Relationship between Measurement Results and Expert Estimates of Cumulative Quantities, on the Example of Pavement Roughness

In many practical situations, we are interested in values of cumulative quantities – e.g., quantities that describe the overall quality of a long road segment. Some of these quantities we can measure, but measuring such quantities requiring measuring many local values and is, thus, expensive and time-consuming. As a result, in many cases, instead of the measurement, we reply on expert estimating such cumulative quantities on a scale, e.g., from 0 to 5. Researchers have come up with an empirical formula that provides a relation between the measurement result and a 0-to-5 expert estimate. In this paper, we provide a theoretical explanation for this empirically efficient formula.