Information Requirements for Service Allocation and Aggregate Verification
Finer service categories can improve allocations while leaving fewer observations for checking each promise. Explore an exact example of the range where both requirements can be met.
A category serves two purposes
A provider offers a fixed menu of service configurations. Participants select categories that fit their needs, and the provider uses each category’s aggregate outcomes to check whether the promised service was delivered.
Finer categories can improve the fit between needs and allocations. They also divide a finite population into smaller monitoring pools. I study the conditions under which the same categories can support both tasks.
Find the range that supports both tasks
This is the paper’s exact 96-agent construction. Demands are equally spaced, and each category provides its members’ mean demand. Move the number of categories to see allocation error fall while the smallest monitoring pool shrinks.
Enough detail. Enough evidence.
- Mean squared allocation error
- 0.00129304Pass: loss ≤ 0.002
- Smallest monitoring pool
- 12agents
- Detection power in that pool
- 99.95%Pass: power ≥ 80%
Each dot is one agent. Each box is one category. Groups are balanced in size and consecutive in demand, and are recomputed for each count; successive designs need not be nested.
Eight categories of twelve agents meet both targets. The mean squared allocation error is 0.00129304 and detection power in each pool is approximately 99.95%.
Computed from Section 6 and Appendix C of the public preprint. These are a constructed population and specified statistical hypotheses, not measured service performance.
| Categories | Smallest pool | Allocation error | Detection power | Result |
|---|---|---|---|---|
| 6 | 16 | 0.00230577 | 99.997% | Allocation fails |
| 7 | 13 | 0.00169712 | 99.983% | Both pass |
| 32 | 3 | 0.00007234 | 88% | Both pass |
| 33 | 2 | 0.00006951 | 70% | Verification fails |
The assumptions and calculation behind the visual
The demands are tᵢ = (i + ½) / 96 for i = 0, …, 95, with utility 1 − (t − r)². At a chosen category count, adjacent groups differ in size by at most one and use their mean demand as the service profile. The resulting global minimum loss is Σ(m³ − m) / (12 × 96³), where the sum runs over category sizes m.
Each agent supplies one independent binary failure observation. Failure probabilities are 0.2 under fulfilled service and 0.8 under a category-wide degradation. The test allows a 10% false-alarm probability per category and requires at least 80% detection power. The most powerful count test randomises at its boundary. One, two and three agents give powers of 40%, 70% and 88%, so each monitored category needs at least three agents.
An existence result with two boundaries
For this population and the stated targets, a suitable design exists exactly when there are between 7 and 32 categories. Fewer than 7 cannot achieve the allocation tolerance, even with the best partition and profiles. More than 32 cannot place at least three agents in every category.
Inside that range, a balanced consecutive design attains the minimum allocation loss and meets the verification requirement. The claim is that a suitable design exists at each count. Arbitrary partitions with the same number of categories can still fail.
The paper also derives constraints on declaration entropy. At a tighter allocation tolerance equal to the eight-category optimum, three bits of category entropy are necessary and sufficient for this construction. This is a source- and tolerance-dependent result.
What changes the feasible range?
The range depends on the population, utility, observation model, observation period and detection target. The per-category false-alarm allowance in the example is not a guarantee about the probability of any false alarm across the whole system.
Small groups are a problem because evidence is finite, not because fine categories are inherently undesirable. More observations or different verification requirements can change the upper boundary. The general theory states the assumptions needed to relate allocation loss and aggregate verification; the exact 7–32 range belongs to this construction.
Information sufficient for a task, evidence sufficient for a claim
Source-side sufficiency for the Information Bottleneck studies when reducing a source preserves the relevance–rate tradeoff. Here I study categories used for both allocation and verification. These are complementary questions within my information requirements research.
This is the manuscript previously titled MISES: Minimal Information Sufficiency for Effective Service, also referred to as the MISES/JAVIC lineage. The link and citation below identify the current public version.
Paper and citation
J. Armstrong, “Information Requirements for Service Allocation and Aggregate Verification,” arXiv:2604.26808, 2026. This explanation follows v3, revised 2026-09-14. Current public record.