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

• Main Authors: Thongchai Dumrongpokaphany, Olga Koshelevaz, Vladik Kreinovichz
• Format: Journal
• Published: 2020
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85074497170&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/67921
• Institution: Chiang Mai University

© 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.