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.
Marasini, D., Quatto, P. (2014). A characterization of linear satisfaction measures. METRON, 72(1), 17-23 [10.1007/s40300-013-0016-x].
A characterization of linear satisfaction measures
MARASINI, DONATA;QUATTO, PIERO
2014
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.
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