Ideological Depth: Structure & Dynamics

• Ideological depth is the structured internal organization of beliefs, evaluations, and social relations that goes beyond surface-level labels.
• It is operationalized through multidimensional models, dynamical systems, and LLM analyses to reveal stable, resilient, and interconnected ideological frameworks.
• Measurement methods range from high-resolution surveys and text analysis to network metrics, offering actionable insights into content, exposure, and belief stability.

Ideological depth denotes the extent to which ideology is not merely an overt slant in statements but a deeper organizing structure of meaning, evaluation, behavior, and social embedding. In recent work, it appears in several related senses: as a framework of thinking and calculation about the world and the reproduction of social relations (Kerne, 31 Mar 2026); as cross-issue constraint and low-dimensional alignment in multidimensional opinion spaces (Baumann et al., 2020, Banisch et al., 2018); as persistence, resilience, and revival in competitive population dynamics (Ausloos et al., 2011, 0906.4962); as homogeneous exposure and like-minded interaction in online systems (Wang et al., 12 Jan 2026); and, in machine learning, as the distinction between surface-level alignment and deeper representational or belief-like stability (Kronlund-Drouault, 2024, Kabir et al., 23 Apr 2025).

1. Conceptual foundations

One influential conceptualization treats ideology not as a loose collection of opinions but as a structured way of representing social, economic, and political relationships. Hall’s formulation—“frameworks of thinking and calculation about the world”—is used to emphasize that ideology tells actors how the social world works, what their place is in it, and what they ought to do; the same line of argument also presents ideology as reproducing the social relations of production (Kerne, 31 Mar 2026). In work on LLMs, ideology is likewise treated expansively: not only as explicit propositions, but as a patterned framework of meaning, analysis, and evaluation that can become internalized by a model (Kronlund-Drouault, 2024).

A second line of work separates ideology from adjacent concepts that are often conflated with it. The paragraph-level study of historical news treats ideology as a set of beliefs about the proper order of society and how to achieve it, while distinguishing it from stance and from polarization: a text may discuss a liberal policy from a conservative stance, and polarization concerns increasing ideological distance over time rather than ideology itself (Sinno et al., 2021). By contrast, high-resolution measurement work on the contemporary United States argues that a one-dimensional liberal–conservative axis is socially shared and empirically useful, but also explicitly states that this representation is imperfect and issue-dependent rather than exhaustive (Sabin-Miller et al., 14 Jan 2025).

Arena	Operationalization of ideological depth	Representative work
Political theory	Framework of meaning, positionality, and reproduction	(Kerne, 31 Mar 2026)
Opinion formation	Cross-issue constraint and ideological alignment	(Baumann et al., 2020, Banisch et al., 2018)
Population dynamics	Persistence, resilience, conversion, tension, revival	(Ausloos et al., 2011, 0906.4962)
Online systems	Homogeneous exposure, like-minded interaction, cognitive isolation	(Wang et al., 12 Jan 2026)
LLMs	Surface alignment versus latent structure or belief stability	(Kronlund-Drouault, 2024, Kabir et al., 23 Apr 2025, Wachter et al., 17 Mar 2025)

Taken together, these accounts suggest that ideological depth is not a single variable. A plausible synthesis is that it names the degree to which ideological organization penetrates beneath visible labels, whether through semantic structure, issue coupling, demographic durability, exposure concentration, or stable response under challenge.

2. Structural and multidimensional models of ideology

In multidimensional opinion models, ideological depth begins when attitudes on different topics cease to vary independently. In the non-orthogonal topic-space model, each agent holds an opinion vector $\mathbf{x}_i=(x_i^{(1)},\dots,x_i^{(T)})$, and topic overlap is encoded by a Gram matrix $\mathbf{\Phi}$ with entries $\Phi_{uv}=\cos(\delta_{uv})$ (Baumann et al., 2020). Opinion evolution is given by

$$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$

When the topic basis is orthogonal, polarization can occur issue by issue without ideological bundling; with nonzero overlap and sufficiently high controversialness $\alpha$, only a subset of sign combinations remains dynamically viable, and an ideological phase emerges in which positions on one topic predict positions on others (Baumann et al., 2020).

A closely related but cognitively richer formulation appears in the argument-communication model. There, agents exchange beliefs about facts rather than issue positions directly, and attitudes are computed through an evaluative map:

$o_s(i)=\sum_{k=1}^{N_A} a_{sk} c_{ki}.$

Here, $a_{sk}$ is whether agent $s$ believes fact $k$, and $c_{ki}$ is the sign and magnitude of that fact’s relevance for issue $\mathbf{\Phi}$0 (Banisch et al., 2018). Ideological depth arises because some facts affect multiple issues, so selective communication among similar agents produces biased argument pools and, eventually, coherent bundles of attitudes across issues. The result is not only bimodality on single issues but alignment along ideological dimensions (Banisch et al., 2018).

In text analysis, the same structural idea appears as multidimensional issue ideology rather than source-level bias. Historical news paragraphs are coded along economic, social, and foreign dimensions, with each paragraph receiving liberal, conservative, neutral, or irrelevant status per dimension; 78.3% of articles contain at least one pair of paragraph labels leaning in different directions, which is direct evidence that article-level ideology is often internally heterogeneous (Sinno et al., 2021). In multifaceted ideology detection, this structure is made hierarchical: a schema with Root, Domain, Facet, and Ideology levels spans 5 domains and 12 facets, with Left, Center, and Right ideology leaves under each facet. The BICo framework then treats ideological depth as multi-granularity concept semantics moving both top-down and bottom-up through that hierarchy (Liu et al., 2024).

These models converge on a common point: ideology becomes “deep” when it is represented as structured dependence rather than as an isolated label. Inference from one issue to another, or from one concept level to another, is the hallmark of such depth.

3. Dynamical rootedness, entrenchment, and competition

A different literature externalizes ideological depth into persistence and resilience. In the Verhulst–Lotka–Volterra family of models, a country’s total population evolves logistically while ideological subpopulations compete through attrition, unitary conversion, and binary conversion:

$\mathbf{\Phi}$1

Here, depth is not doctrinal complexity but dynamical robustness: low attrition, strong recruitment, resistance to extinction, and even phoenix-like resurrection under changing conditions (Ausloos et al., 2011). The related model of ideological struggle adds a normalized tension index,

$\mathbf{\Phi}$2

which measures how far ideology $\mathbf{\Phi}$3 falls below its standalone benchmark when ideology $\mathbf{\Phi}$4 is present (0906.4962). This treats ideological depth as competitive rootedness in a finite, evolving social body.

A more psychologically parameterized but still one-dimensional model treats ideology as a scalar position $\mathbf{\Phi}$5 and political stimuli as positions $\mathbf{\Phi}$6 on the same axis, with dissonance $\mathbf{\Phi}$7 and event-level updating. Its simplest rule,

$\mathbf{\Phi}$8

uses $\mathbf{\Phi}$9 as a soft-boundary entrenchment factor, making extreme positions harder to move (Sabin-Miller et al., 13 Oct 2025). The paper is explicit that it does not operationalize ideological depth as a separate latent trait; instead it models a scalar ideological coordinate with extremity-dependent rigidity and party-mediated reinforcement (Sabin-Miller et al., 13 Oct 2025).

In physical-agent models, ideological depth is operationalized even more concretely as memory depth. Agents store the last $\Phi_{uv}=\cos(\delta_{uv})$0 inferred ideological encounters and form a weighted memory sum

$\Phi_{uv}=\cos(\delta_{uv})$1

with current ideology determined by $\Phi_{uv}=\cos(\delta_{uv})$2 (Li et al., 2024). For homogeneous “pushover” agents, the model exhibits a critical memory threshold

$\Phi_{uv}=\cos(\delta_{uv})$3

so that, with detection error $\Phi_{uv}=\cos(\delta_{uv})$4, complete polarization emerges above about $\Phi_{uv}=\cos(\delta_{uv})$5 (Li et al., 2024). In that setting, depth means historical integration in the update rule, and it determines whether the collective remains near a symmetric mixed state or undergoes full ideological symmetry breaking.

These dynamical approaches suggest a broader interpretation: ideological depth can be treated as endurance across time and perturbation, not only as semantic richness. In such models, “deep” ideologies are those with stable attractors, broad basins of attraction, or strong retention under competition.

4. Measurement in text, media, and political communication

Empirical work measures ideological depth by moving beyond coarse source labels or single-shot self-placement. High-resolution survey-based work uses 100-point sliders for general ideology, issue-specific ideology across 13 issues, policy-agreement ideology across 10 statements, and external assessments of 68 political opinion statements. General self-placement is highly stable across the survey, with an average absolute beginning–end difference of 5.25 points, while policy-agreement ideology is systematically centralizing and liberalizing relative to subjective ideology (Sabin-Miller et al., 14 Jan 2025). That result implies that broad ideological self-concepts and issue bundles are related but not identical.

The paragraph-level historical-news dataset operationalizes ideological content directly in text rather than through outlet identity. It contains 721 fully adjudicated paragraphs from 175 articles spanning 1947–1974, with separate economic, social, and foreign labels; the resulting data show that proclaimed source ideology is an insufficient proxy for the ideological substance of a text (Sinno et al., 2021). This is one of the clearest empirical demonstrations that ideological depth can reside within a document’s internal structure.

LLMs have also been used as flexible measuring instruments. Direct numeric elicitation of senator ideal points yields scores highly correlated with established measures: 0.97 with DW-NOMINATE, 0.94 with CFScores, and 0.88 with TBIP (O'Hagan et al., 2023). The same framework detects coded or implicit ideology in short texts, including spikes at the far-right dog whistle “1488,” and assigns plausible ideological scores to constructed dinner-table vignettes in which the political signal is distributed across weak contextual cues rather than explicit slogans (O'Hagan et al., 2023). This supports the claim that ideology can be subtle and diffuse in language.

Weakly supervised large-scale pipelines operationalize ideology through external signals rather than expert annotation of each dataset. A context-agnostic and automatic approach based on media slant, lexical features from the Universal Sentence Encoder, hashtags, and resharing features reaches up to 0.953 ROC-AUC for left–right detection and 0.785 ROC-AUC for far-right detection (Ram et al., 2022). The same study argues that different ideological proxies recover different prototypes of ideology, so proxy choice is itself part of the measurement problem (Ram et al., 2022).

In multimodal settings, ideology may be measured as presentation rather than latent conviction. Image-based regression against U.S. politicians’ DW-NOMINATE scores finds that four Twitter-attributed state-linked campaigns—Iran, Russia, China, and Venezuela—present a conservative ideological presentation in the images they share, with narrower and more unimodal distributions than the politician baseline (Joshi et al., 2022). The paper is careful that this reflects visual ideological presentation rather than the operators’ true beliefs (Joshi et al., 2022).

5. Ideological depth in online platforms and social networks

In online systems, ideological depth is often modeled as ideological isolation: increasing exposure to homogeneous content and like-minded interactions (Wang et al., 12 Jan 2026). The survey literature organizes this isolation into four coupled forms: structural isolation in the network, content-based isolation in the feed, interactional isolation in user behavior, and cognitive isolation in belief reinforcement (Wang et al., 12 Jan 2026). This shifts the meaning of depth from “how extreme is a belief?” to “how deeply is a user embedded in a homogeneous ideological environment?”

The formal setup uses a social graph $\Phi_{uv}=\cos(\delta_{uv})$6, a user belief vector $\Phi_{uv}=\cos(\delta_{uv})$7 in an ideological space $\Phi_{uv}=\cos(\delta_{uv})$8, and feed content embeddings $\Phi_{uv}=\cos(\delta_{uv})$9. Content affinity is

$$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$0

and the exposure centroid is

$$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$1

A conceptual isolation score is then

$$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$2

with greater isolation interpreted as both terms becoming small: exposure is close to belief and low in ideological variance (Wang et al., 12 Jan 2026). Belief reinforcement is modeled by

$$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$3

so repeated aligned exposure becomes a mechanism of entrenchment (Wang et al., 12 Jan 2026).

The measurement toolkit is correspondingly heterogeneous. Structural depth is quantified through modularity, conductance, assortativity, boundary connectivity, algebraic connectivity, and random-walk-based measures such as Random Walk Controversy. Feed depth is measured through topic entropy, semantic entropy, exposure entropy, exposure bias, and cross-cutting ratio. Behavioral depth is measured through engagement symmetry, interaction entropy, like-based polarization, and temporal narrowing of recommendation sequences (Wang et al., 12 Jan 2026). The survey’s principal conclusion is that no single metric suffices: ideological depth in online systems is best treated as a multi-level embedding across topology, content, interaction, and cognition (Wang et al., 12 Jan 2026).

6. Ideological depth in LLMs

Work on LLMs has made ideological depth a central distinction. One line of argument rejects the idea that ideology in LLMs is only a visible slant in answers. The claim is that political alignment can reshape semantic organization itself: DPO/ORPO alignment is hypothesized to be more surface-level, “acting like a roleplay prompt,” whereas unsupervised text-based alignment is presented as deeper and capable of affecting “the deepest levels of AI models,” including MLP layers and embedding space; guarded alignment is treated as an external monitoring layer rather than direct ideological transformation of the base model (Kronlund-Drouault, 2024). Empirically, that study uses “relative position” and “absolute position” evaluators, with GPT-4, Mistral, and Claude serving as evaluators, but it explicitly does not provide an exact scoring function, statistical tests, or latent-space geometry analysis beyond exploratory examples (Kronlund-Drouault, 2024).

A second line of work operationalizes ideological depth as belief depth: the capacity to consistently defend positions under argumentative pressure. For original opinion $$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$4 and challenged opinion $$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$5, argumentative consistency is

$$\dot{x}_i^{(v)}= - x_i^{(v)} + K \sum_j A_{ij}(t)\,\tanh\!\left(\alpha [\mathbf{\Phi}\mathbf{x}_j]^{(v)}\right).$$6

and model-topic pairs are labeled as true_left, pret_left, true_right, or pret_right depending on whether stance is stable and in which ideological direction it points (Kabir et al., 23 Apr 2025). Across 12 LLMs and 19 economic policies from the Political Compass Test, consistency ranges from 58% to 95% for left-leaning models and from 63% to 89% for right-leaning models, with semantic entropy distinguishing true from pretending beliefs at AUROC = 0.78 (Kabir et al., 23 Apr 2025). The substantive conclusion is that models exhibit topic-specific belief stability rather than a single coherent ideology (Kabir et al., 23 Apr 2025).

A third line argues that ideological outputs must be decomposed into willingness to engage and ideological direction once engaged. Using a 2PL model for Prefer Not to Answer and a GPCM for answered ideological responses, the IRT-based framework finds that off-the-shelf models often avoid ideological engagement rather than express strong socio-economic bias. Reported refusal rates are 92.55% for ChatGPT 3.5 and 55.02% for LLaMA 3.2-1B-Instruct, compared with very low refusal rates in ideologically fine-tuned variants (Wachter et al., 17 Mar 2025). This reframes depth as stable latent ideological responding across items of varying difficulty, not mere forced-choice partisanship (Wachter et al., 17 Mar 2025).

Prompt conditioning and creator context add another layer. Persona-based probing across seven open-source models shows four regularities: larger models have broader ideological coverage, susceptibility to explicit ideological cues grows with scale, right-authoritarian priming shifts models more strongly than left-libertarian priming, and thematic persona content induces systematic shifts that amplify with size (Bernardelle et al., 22 Aug 2025). In a separate bilingual study of 17 models, normative assessments of 4,300 political persons vary by creator region and by prompting language, with systematic differences between English and Chinese responses and between Western and non-Western models (Buyl et al., 2024). These results imply that ideological depth in LLMs is simultaneously structured and steerable: deeper than random prompt fragility, but far from immutable.

7. Limits, controversies, and implications

A recurrent controversy concerns dimensionality. Some work shows that a one-dimensional liberal–conservative scale is socially shared and empirically useful in the contemporary United States (Sabin-Miller et al., 14 Jan 2025). Other work insists that ideology is irreducibly multidimensional, whether because issue positions align differently across economic, social, and foreign domains (Sinno et al., 2021), because topic overlap creates emergent correlations in a skew multidimensional space (Baumann et al., 2020), or because multifaceted ideology requires a hierarchy of domains and facets rather than one generic axis (Liu et al., 2024). The disagreement is not strictly contradictory: it reflects different levels of abstraction and different empirical tasks.

A second controversy concerns whether measured ideology is belief, presentation, perception, or proxy. Image-based analyses infer ideological presentation, not latent conviction (Joshi et al., 2022). Direct LLM ideological scaling is powerful but may measure a socially synthesized perception of ideology rather than a ground-truth latent position; the paper itself characterizes LLMs as “Zeitgeist machines” in that sense (O'Hagan et al., 2023). Weak-supervision pipelines based on hashtags, politician endorsements, or media slant explicitly show that proxies are not interchangeable and that some travel poorly across datasets (Ram et al., 2022). In LLM evaluation, avoidance, calibration, and underspecified scoring functions complicate any simple claim that a model “has” an ideology (Kronlund-Drouault, 2024, Wachter et al., 17 Mar 2025).

A third controversy is normative. The socio-political critique of AI development argues that apparent neutrality may simply reproduce dominant ideology and that the tangling of corporate and university objectives raises the question “Who is being empowered?” (Kerne, 31 Mar 2026). Work on LLM alignment warns both of “societal uniformity” produced by dominant ideological alignment and of the opposite risk that alternative alignment pipelines could allow “disguised extremist views” to gain traction (Kronlund-Drouault, 2024). Cross-model differences in moral assessments of political figures are used to argue that ideological “unbiasing” is itself politically charged and may invite instrumentalization (Buyl et al., 2024). In online platforms, mitigation strategies such as cross-community edge addition, diversity-aware recommendation objectives, and serendipity-aware reranking all involve explicit trade-offs between relevance, diversity, and fairness (Wang et al., 12 Jan 2026).

The broad implication is that ideological depth is best understood as layered rather than singular. It can name semantic organization, issue constraint, demographic persistence, network insulation, cognitive entrenchment, or stance stability under challenge. What unifies these uses is the claim that ideology becomes “deep” when it ceases to be a surface label and instead structures how meanings connect, how opinions cohere, how systems persist, and how agents—human or artificial—interpret the social world.