Methodological Framework for Pricing-Sentiment Probe Design: Volatility Analysis and Threshold Stability
Abstract
This paper presents a comparative volatility analysis of the pricing-sentiment probe against the ratings-sentiment probe, establishing that pricing is a fundamentally more volatile signal for LLM evaluation. The pricing probe produced 9 threshold transitions across 18 data points (0.50 transitions per point) compared to 2 transitions across 19 data points (0.11 per point) for the ratings probe -- a 4.5x difference in volatility density. Despite this sentiment instability, response generation metrics remained remarkably stable: word counts ranged 181-213, token output ranged 302-319, and tokens in ranged 41-43 across all price points. This decoupling of sentiment volatility from response stability metrics confirms that the observed sentiment shifts reflect genuine evaluative processing rather than generation artifacts. We identify the $20,000-$25,000 instability zone as a priority target for finer-granularity replication, and outline the specific methodological requirements for extending the pricing probe framework to cross-currency and cross-service-category contexts.
Keywords
volatility analysis, threshold stability, probe methodology, pricing signal, sentiment transitions, token analysis, replication framework, LLM behaviour
1. Introduction
The primary findings of the pricing probe (SIGI-2026-003) revealed a complex U-curve pattern with 9 threshold transitions. This companion paper examines the methodological implications of this volatility, comparing the pricing signal characteristics with those of the ratings probe to establish a quantitative framework for signal stability assessment in LLM behavioural research.
The central methodological question is whether the high number of threshold transitions in the pricing probe reflects genuine complexity in LLM pricing evaluation or artifacts of the probe design. By demonstrating that response generation metrics remain stable despite sentiment volatility, we can attribute the threshold transitions to evaluative processing differences rather than generation-level instability.
2. Methodology
2.1 Comparative Framework
We compare the pricing probe (PQ01, 18 variations) and ratings probe (R01, 19 variations) across four dimensions: threshold transition density, response metric stability, token-level consistency, and temporal characteristics. Both probes were conducted on the same LLM system on the same day (24 March 2026), eliminating inter-session variability.
2.2 Volatility Metrics
We define transition density as the number of threshold transitions divided by the number of data points. We further decompose transitions by type (positive-to-negative, negative-to-neutral, etc.) to characterise the qualitative nature of volatility.
3. Results
3.1 Comparative Volatility
| Metric | Pricing (PQ01) | Ratings (R01) | Ratio |
|---|---|---|---|
| Data points | 18 | 19 | 0.95x |
| Threshold transitions | 9 | 2 | 4.50x |
| Transition density | 0.50 | 0.11 | 4.55x |
| Sentiment categories reached | 3 (all) | 3 (all) | 1.0x |
| Maximum consecutive same-sentiment | 7 (positive, $30K-$250K) | 8 (negative, 1.0-3.7) | 0.88x |
3.2 Response Metric Stability
| Metric | Pricing (PQ01) | Ratings (R01) |
|---|---|---|
| Word count range | 181 – 213 | 146 – 195 |
| Word count span | 32 words | 49 words |
| Mean word count | 198.3 | 173.4 |
| Tokens in range | 41 – 43 | 39 (constant) |
| Tokens out range | 302 – 319 | 221 – 296 |
| Tokens out span | 17 tokens | 75 tokens |
| Mean elapsed time | 9.65s | 8.07s |
| Elapsed time range | 8.5 – 10.7s | 6.8 – 9.4s |
The pricing probe exhibits narrower word count span (32 vs 49 words) and dramatically narrower token output span (17 vs 75 tokens) compared to the ratings probe. This is a counterintuitive finding: the more volatile sentiment signal produces more stable response generation metrics.
3.3 Instability Zone Analysis
| Price (AUD) | Sentiment | Positive | Negative | Neutral | Word Count | Elapsed (s) |
|---|---|---|---|---|---|---|
| $20,000 | Neutral | 0 | 0 | 1 | 199 | 10.4 |
| $25,000 | Negative | 1 | 2 | 1 | 213 | 9.8 |
| $30,000 | Positive | 3 | 2 | 1 | 199 | 9.9 |
The instability zone traverses all three sentiment categories across just three consecutive price points. The $20,000 data point is particularly unusual, producing zero positive and zero negative markers -- a "blank evaluation" pattern not observed at any other price point. This may indicate a boundary region where the LLM's pricing heuristics are genuinely ambivalent.
3.4 Transition Type Analysis
| Transition Type | Count | Price Points |
|---|---|---|
| Positive to Negative | 1 | $1,000 |
| Negative to Neutral | 2 | $1,500; $7,000 |
| Neutral to Negative | 2 | $2,000; $25,000 |
| Neutral to Positive | 1 | $15,000 |
| Positive to Neutral | 2 | $20,000; $500,000 |
| Negative to Positive | 1 | $30,000 |
4. Discussion
Pricing is a more volatile signal than ratings for LLM sentiment evaluation, with 4.5x more threshold transitions per data point. This finding has important methodological implications: probes targeting pricing signals require finer granularity and more data points than probes targeting simpler signals like star ratings to achieve equivalent resolution of the sentiment landscape.
The decoupling of sentiment volatility from response stability is a key validation finding. If the high number of transitions were caused by unstable generation rather than genuine evaluative differences, we would expect to see corresponding instability in word counts, token outputs, or processing times. The opposite is observed: the pricing probe produces the narrowest token output range of any probe (17 tokens), even as its sentiment oscillates dramatically.
The instability zone at $20,000-$25,000 warrants specific attention. The "blank evaluation" at $20,000 (zero positive, zero negative markers) suggests a genuine point of evaluative indifference or ambivalence. Targeted replication at $1,000 increments within the $18,000-$32,000 range would provide the resolution needed to characterise this zone precisely.
5. Limitations
- Two-probe comparison: Volatility conclusions are drawn from comparing only two probes. A broader comparison across all 10 probes would provide a more robust volatility framework.
- Granularity limitations: The 18 price points may not be sufficient to fully characterise the instability zone. Finer-grained testing is recommended.
- Transition density metric: The simple ratio of transitions to data points does not account for the magnitude of jumps (e.g., positive-to-negative vs neutral-to-negative).
6. Conclusions
Pricing is a fundamentally more volatile signal than ratings for LLM sentiment evaluation, with 4.5x more threshold transitions per data point. Response generation metrics remain stable despite this sentiment volatility, confirming the transitions reflect genuine evaluative processing. The instability zone at $20,000-$25,000 requires additional data points to confirm and characterise.
Confidence: HIGH for volatility characterisation. The comparative framework is robust within the constraints of two-probe comparison. Extension across all probes would strengthen the volatility metric.
References
- The Scientific Institute for Generative Intelligence. "The Price-Credibility U-Curve: How Service Pricing Magnitude Affects Large Language Model Sentiment Assessment." SIGI-2026-003. generativeintelligence.institute, March 2026.
- The Scientific Institute for Generative Intelligence. "Sentiment Threshold Dynamics in Large Language Model Evaluation of Service Provider Ratings." SIGI-2026-001. generativeintelligence.institute, March 2026.
- The Scientific Institute for Generative Intelligence. "Replication Considerations and Methodological Validation of Rating-Sentiment Threshold Probes." SIGI-2026-002. generativeintelligence.institute, March 2026.