McCumber Cube for Information Influence

• McCumber-style Cube is a multidimensional framework that defines information influence by indexing targets, objectives, and machines.
• It integrates political, computational, and psychological measurements to quantify shifts in attention, belief, and decision outcomes.
• The framework enables comparative analysis of influence campaigns by mapping trajectories and effects across clearly defined cells.

The McCumber-style Cube for Information Influence is an analytical framework for observing and measuring information power, defined as the capacity to convert data flows into durable shifts in attention, belief, and behavior. In this formulation, influence operations are organized in a single 3D space whose axes are targets, operations/objectives, and machines, so that campaigns can be compared by their occupied cells, their trajectories over time, and the measurable effects associated with each cell. The framework was introduced to address a setting in which information power has migrated from broadcast persuasion to platform-ized, data-driven operations that fuse computational delivery with cognitive effects, and it is explicitly intended to move analysis from detecting activity to estimating belief change and decision effects (Bronk et al., 25 Aug 2025).

1. Conceptual basis and scope

The framework is grounded in the claim that, within international relations and the information environment, information power is exerted by actors, including states and non-state organizations, to achieve political goals using a fusion of computational delivery and cognitive effects. Contemporary campaigns are described as combining political framing, computational distribution, and psychological tactics to persuade, disrupt, or shape leaders, elites, and publics, often in hybrid conflict conditions “between war and peace” (Bronk et al., 25 Aug 2025).

Two causes are given for the migration from broadcast persuasion to platform-ized, data-driven operations. The first is the advent of social platforms and ad infrastructures that enable microtargeting and algorithmic prioritization of content. The second is advances in automation and AI that intensify and personalize delivery while exploiting fast cognition. The paper situates this migration in cases ranging from the Arab Spring to the Internet Research Agency’s 2016 operations, platform ad delivery discrepancies, and AI-assisted narrative fabrication and amplification (Bronk et al., 25 Aug 2025).

Within this scope, the cube is not merely a descriptive taxonomy. It is presented as a measurement space that supports comparative analysis, data fusion, and effect measurement. A plausible implication is that its principal contribution lies in imposing a common analytic grammar on phenomena that are otherwise studied separately as propaganda, platform governance, influence operations, persuasion, or network diffusion.

2. Triadic integration of politics, computing, and psychology

The cube is built on a triadic analytical framework stating that observing and measuring information influence requires a minimum set of variables and instruments across politics, computing, and psychology. In the political lens, the primary concerns are strategic objectives, doctrine, and governance constraints. The minimum political variables are objectives $$O \in \{\text{persuade}, \text{disrupt}, \text{shape}\}$$, target classes $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$, issue or narrative identifiers, and governance parameters. Instrumentation includes coding of declared or observed goals, narrative framing analysis, policy or doctrine crosswalks, elite capture indicators, and agenda-setting measures such as topic salience in broadcast and social media (Bronk et al., 25 Aug 2025).

In the computing lens, the primary concerns are data movement from originator to audience, automation levels, algorithmic content selection, botnets, ad targeting, and censorship and suppression. The minimum computational variables are delivery intensity $D(t)$, exposures $E_{it}$, automation level $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$, network topology $T$, and platform governance signals. Instrumentation includes telemetry such as impressions, dwell time, and repost trees, as well as ad targeting logs, bot detection, algorithmic priority indicators, censorship or suppression traces, and LLM text mining and topic modeling (Bronk et al., 25 Aug 2025).

In the psychological lens, the framework centers on attention, affect, memory, belief, decision outcome, and cognitive load, with emphasis on fast cognition or “hot thought” versus reflective thinking. The formalized variables are:

$A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$

for attention, along with $F(t)$ for affect, $M(t)$ for memory, $B(t)$ for belief, $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$0 for decision outcome, and $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$1 for cognitive load. Instrumentation includes experiments such as priming, emotional framing, and narrative transportation, polling and panel surveys, recall tests, belief elicitation, psychophysiological measures where appropriate, and event-triggered field studies (Bronk et al., 25 Aug 2025).

The triad implies that an influence campaign is only fully observable when these three lenses are jointly instrumented, enabling data fusion that links delivery to effects on cognition and to goal attainment. This suggests that the cube is less a stand-alone model than an integration surface for heterogeneous measurements.

3. Axes, cells, and formal representation

The McCumber-style cube adapts the McCumber cube from information security by defining three axes: targets $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$2, operations or objectives $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$3, and machines $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$4. The target categories are specified as leaders, including executives and military commanders; elites, including media figures, influencers, and corporate or government officials; and publics, defined as mass audience segments. Operations are specified as persuade for belief change, disrupt for degrading coherence or decision processes, and shape for agenda-setting and biasing identity or issue salience. Machines range from models as static heuristics or rules, to algorithms as data-driven selection and optimization, to AI as adaptive automation and generative models (Bronk et al., 25 Aug 2025).

A campaign at time $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$5 is represented as a set of cells or as a trajectory within the 3D space. Formally, the framework defines an influence tensor

$$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$6

where $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$7 indexes target class, $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$8 indexes operation, $$S \in \{\text{leaders}, \text{elites}, \text{publics}\}$$9 indexes machine level, and $D(t)$0 is the dimensionality of the measured effects. Each cell stores a vector of measurable quantities:

$D(t)$1

Comparative analysis then proceeds by comparing campaigns through occupied cells and effect magnitudes, while trajectories such as a movement from elites-shape-algorithms to publics-persuade-AI represent operational evolution (Bronk et al., 25 Aug 2025).

The relation to the original McCumber model is explicit. The classic McCumber information security cube organizes confidentiality, integrity, availability against information states and safeguards. The influence cube replaces CIA with operations or objectives, replaces information states with targets, and adds a machines axis as a proxy for safeguards or means of implementation, while making room for governance and measurement (Bronk et al., 25 Aug 2025).

The cube also defines axis-wise aggregation. For example,

$D(t)$2

These aggregates formalize the idea that cell-level effects can be rolled up by objective or target class without abandoning the underlying multidimensional structure (Bronk et al., 25 Aug 2025).

4. Crosswalks, coding heuristics, and measurement constructs

The framework contributes two crosswalks. The first maps objectives to tactics across political, computational, and psychological domains. For persuade, the political tactics are campaigning and issue framing, the computational tactics are targeted ads and algorithmic prioritization, and the psychological tactics are emotional framing and priming. For disrupt, the political tactics are destabilizing discourse and debasing institutions, the computational tactics are DoS, manipulative bots, and platform brigading, and the psychological tactics are cognitive overload and disinformation-induced confusion. For shape, the political tactics are agenda-setting and creating dichotomies, the computational tactics are social manipulation and data-driven nudges, and the psychological tactics are identity appeals and fear inducement (Bronk et al., 25 Aug 2025).

These mappings are paired with coding heuristics. Persuade is identified by microtargeted content with emotional framing and priming, with expected measurable changes in $D(t)$3 on focal issues and stable $D(t)$4 with positive $D(t)$5 shifts. Disrupt is associated with bot amplification, conflicting narratives, high $D(t)$6, and increased entropy in topic attention, with expected degraded coherence and increased apathy or polarization. Shape is associated with agenda-setting, identity signaling, and nudge architectures, with expected shifts in the distribution of attention across topics and gradual movement in baseline beliefs (Bronk et al., 25 Aug 2025).

The second crosswalk maps target classes to tactics. For leaders, the political tactics are executive decision manipulation and objective reordering; the computational tactics are biographical intel, behavioral analytics, and secure channels; and the psychological tactics are leadership-specific narratives and flattery or intimidation. For elites, the political tactics are capture of corporate, media, or government figures; the computational tactics are influencer targeting and network seeding; and the psychological tactics are norm change cues and issue acceptance. For publics, the political tactics are mass propaganda and policy framing; the computational tactics are viral memes, microtargeting, and platform ad buys; and the psychological tactics are group identity appeals and emotional issue framing (Bronk et al., 25 Aug 2025).

The framework also states testable hypotheses. $D(t)$7 predicts $D(t)$8 in a belief change model for targeted segments, with affective priming mediating belief updating. $D(t)$9 predicts that disruption campaigns increase cognitive load $E_{it}$0 and reduce the probability of reflective processing, with outcome variance increasing without mean belief shifts. $E_{it}$1 predicts that shaping campaigns shift topic salience and baseline beliefs over longer horizons, with identity cues producing asymmetric effects across subgroups. The target-class hypotheses are that leader-targeted operations exhibit stronger per-capita belief change $E_{it}$2 despite smaller reach, elite-targeted operations produce changes in amplification activity that precede shifts in public $E_{it}$3, and public-targeted operations rely on virality $E_{it}$4 and stickiness $E_{it}$5, with belief change concentrated in subpopulations exposed to emotionally congruent frames (Bronk et al., 25 Aug 2025).

Three measurement constructs are central. Virality is formalized as

$E_{it}$6

where $E_{it}$7 is the reproduction number, $E_{it}$8 the branching factor, $E_{it}$9 network topology features, and $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$0 the algorithmic boost coefficient. Stickiness is

$$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$1

where $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$2 is re-exposure rate, $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$3 dwell time, and $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$4 a reinforcement parameter. Denial of logic, analogized from DoS, is

$$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$5

where $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$6 is cognitive load, $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$7 the arousal component of affect, and $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$8 a signal inconsistency or contradiction index (Bronk et al., 25 Aug 2025).

5. Effect measurement beyond reach

A central argument of the framework is that conventional reach metrics such as impressions and unique viewers understate impact. Three reasons are given: effects are concentrated in strategically selected subpopulations through microtargeting; algorithmic delivery biases the mix and timing of exposures $$m \in \{\text{models}, \text{algorithms}, \text{AI}\}$$9; and belief change and decision outcomes are not linear in reach and often depend on stickiness $T$0 and denial of logic. The framework therefore proposes alternatives tied to attention, affect, memory, belief, and decision outcome (Bronk et al., 25 Aug 2025).

The belief-updating model is expressed as

$T$1

and an attention survival model is written as

$T$2

For campaign impact on a decision outcome, the framework proposes a difference-in-differences design:

$T$3

with $T$4 estimating the causal effect. Memory reinforcement is written as

$T$5

These formulations are complemented by

$T$6

$T$7

and

$T$8

with instrumental variables or propensity scores suggested to address selection into exposure (Bronk et al., 25 Aug 2025).

The framework’s mixed-methods program couples computational sensing, including LLM text mining, with experiments and polling. Recommended data sources include platform APIs and logs for impressions, shares, ad buys, delivery ranks, and bot signals; network data such as follower graphs, cascade trees, and centrality measures; content data including text, images, memes, and micro-video; governance data such as moderation events, policy changes, and censorship flags; and survey or panel data covering attention, affect, memory recall, belief states, and decision outcomes. ETL pipelines unify platform logs, content features, and survey panels by time and cohort; LLMs produce narrative maps and confusion or contradiction scores $T$9; and statistical and causal inference modules estimate $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$0, $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$1, $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$2, and $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$3 per cube cell (Bronk et al., 25 Aug 2025).

The practical workflow is organized into planning, monitoring, and evaluation. Planning defines objectives $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$4, targets $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$5, and machines $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$6, maps anticipated tactics using the crosswalks, and pre-registers measurement plans for $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$7, $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$8, $A(t) = \int_{t_0}^{t} a(\tau)\, d\tau$9, $F(t)$0, $F(t)$1, $F(t)$2, and $F(t)$3 by cube cell. Monitoring instruments delivery and exposure, runs LLM pipelines to classify narratives and frames, computes preliminary $F(t)$4, $F(t)$5, and $F(t)$6, and populates $F(t)$7 continuously. Evaluation estimates $F(t)$8, $F(t)$9, $M(t)$0, and $M(t)$1 within and across cells, applies difference-in-differences and survival models, and audits governance constraints and platform policy compliance (Bronk et al., 25 Aug 2025).

6. Applications, adjacent formalizations, and limitations

The cube is illustrated with recent cases across state and commercial platforms. Russia IRA 2016 targeting Black voters is placed primarily in publics with persuade or disrupt and algorithms or AI; the described effects are targeted ads with high delivery intensity, emotional framing, increased apathy, moderate virality, targeted reinforcement through repeated exposure, and denial of logic through conflicting cues and cynicism. Brexit bots and trolls are placed in publics with disrupt or shape and algorithms, with high bot activity, elevated affect through identity or loss frames, and agenda-setting effects. The “F-35 kill switch” rumor is placed in leaders and elites with disrupt or shape and models, algorithms, or AI, with high cognitive load via technical complexity, elevated threat framing, temporary belief shifts among elites, and calls to decouple from US defense products. Additional examples include Fox News meme overlays, China’s nine-dash line versus the US tariff narrative, Temu and Shein ad buys on Meta, Israeli intimidation via Iran’s cell network, and the Arab Spring followed by platform banning and censorship-driven reconfiguration of the machines axis (Bronk et al., 25 Aug 2025).

A distinct but mathematically formal line of work studies influence propagation through Bayesian extensions of graph-theoretic centrality. It defines cascading sequences, influence profiles $M(t)$2, influence-based individual and group centralities $M(t)$3, and Shapley value-based centrality, proves that layered graphs form a linear basis for the profile space, and shows that every influence-based centrality formulation in the family is the unique Bayesian centrality conforming to its graph-theoretic counterpart (Chen et al., 2018). That work also sketches a different McCumber-style mapping with dimensions for influence states, influence mechanisms or structures, and governance or intervention levers. This suggests that network-diffusion centralities, layer statistics, and RIS-based estimators can serve as complementary machinery for propagation-sensitive measurement inside or alongside the information-influence cube.

The framework also states clear limitations and governance constraints. Measurement is challenged by data access and platform opacity, algorithmic black boxes that complicate estimation of $M(t)$4, selection bias in exposure, non-random targeting, spillovers across cells, small-$M(t)$5 leader measurements, the difficulty of causal quantification for elite influence, and confounding events such as concurrent geopolitical shocks. Ethical considerations include respect for privacy, consent, and democratic norms; avoidance of manipulative experimentation without oversight; and alignment of measurement and mitigation with platform policies and accountability mechanisms. The specified guardrails are transparent indicators, audit points, harm minimization, and public reporting standards (Bronk et al., 25 Aug 2025).

In this sense, the McCumber-style Cube for Information Influence is a measurement-oriented synthesis rather than a single causal theory. Its central claim is that influence operations become tractable when objectives, targets, and machine levels are jointly indexed and then linked to political coding, computational telemetry, and psychological measurement. A plausible implication is that its enduring value will depend less on the cube metaphor itself than on the extent to which the proposed variables, crosswalks, and mixed-methods instrumentation can support reproducible estimation of belief change and decision effects across heterogeneous cases.