Translating discrete estimates into a less detailed scale: An optimal approach

Abstract

© 2019 by the Mathematical Association of Thailand. All rights reserved. In many practical situations, we use estimates that experts make on a 0-to-n scale. For example, to estimate the quality of a lecturer, we ask each student to evaluate this quality by selecting an integer from 0 to n. Each such estimate may be subjective; so, to increase the estimates’ reliability, it is desirable to combine several estimates of the corresponding quality. Sometimes, different estimators use slightly different scales: E.g., one estimator uses a scale from 0 to n + 1, and another estimator uses a scale from 0 to n. In such situations, it is desirable to translate these estimates to the same scale, i.e., to translate the first estimator’s estimates into the 0-to-n scale. There are many possible translations of this type. In this paper, we find a translation which is optimal under a reasonable optimality criterion.