1. A characterization of linear satisfaction measures
- Author
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Donata Marasini, Piero Quatto, Marasini, D, and Quatto, P
- Subjects
Statistics and Probability ,Ordinal data ,Measure (data warehouse) ,Simplex ,Index (economics) ,Satisfaction measure ,Representation theorem ,Ordinal Scale ,Nagumo Kolmogorov de Finetti Theorem ,Function (mathematics) ,Variable (computer science) ,Statistics ,SECS-S/01 - STATISTICA ,Rating ,Mathematics - Abstract
It is natural to assume for rating data an ordinal scale consisting of k categories (in ascending order of satisfaction). At first glance, ratings can be summarized by a location index (as the median), resulting in a synthesis that takes into account the ordinal nature of data. On the other hand, ratings are often converted into scores and treated as a quantitative variable. More generally, it is possible to measure satisfaction by means of a real-valued function defined on the standard simplex and fulfilling some appropriate conditions. In such a context, the aim of this paper is twofold: firstly, to provide a general definition of satisfaction measures and, secondly, to prove a representation Theorem for these measures. © Sapienza Universitá di Roma 2013.
- Published
- 2014