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Social Indicators Research

Erschienen in:

08.12.2017

The Balanced Worth: A Procedure to Evaluate Performance in Terms of Ordered Attributes

verfasst von: Carmen Herrero, Antonio Villar

Erschienen in: Social Indicators Research | Ausgabe 3/2018

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Abstract

There are many problems in the social sciences that refer to the evaluation of the relative performance of some populations when their members’ achievements are described by a distribution of outcomes over a set of ordered categories. A new method for the evaluation of this type of problems is presented here. That method, called balanced worth, offers a cardinal, complete and transitive evaluation that is based on the likelihood of getting better results. The evaluation of each society is based on the probability of obtaining better results with respect to the others. The balanced worth is a refinement of “the worth” (Herrero and Villar in PLoS ONE 8(12):e84784, 2013. https://doi.org/10.1371/journal.pone.0084784) that overcomes its excessive sensitivity to the differences, due to the presence of ties. We also discuss how this method can be applied for the case of heterogeneous populations and show how it can be applied in different contexts. An empirical example, regarding life satisfaction in Spain is used to illustrate the working of this method.

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This happens, for instance, when analysing the citation impact of research articles regarding different disciplines. As the number of citations is rather idiosyncratic, one usually takes the shares of the papers in the different percentiles of each discipline to make an analysis independent of the differences in the mean and the variance of the citations distributions.

Note that, for a given problem, the probability of ties will depend on the number of admissible categories defined. The difference between the balanced worth and the worth will thus be smaller the finer the grid of possible outcomes and vanishes for continuous distributions.

We say that group k is fully dominated when \( p_{kj} = 0\,,\,\,\forall \,\,j \ne k \).

Let us recall here that inequality measures typically give more weight to the realizations in the lower part of the distribution. This makes sense when heterogeneity is bad but this is not always the case. For instance when comparing years of schooling across generations in a given country, one would typically like to find that the young generation has higher values than the old one, so that perfect equality is not the desideratum.

In the empirical application regarding life satisfaction individual answers have been grouped into a rougher set of categories. One may reasonably wonder what the purpose is of losing information by grouping those data into broader categories when we have all the individual numerical responses. The main reason is that when dealing with subjective evaluations in terms of numerical scales, there is no guarantee that numbers mean the same for different people (your 7 and my 7 may well represent very different things). Moreover, individual scales need not be linear (i.e. an evaluation 8 need not be twice one of 4, even for a single individual). Grouping numerical answers into categories may thus helps illuminate some structural features of the groups, enhance robustness and reduce the comparability assumptions required.

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Titel: The Balanced Worth: A Procedure to Evaluate Performance in Terms of Ordered Attributes
verfasst von: Carmen Herrero
Antonio Villar
Publikationsdatum: 08.12.2017
Verlag: Springer Netherlands
Erschienen in: Social Indicators Research / Ausgabe 3/2018
Print ISSN: 0303-8300
Elektronische ISSN: 1573-0921
DOI: https://doi.org/10.1007/s11205-017-1818-7

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