Employing the Components of the Human Development Index to Drive Resources to Educational Policies Annibal Parracho Sant’Anna • Rodrigo Ota ´vio de Arau ´ jo Ribeiro • Steven Dutt-Ross Accepted: 19 November 2010 Ó Springer Science+Business Media B.V. 2010 Abstract A new form of composition of the indicators employed to generate the United Nations Human Development Index (HDI) is presented here. This form of composition is based on the assumption that random errors affect the measurement of each indicator. This assumption allows for replacing the vector of evaluations according to each indicator by vectors of probabilities of being the best or the worst according to such attribute. The probabilistic composition of such probabilities of preference according to each indicator into probabilities of being the best or the worst according to all of them generates indices that may unveil, on one hand, performances to be followed and, on the other hand, extreme conditions that an additive composition would hide. Differences between the results of application of the diverse forms of composition are examined in the case of the HDI and in the case of the districts version of the HDI employed to compare Brazilian municipalities. It is verified that the smallest correlation between the education enrolment rate and the other indicators in the Brazilian case enlarges such differences. Keywords Human development index  Decision aid  Probabilistic composition  Education 1 Introduction Different forms of combining distinct indicators may lead to diverse combined evaluations. The United Nations Human Development Index (HDI) is formed by adding summands A. P. Sant’Anna (&)  R. O. de Arau ´jo Ribeiro  S. Dutt-Ross Universidade Federal Fluminense (UFF), Nitero ´i-RJ, Brazil e-mail: annibal.parracho@gmail.com R. O. de Arau ´jo Ribeiro e-mail: rodrigo.ribeiro@dtmarketing.com.br S. Dutt-Ross Fundac ¸a ˜o Getulio Vargas (FGV), Rio de Janeiro-RJ, Brazil e-mail: Steven.Ross@fgv.br 123 Soc Indic Res DOI 10.1007/s11205-010-9759-4