Posetic Tools in the Social Sciences: A Tutorial Exposition

In this chapter, we provide a brief outline of the main motivations why partial order theory is of key importance in the statistical analysis of socio-economic data, presenting some of the more recent tools available for practical applications. We focus in particular on four typical problems in the analysis of socio-economic data, namely: (i) the construction of rankings, (ii) the evaluation of multidimensional latent traits, like deprivation, (iii) the comparison of statistical populations scored on multi-indicator systems and (iv) the measurement of multidimensional ordinal inequality. The exposition has a didactic aim; statistical procedures are sketched avoiding technical details, but discussing simple examples and providing the relevant software code, in the R language.