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A characterization of linear satisfaction measures

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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.

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Authors and Affiliations

  1. Dipartimento di Economia, Metodi quantitativi e Strategie d’impresa, Università degli Studi di Milano-Bicocca, Milan, Italy

    Donata Marasini & Piero Quatto

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  1. Donata Marasini
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  2. Piero Quatto
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Correspondence to Piero Quatto.

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Marasini, D., Quatto, P. A characterization of linear satisfaction measures. METRON 72, 17–23 (2014). https://doi.org/10.1007/s40300-013-0016-x

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  • DOI: https://doi.org/10.1007/s40300-013-0016-x

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