Measurability and Interpersonal Comparability of Assessment Data

We consider the problem of a university which should rank students based on several professors' assessments. Professors assessments may differ from one another. In this problem, it is well known as Arrow's impossibility theorem [1] that if any interpersonal comparison of professors' assessment data is prohibited, then the university's aggregation should depend only on one particular professor's assessment. If we aim to provide an escape route from Arrow's impossibility theorem, we need some assessment scale should be interpersonally comparable [6]. In this study, we first introduce a formal definition of measurability and interpersonal comparability of any scale of assessment data. We then discuss the feature of informational structures with which a given measure is measurable or interpersonally comparable.