Last modified: 2018-05-22

#### Abstract

In this work, we propose an innovative way to introduce the information of weights in the construction of synthetic indicators with mixed variables. The construction of synthetic indicators is a consolidated practice to describe complex and unobservable concepts. This purpose is usually achieved following some fundamental steps, such as the definition of the aggregation method and the weights of the elementary variables.

In literature, most of the indicators are developed on a macro level to compare large entities, such as countries and other institutions; for this reason, the constituting variables are proportions or averages, which are quantitative. As a consequence, the most common aggregation procedures are the arithmetic and geometric mean, and the weights are included in those means.

Nowadays, the request for indicators on the micro level is getting more and more common, and the available information is often measured on the ordinal or dichotomous scale. The theory of partially ordered sets permits to manage these variables to construct synthetic indicators. This theory allows to compare the elements of a group by their reciprocal order and compute a score which represents the position of the element respect to the others (average rank).

One of the most significant limitations to the use of this approach for the construction of indicators is the absence of a coherent method to introduce the values of weights of the variables. In this work, we propose a solution to this limitation and present an application to the measurement of the severity of disability in a population of adult and elderly people in Europe.