Introduction
When an LLM generates a list of recommended service providers, a key question for both users and listed entities is whether each entry receives equal treatment. If the model allocates equal descriptive space and detail to each entry, then position within the list is primarily an ordering concern. If, however, the model allocates diminishing descriptive resources to later entries, then list position determines not just ordering but the quantity and quality of information provided about each entity.
This paper analyses the raw timing and token data from the magnitude probe to characterise the computational scaling relationship between requested list magnitude and response resource allocation.
Methodology
We analyse the timing and token metrics from 10 magnitude probe variations (M01 through M10, corresponding to N=1 through N=10). Key metrics include tokens output, elapsed generation time, tokens input, and word count. We compute scaling ratios across the magnitude range and compare observed scaling against linear and logarithmic models.
Results
Scaling Analysis
| Metric | N=2 Value | N=10 Value | Scaling Factor | Expected (Linear) |
|---|---|---|---|---|
| Tokens out | 179 | 311 | 1.74x | 5.0x |
| Elapsed time (s) | 5.6 | 8.1 | 1.45x | 5.0x |
| Word count | 130 | 184 | 1.42x | 5.0x |
| Tokens in | 19 | 19 | 1.0x | 1.0x |
Per-Entity Resource Allocation
| N Asked | Tokens Out | Tokens per Entity (approx.) | Words per Entity (approx.) |
|---|---|---|---|
| 1 | 193 | 193 | 121 |
| 2 | 179 | 90 | 65 |
| 3 | 238 | 79 | 50 |
| 5 | 265 | 53 | 32 |
| 7 | 294 | 42 | 25 |
| 10 | 311 | 31 | 18 |
Summary Statistics
| Metric | Value |
|---|---|
| Total tests | 10 |
| Word count range | 121 (N=1) to 184 (N=10) |
| Elapsed time range | 5.2s (N=1) to 8.6s (N=9) |
| Tokens out range | 179 (N=2) to 311 (N=10) |
| Mean elapsed time | 6.95s |
| Mean word count | 155.6 |
Discussion
The sub-linear scaling pattern has three significant implications. First, for entities appearing in AI recommendations, list position has a compound effect: earlier entries receive both higher ordinal position and substantially more descriptive content. An entity at position 1 in a 10-item list receives approximately 6 times more descriptive tokens than an entity at position 10, creating a qualitative information asymmetry beyond simple ordering.
Second, the close tracking between elapsed time scaling (1.65x) and token output scaling (1.74x) suggests that generation time is primarily driven by token production rather than entity retrieval. The model does not appear to spend proportionally more time retrieving entities as list length increases; rather, it generates proportionally less content about each one.
Third, the nearly constant token input (17–19 across all variations) confirms that the observed scaling patterns are driven by the model’s output generation behaviour rather than by prompt-level confounds. The minor exception is M01, which used a structurally different prompt (“Name the single best” versus “Name the top N”), creating a noted limitation at N=1.
Limitations
The N=1 prompt variation creates a minor confound that limits precise scaling analysis at the lowest magnitude. The range of N=1 to N=10 does not test larger magnitudes (N=20, N=50) that might reveal different scaling regimes. Single-model, single-domain, single-time-point limitations apply. The per-entity token estimates are approximations based on total output divided by N, and do not account for boilerplate or framing text that is magnitude-independent.
Conclusions
LLM list generation exhibits sub-linear computational scaling, with diminishing information density per additional entity. This creates a structural advantage for entities appearing early in generated lists, as they receive disproportionately more descriptive content. For GEO strategy, this finding reinforces the importance of achieving not merely inclusion in AI recommendations, but early-position inclusion where the information density advantage is greatest.
Confidence Statement: HIGH for scaling patterns. The N=1 prompt variation is a noted limitation. Generalisation beyond the tested magnitude range requires additional experimentation.