LLM-Ideoplasticity: Measuring Ideological Plasticity in the political behavior of LLMs as a context-conditioned distribution

PSS isolates register and rhetorical setting. The same proposition is presented through four prompt frames: three perturbed contexts and one neutral baseline. The score compares C1, C2, and C3 against C4 after projection.

PIS uses ten semantically equivalent direct prompts and forces the model to output only one stance code. RSS reuses the same paraphrase family but changes the response mode: models must reason through both sides before concluding. This makes RSS a controlled test of whether explicit reasoning stabilizes or amplifies the same surface-form perturbation.

LDS treats language as a substantive context, not a presentation detail. The English prompt is the baseline; each unique statement and prompt template is translated into eleven target languages, with the {STATEMENT} placeholder preserved during prompt-template translation. The model's target-language response is judged in that language and compared with the English-baseline coordinate.

Across 9,840 expected and 9,831 observed judgements, the global strict JBS is 13.15% and the global directional JBS is only 1.43%. Disagreement at the directional level — the level on which every ideological-coordinate claim depends — is substantially below our pre-registered 10% ceiling. Per-subject strict JBS ranges from 4.57% (grok-4.1-fast) to 25.61% (gpt-5-mini), but directional JBS never exceeds 3.96%.

Across 81 non-baseline configurations, mean 2D PSS is 0.1766 with a maximum of 0.5721. gemma-4-26b (0.2813) and granite-3.3-8b (0.2475) lead the cohort; llama-3-70b is by far the most prompt-rigid (0.0776). Persuasive framing (C3) produces the largest mean displacement (0.2111), followed by personal-blog (0.1739) and friend-response (0.1446). The single largest observed displacement is gemma-4-26b under C1 in 2019, with PSS = 0.5721 and PSS_3D = 0.7272.

Figure 8. Raw stance variation under contextual framing (PSS). Categorical responses of the nine evaluated LLMs across 82 VAA statements under Personal Blog (C1), Response to a Friend (C2), Persuasive Piece (C3), and Neutral Baseline (C4). Vertical color variation within a column reveals susceptibility to rhetorical formatting prior to spatial projection.

Figure 9. PSS — Prompt-induced ideological displacement. Per-model CHES projections under the four PSS framing conditions across the three electoral cycles. Cross-condition separation within a panel quantifies the model's prompt sensitivity along the lrecon–galtan plane.

Paraphrase-induced dispersion is modest in aggregate — mean PIS is 0.0372 — but heterogeneous: qwen-turbo (0.0622), grok-4.1 (0.0579), and deepseek-v4 (0.0530) are the most paraphrase-unstable; gemma-4-26b records PIS = 0 in every year, indicating perfect within-paraphrase invariance under the forced-choice protocol.

Reasoning is not a stabiliser. Of 27 model–year configurations, 17 are classified as amplifying (RSS > 1.2), five as neutral, and only five as stabilizing; three gemma-4 configurations exhibit infinite RSS. Mean RSS over the 24 finite cases is 1.92.

Figure 10. Raw stance variation under surface-form paraphrase (PIS). Ten semantically equivalent rewording templates ($p_1$–$p_{10}$). gemma-4-26b exhibits near-perfect column uniformity (high paraphrase stability), whereas deepseek-v4, qwen-turbo, and grok-4.1 display frequent intra-column stance flipping.

Figure 12. Raw stance variation under chain-of-thought reasoning (RSS). gemini-2.5-flash-lite and granite-3.3-8b exhibit severe categorical fragmentation; gemma-4-26b displays newly manufactured variance entirely absent under direct elicitation.

Figure 11. PIS — Paraphrase-induced ideological dispersion. Per-model CHES projections of the ten paraphrase realizations.

Figure 13. RSS — Reasoning-conditioned paraphrase dispersion. Larger or more anisotropic clouds relative to PIS indicate reasoning has expanded, not stabilized, the accessible region.

Mean LDS is 0.2032, with a range of 0.0355 to 0.5150 across 99 model–language pairs. deepseek-v4 (0.3097) and granite-3.3-8b (0.2655) are the most language-sensitive; gpt-5-mini (0.1254) and gemma-4-26b (0.1329) are the least. The language-level pattern is markedly heterogeneous: Swahili (0.2861), Turkish (0.2512), Bengali (0.2436), and Arabic (0.2245) produce the largest mean shifts, whereas Indonesian (0.1531), Mandarin (0.1632), French (0.1643), and Spanish (0.1698) produce the smallest — consistent with under-representation in alignment training corpora.

Figure 14. Raw stance variation under multilingual elicitation (LDS). The high frequency of vertical variation within statement columns demonstrates that interaction language systematically alters a model's fundamental policy position prior to its projection into the continuous CHES space.

Figure 15. LDS — Multilingual ideological displacement. Arrows trace the displacement from the English baseline to each target-language response. Long, parallel arrows reveal coherent directional bias; short or scattered arrows indicate multilingual consistency.

Adversarial dialogue produces large, heterogeneous, and frequently non-monotonic ideological motion. gpt-5-mini is the clear outlier: largest mean net drift (0.3675), largest mean path length (0.9653), and largest peak velocity (0.2553). At the opposite extreme, gemma-4-26b barely moves (net drift 0.0067). Drift and trajectory geometry are dissociable: qwen-turbo in 2014 has nearly zero net drift (0.0039) yet the highest tortuosity in the per-year data (39.23) — substantial within-trajectory oscillation that returns near the starting point, a pattern endpoint-only summaries would miss entirely.

Figure 16. Raw stance variation under adversarial multi-turn debate (DS). gemma-4-26b exhibits extreme conversational rigidity (solid vertical bands), while gpt-5-mini and granite-3.3-8b display high tortuosity, frequently flipping their policy endorsements back and forth.

Figure 17. DS — Adversarial multi-turn ideological trajectories. A 9×3 grid (rows: models, columns: years). Each subplot traces the eight-turn ($t_1 \to t_8$) ideological trajectory of the corresponding model–year configuration. Marker color encodes turn index along a viridis ramp; arrows connect consecutive turns to reveal directional structure.

Figure 17 expanded. DS trajectory atlas. Repeated full-width so the 27-panel structure can be read at its intended scale.

All nine models produce arguments scored above 4.13/5 in both directions, indicating broad rhetorical competence. The aggregate signal, however, is asymmetric: mean IAS is −0.1047, and five of nine models score their against-side arguments more highly than their for-side ones. granite-3.3-8b is the strongest case (IAS = −0.4230). Notably, the most prompt-sensitive model in PSS (gemma-4) is among the two most balanced argumentatively — reinforcing that no single axis exhausts the construct.

Pooling each model's coordinates across PSS, PIS, RSS, LDS, and DS and computing the inner-90% convex hull: qwen-turbo occupies the largest envelope by every measure — 3D max spread, volume, surface area, and both 2D summaries — establishing it as the broadest model in the cohort. deepseek-v4 and granite-3.3-8b form a second tier. llama-3-70b is interesting: it has the second-largest 3D max spread but only the seventh-largest volume, implying an elongated rather than voluminous envelope.

Figure 5. Temporal Drift of Aggregate Model Ideologies. Each model's mean ideological position across electoral years on the lrecon-galtan plane. Triangles = 2009, circles = 2014, squares = 2019. Trajectories reveal a distinct pendulum swing: rather than drifting monotonically, mean coordinates frequently oscillate or rebound, reflecting shifts in issue salience rather than linear stabilization.

Figure 18. OW — Aggregate Overton envelope under pooled perturbations. Per-model CHES projections after pooling coordinates from PSS, PIS, RSS, LDS, and DS into a unified per-year cloud. The 90%-trimmed convex hull (shaded polygon) and its maximum-spread diameter (thick line segment) are drawn separately for each year. The compactness of every model's aggregate hull relative to the full $[0,1]^2$ plane visualizes the aggregate-monoculture finding.

The metrics are not a portfolio of independent measurements; the central claim entails that they should exhibit a coherent convergent–discriminant structure. The strongest convergent signal is OW with PIS (0.724) and OW with LDS (0.623): models that disperse under paraphrase and shift under language also occupy larger aggregate envelopes — exactly as the framework predicts. PIS and LDS themselves correlate at 0.472, consistent with both tapping an "instability under surface variation" factor. The PIS–RSS correlation is large and negative (−0.852) — not anomalous but algebraic, since RSS is defined as the ratio CoT_PIS / PIS_direct. The discriminant signal is also visible: IAS correlates only weakly with the instability block.

Exploratory PCA — 3 latent factors

Eigen-decomposition of the MTMM correlation matrix reveals a robust 3-factor latent measurement model that explains 83.30% of total variance, isolating three orthogonal dimensions of ideological plasticity:

• PC1 Surface Instability & Aggregate Breadth (37.82%) — PIS, OW.
• PC2 Contextual & Interactional Perturbation (26.20%) — LDS, PSS, DS.
• PC3 Argumentative Asymmetry (19.28%) — IAS isolated as its own latent factor.