edition, MIT Press — separates “policy” (learned) from “policy override” (engineered).
• Industrial-control and adtech literature uses “lever” / “override factor” terminology consistently; the design pattern long predates any specific commercial product.

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Why a multiplicative composite (not additive)

1. Hard-stop semantics. A multiplicative composite has the property that score(c) = 0 whenever any factor is zero. This is the right behavior for ranking: if a candidate has zero propensity (model is sure the customer won’t respond), zero relevance (request-time signals say “wrong channel”), zero impact (business value is negative or absent), or zero emphasis (operator has explicitly suppressed), the candidate should not appear in the ranking regardless of how strong the other factors are. An additive composite cannot achieve this without explicit if-zero-then-zero filtering, which is fragile.
2. Scale invariance. Multiplicative scoring is invariant to constant rescaling of any single factor, which makes per-factor calibration independent — operators can tune Wp without affecting the relative scores produced by relevance, impact, or emphasis. Additive scoring requires global rescaling whenever any single weight changes.

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Why these specific factor names

• Propensity — the customer’s likelihood to respond. A standard ML term used across causal-inference, recommender-systems, and credit-scoring literature.
• Relevance — the contextual fit between the candidate and the current request. Standard information-retrieval term (Salton & McGill 1983, Introduction to Modern Information Retrieval).
• Impact — the business value impact of the candidate. Standard economics / decision-theory term.
• Emphasis — the operator’s manual priority lever for the candidate. Standard project-management / operations-research term.

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Implementation