View PDF HTML (experimental)

Abstract:A service system may use the same categories to assign standard allocations and to check whether each service is fulfilled. Finer categories can match individual needs more closely, but they divide the observations available for monitoring. We study this conflict for a fixed menu from which participants select by declaring a category, with fulfilment assessed from each category's aggregate outcomes during a fixed period. We relate allocation loss to variation in preferred allocations within categories and identify conditions under which aggregate observations preserve the verification performance of individual records. For nested refinements under stated utility and observation assumptions, an allocation-loss tolerance and a per-category detection target define a feasibility band. Categories must be fine enough to provide suitable allocations but sufficiently populated to support verification. A source-dependent lower bound on declaration entropy and a minimum contributor requirement give necessary information and population constraints. For an explicit finite population with quadratic utility and binary service outcomes, we prove the exact feasible range across all categorical designs and exhibit designs attaining the information lower bound at specified tolerances. The results provide conditions for choosing categories jointly for allocation and verification.

Submission history

From: Joss Armstrong [view email]
[v1] Wed, 29 Apr 2026 15:36:41 UTC (735 KB)
[v2] Wed, 6 May 2026 22:45:30 UTC (797 KB)
[v3] Mon, 14 Sep 2026 09:32:29 UTC (28 KB)