Direct-Promotion Regime: Definition and Applications

• Direct-promotion regimes are institutional frameworks that use explicit, codified rules to promote entities solely based on observable actions and measurable outcomes.
• They employ algorithmic modeling techniques such as two-stage frameworks and state-space models to optimize resource allocation under budget and risk constraints.
• Applications span digital marketing, educational progression, and political advancement, providing measurable efficiency gains while highlighting trade-offs in equity and organic growth.

A direct-promotion regime denotes a set of institutional, algorithmic, or organizational rules under which entities—users, students, employees, sellers, or political agents—are advanced, incentivized, or promoted purely on the basis of observable, quantifiable actions or ties, with the decision flow centralized and explicit rather than mediated by indirect, organic, or peer-driven processes. The concept appears across fields, including large-scale digital marketing, educational progression systems, task delegation in organizations, autocratic bureaucratic politics, and controlled experimental platforms, each with distinctive operationalizations but unified by their reliance on direct and codified assignment of incentives or advancement.

1. Core Definitions and Regime Characterization

A direct-promotion regime, in its canonical form, involves the central administrator (platform, institution, principal, or patron) allocating discrete, directly measurable incentives, promotions, or access to resources to subjects or agents as a function of observed features, past actions, or network relationships. The hallmark is the absence of “organic” (peer-to-peer or emergent) growth processes—promotions are not left to indirect signals but are actioned explicitly and systematically. For example, in massive-scale consumer platforms, users receive monetary incentives (coupons, vouchers, cash-back) directly assigned to prompt pre-specified actions such as purchases, activations, or service adoptions; in higher education, direct-promotion rules may require full passing of courses each term to proceed, abolishing transitional statuses or exam debt (Shen et al., 2021, Paz, 21 Nov 2025, Park et al., 2015, Wu et al., 2019).

A defining property is that the promotion rule is mechanistic, personalized, and designed to be optimized for aggregate objectives, e.g., maximizing overall return on investment (ROI), throughput, or consumer surplus under fixed resource constraints. The directness guarantees intervention traceability and model-driven policy adjustment.

2. Algorithmic Modeling and Optimization in Consumer Platforms

In large-scale marketing and digital ecosystem applications, direct-promotion regimes are formalized as resource allocation problems subject to budget, fairness, or risk constraints. The state-of-the-art two-stage framework (Shen et al., 2021) entails:

• Stage 1: Estimation of the user-level promotion–response curve $f_i(c)$, where $f_i(c) := \Pr[y_i = 1 \mid x_i, do(c_i=c)]$ represents the probability of target action conditional on user $i$'s features and assigned incentive $c$. This process leverages inverse propensity scoring (IPS) to correct for treatment selection bias, yielding unbiased curve estimates from logged observational data.
• Stage 2: With individualized response surfaces, a budget-constrained linear program (LP) is solved to select optimal incentive levels per user, trading off the expected benefit $f_i(c)$ against campaign budget $B$ or equivalent cost constraints. The LP admits scalable solutions via dual Lagrangian shadow-pricing and can be deployed in real-time at massive scale.

The Deep-Isotonic-Promotion-Network (DIPN) architecture enforces strict monotonicity and smoothness in user response curves, improving both sample efficiency and robustness to noise. Empirical evaluation demonstrates that DIPN achieves lower LogLoss and Reversed Pair Rate (RPR), higher AUC, and essentially zero budget-violation error compared to DNN baselines, as well as significant real-world gains in coupon spend efficiency and user engagement (Shen et al., 2021).

3. Multi-period and State-space Promotion in Marketing

Dynamic direct-promotion regimes account for temporal and channel interactions. The Dynamic Propensity Model (DPM) framework (Park et al., 2015) models each customer as possessing an evolving latent propensity $x_t^i$ toward the target action, updated dynamically via marketing "touches" and subject to attenuation:

$$x_{t+1}^i = c + \phi x_t^i + \alpha^\top r_t^i + \beta^\top m_t^i + \varepsilon_{t+1}^i$$

Here, primary (direct) and secondary (semi-targetable) touch inputs $(m_t^i, r_t^i)$ produce distinct, channel-specific incremental lifts. The promotion regime is encapsulated by the selection of direct channels based on their $\beta_j$ weights, attenuated over time by the persistence parameter $\phi$. Sequential decision-making is achieved by estimating the marginal lift for each channel and adapting strategies as a function of measured carryover effects. Estimation leverages joint particle filtering and stochastic gradient descent.

DPM explains both the immediate (direct) and lasting (propagated) effects of channel exposure, enabling the regime to optimize timing, intensity, and channel selection to maximize purchase trajectories.

4. Direct-Promotion and Enduring Effect Models

Recent advances extend direct-promotion regime modeling to account for both immediate (direct) and downstream (enduring) effects. The Customer Direct and Enduring Effect (CDEE) framework (Yang et al., 2022) trains multitask deep nets to estimate, for each customer-incentive pair:

• Direct effect $D_i(t)$: Probability of purchase during the promotion window
• Enduring effect $E_i(t)$: Expected cumulative post-promotion spend

A budget-constrained integer programming allocator selects treatments to maximize expected enduring lift while keeping the aggregate direct effect-derived cost within $B$, using hybrid zero-inflated losses (e.g., Tweedie, Bernoulli, and cross-entropy) on RCT data for unbiased estimation. Model validation employs out-of-sample matched evaluation on randomized records, ensuring unbiased estimation of uplift and robustly supporting statistical significance of observed ROI and retention gains (Yang et al., 2022).

5. Direct-Promotion Regimes in Institutional Progression and Education

Direct-promotion regimes also structure advancement and attrition in organizational or educational contexts (Paz, 21 Nov 2025). In educational settings, the removal of transitional statuses (e.g., regularity, finals debt) and their replacement with strict per-term pass/fail progression rules gives rise to a direct-promotion regime: course progression is unambiguous (either cleared or failed), with no possibility to carry debt forward.

Simulation-based evidence, using calibrated agent-based models and historical administrative data, establishes that such regimes create a "promotion wall"—dropout risk becomes highly front-loaded, overall attrition increases, and equity gaps (e.g., between low- and high-resilience student groups) widen, even as psychological stress is reduced and belonging partially increases. Introduction of targeted, capacity-limited safety nets (e.g., remedial instruction for near-pass failures) can partially dismantle the promotion wall, lowering dropout rates and narrowing equity gaps at the expense of increased remedial capacity requirements (Paz, 21 Nov 2025).

Table: Core Regime Features in Higher Education Context

Scenario	Attrition Pattern	Equity Gap Growth	Mean Stress	Mean Belonging	Mean Finals Debt
Historical Regularity	Gradual, spread	+15.8 pp	0.98	0.18	72.7
Direct Promotion	Sharp, front-loaded	+26.1 pp	0.60	0.52	0
Direct + Safety Net	Intermediate	+22.7 pp	0.55	0.49	1.0

This quantifies the structural shifts entailed by direct-promotion institutional regimes and the associated efficiency-equity trade-offs.

6. Direct-Promotion in Political and Organizational Contexts

In bureaucratic politics and organizational design, direct-promotion regimes are enacted via centralized advancement mechanisms anchored in explicit patronage or merit indices rather than through competitive peer ranking or indirect signaling (Wu et al., 2019, Durandard, 2023).

• In autocratic political systems (e.g., Chinese bureaucracy), direct-promotion graphs $G^P$ encode patron-client links for pivotal rank advancements (e.g., rank 4→5), with network centrality and early-stage ties tightly predictive of ultimate career standing. Degree and HITS authority scores in such networks are statistically significant drivers of final rank; early network accumulation “locks in” promotion trajectories, with a small patron class controlling advancement (Wu et al., 2019).
• In dynamic organization task delegation models, direct-promotion regimes are implemented as index contests: each worker is dynamically assigned opportunity and promoted upon crossing an individual threshold determined by their performance index, independent of peer rankings. This structure ensures meritocratic, incentive-compatible advancement and produces empirical patterns such as fast-track promotions, seniority effects, and persistent disparities due to initial index advantages (Durandard, 2023).

7. Direct-Promotion Regimes: Information Design and Game-theoretic Foundations

Platforms mediating between sellers and buyers can leverage direct-promotion policies in strategic environments. Specifically, price-dependent promotion and confounding information disclosure are combined to maximize long-run consumer surplus when sellers price myopically (Gur et al., 2019). The promotion policy $\alpha_t(p, \phi, history)$, potentially randomized, directly determines advancement (promotion) allocation as a function of seller price and platform-private information about arrival types. By employing confounding promotion—randomizing assignment to fix sellers' posteriors and prevent learning of true underlying demand composition—the platform can induce a Bayesian Nash equilibrium where myopic seller responses and platform-specified promotion maximize desired objectives, even under horizon-maximin robustness.

This regime exploits dynamic programming and concavification of the confounding-value function $W^C(\mu)$, enabling the selection of signals and static confounding rules that anchor beliefs and maintain long-term optimization gains.

• (Shen et al., 2021) “A framework for massive scale personalized promotion”
• (Park et al., 2015) “DPM: A State Space Model for Large-Scale Direct Marketing”
• (Yang et al., 2022) “Personalized Promotion Decision Making Based on Direct and Enduring Effect Predictions”
• (Gur et al., 2019) “Information Disclosure and Promotion Policy Design for Platforms”
• (Durandard, 2023) “Dynamic delegation in promotion contests”
• (Paz, 21 Nov 2025) “The Promotion Wall: Efficiency-Equity Trade-offs of Direct Promotion Regimes in Engineering Education”
• (Wu et al., 2019) “Uncovering Political Promotion in China: A Network Analysis of Patronage Relationship in Autocracy”