Child Well-Being in Rich Countries: UNICEF's Ranking Revisited, and New Symmetric Aggregating Operators Exemplified

In a report published in 2007 UNICEF measured six dimensions of child well-being for the majority of the economically advanced nations. No overall scores are given, but countries are listed in the order of their average rank on the dimensions, which are therefore implicitly assigned 'equal importance'. In this study we take 'equal importance' to mean that the final aggregation is symmetrical in the scores and the ranks, i.e. permuting them leaves the aggregate unchanged. We rank the countries by aggregating the numerical information using a variety of techniques, geared to the measurement scales we distinguish ('ordinal', 'interval', 'ratio'). The aggregators are symmetrical and mildly demanding, emphasizing good performance across the board. The rankings obtained deviate from the UNICEF ranking, but not over-dramatically. Our purpose is not only to study alternative approaches for the particular data at hand, but also to introduce and exemplify new and useful aggregation techniques: we propose ways to select weights for OWA-operators and weighted geometric means, and we suggest how to circumvent the choice of a power for the power means. In addition we extend the Borda method so that it values dominance as well.