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A characterization of linear satisfaction measures

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  • Donata Marasini
  • Piero Quatto

Abstract

It is natural to assume for rating data an ordinal scale consisting of $$k$$ 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. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • Donata Marasini & Piero Quatto, 2014. "A characterization of linear satisfaction measures," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 17-23, April.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:1:p:17-23
    DOI: 10.1007/s40300-013-0016-x
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    References listed on IDEAS

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    1. Cerchiello, Paola & Giudici, Paolo, 2012. "On the distribution of functionals of discrete ordinal variables," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2044-2049.
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    Cited by:

    1. Donata Marasini & Piero Quatto & Enrico Ripamonti, 2016. "Fuzzy Analysis of Students’ Ratings," Evaluation Review, , vol. 40(2), pages 122-141, April.
    2. Donata Marasini & Piero Quatto & Enrico Ripamonti, 2017. "Inferential confidence intervals for fuzzy analysis of teaching satisfaction," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(4), pages 1513-1529, July.

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