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In this paper we propose a new aggregation method for constructing compositeindicators that is based on a penalization of the power means. The ideaunderlying this approach consists in multiplying the power mean by a factorthat takes into account for the horizontal heterogeneity among indicators withthe aim of penalizing the units with larger heterogeneity. In order to measurethis heterogeneity, we scale the vector of normalized indicators by their powermeans, we compute the variance of the scaled normalized indicators transformedby means of the appropriate Box-Cox function, and we measure the heterogeneityas the counter image of this variance through the Box-Cox function. Theresulting penalization factor can be interpreted as the relative error, or theloss of information, that we obtain substituting the vector of the normalizedindicators with their power mean. This penalization approach has the advantageto be fully data-driven and to be coherent with the same principle underlyingthe power mean approach, that is the minimum loss of information principle aswell as to allow for a more refined rankings. The penalized power mean of orderone coincides with the Mazziotta Pareto Index.

A new class of composite indicators: the penalized power means