On unit free assessment of the extent of multilateral distributional variation

Summary Multilateral comparison of outcomes drawn from multiple groups pervade the social sciences and measurement of their variability, usually involving functions of respective group location and scale parameters, is of intrinsic interest. However, such approaches frequently mask more fundamental differences that more comprehensive examination of relative group distributional structures reveal. Indeed, in categorical data contexts, location- and scale-based techniques are no longer feasible without artificial and questionable cardinalisation of categories. Here, Gini’s transvariation measure is extended and employed in providing quantitative and visual multilateral comparison tools in discrete, continuous, categorical, univariate, or multivariate settings which are particularly useful in paradigms where cardinal measure is absent. Two applications, one analysing Eurozone cohesion in terms of the convergence or divergence of constituent nations income distributions, the other, drawn from a study of ageing, health, and income inequality in China, exemplify their use in a continuous and categorical data environment.

Non-parametric estimation and evaluation of capability sets

A major difficulty for the application of Amartya Sen’s capability approach is that individual capability sets cannot readily be observed. This article proposes a non-parametric framework to construct such sets, on the basis of observed functionings of individuals that are taken to belong to a group sharing the same capability set. Within this framework, the earlier theoretical proposals of Muellbauer to compare different capability sets can be easily implemented. Associated robust empirical estimators are provided and applied to EU-SILC data on household income, material living conditions, housing quality and health; we illustrate our approach with a multilateral comparison of 32 European countries, with a comparison of both a ‘fixed ray’ and a ‘multiple rays’ evaluation metric to compare French and German capability sets, and with a multilateral comparison of socioeconomic sub-groups in France.

The Mathematics of 'Amerind'

SUMMARY After discussion of several methodological issues, a simpfe method for evaluating nonbinary wordlist comparisons probabilistically is introduced, and the data of Joseph H. Greenberg's "Amerind Etymological Dictionary" (1987: 181-270) are evaluated by that method. It is found that the similarities Green-berg has adduced as evidence for the genetic unity of 'Amerind' fall within the range to be expected by chance alone, and concluded that Greenberg's method of 'multilateral comparison' is utterly unreliable, as well-informed specialists have long claimed. RÉSUMÉ Suivant une discussion de plusieurs questions methodologiques, l'auteur introduit une methode simple pour 1'evaluation probabilistique des listes de mots non binaires de comparaison. Ensuite les donnees tirees du 'dictionnaire etymologique amerindien' de Joseph H. Greenberg (1987:181-270) sont eva-luees a la base de cette methode. Le resultat des calculs demontre que les simi-larites apportees par Greenberg comme preuve pour l'unite genetique de 1''Amerind' tombe a l'interieur de la gamme a laquelle on pourrait s'attendre a la base du hasard seulement. La conclusion de l'auteur est que la methode de 'comparaison multilaterale' de Greenberg n'est absolument pas fiable, comme les specialistes bien-informes des langues amerindiennes I'avaient deja note. ZUSAMMENFASSUNG Im Anschluß an eine Diskussion verschiedener methodologischer Fragen stellt der Autor eine einfache Methode zur probabilistischen Bewertung nicht-binarer komparatistischer Wortlisten vor. Danach werden Daten bewertet, die Joseph H. Greenbergs "Amerind Etymological Dictionary" (1987:181-270) entnommen sind. Das Ergebnis ist, daß die Ahnlichkeiten, die Greenberg als Nachweis für die genetische Einheit einer 'Amerind'-Grundsprache heran-gefuhrt hat, sich durchaus innerhalb der Breite dessen befinden, was man aus bloßem Zufall erwarten kann. Der Autor kommt zum SchluB, daB Greenbergs Methode eines 'multilateralen Vergleichs' vollkommen unzuverlassig ist, wie wohlinformierte Spezialisten von Indianersprachen schon seit langem behaup-tet haben.