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.
Similar content being viewed by others
References
Cerchiello, P., Dequarti, E., Giudici, P., Magni, C.: Scorecard models to evaluate perceived quality of academic teaching. Stat. Appl. 2, 145–155 (2010)
Cerchiello, P., Giudici, P.: On the distribution of functionals of discrete ordinal variables. Stat. Probab. Lett. 82, 2044–2049 (2012)
Chiandotto, B., Gola, M.: Questionario di base da utilizzare per l’attuazione di un programma per la valutazione della didattica da parte degli studenti, Rapporto di Ricerca RdR1-00. Gruppo di Ricerca MIUR-CNVSU (2000)
Giovagnoli, A., Regoli, G.: Representation theorems for measures of location and for measures of dispersion. In: Stochastic orders and decision under risk. Lecture notes-monograph series, vol. 19, pp. 141–156 (1991)
Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1988)
Marasini, D., Quatto, P.: A family of indices for teaching evaluation. Experiences in Italian Universities. Studies in theoretical and applied statistics, Springer, Berlin (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marasini, D., Quatto, P. A characterization of linear satisfaction measures. METRON 72, 17–23 (2014). https://doi.org/10.1007/s40300-013-0016-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40300-013-0016-x