Theory 03/Granularity/Measurement and governance
The Resolution Tax
Any system that measures or manages a process at a resolution coarser than the process's own scale pays a tax proportional to the ratio of the two, and the tax appears as either missed events or false alarms — never as a neutral loss of detail.
01What is already known
Signal processing has the sampling theorem; policy has the problem of indicators. Both describe what happens when an observer's resolution is coarser than the phenomenon. What has not been generalised is the consequence: coarse observation does not simply blur, it systematically distorts in a direction set by the shape of the underlying distribution.
02The mechanism
Observation at resolution r acts as a filter that averages over intervals of width r. If the process varies within those intervals, the average is not a typical value — for skewed or rare-event processes it is systematically unrepresentative. Management then acts on the average, applying corrections at the wrong magnitude and time. The tax is the difference between the outcome under coarse management and the outcome under exact management, and it scales with the ratio of process scale to resolution.
03Predictions
- Management error should scale with the resolution ratio, not with the quality of the measurement at that resolution.
- Finer measurement should help only until resolution approaches the process scale, after which it adds noise without benefit.
- Rare-event processes should show systematically larger taxes than smooth processes at equal resolution.
04Refutation
If management outcomes are invariant to resolution once measurement error is controlled, the tax is imaginary and the effect is only noise.
Natural experiments where the same process is monitored at two resolutions — national versus local, monthly versus daily, sensor versus survey — and management decisions differ. Compare decision quality, not measurement accuracy.