Magic hypercube and index of welfare and sustainability

This paper systematically surveys the use of different approaches for the magic square (MS) as an indicator of welfare, a formal system of necessary relations to deal with conflicts of socioeconomic objectives. The starting point is the article of Kaldor (1971) followed by contributions by the OECD from the 1970’s resulting in a diagram which allowed a visual diagnosis of macroeconomic performance. Such representations were re-examined by Medrano-B and Teixeira (2013), who introduced a required normalization of the variables. Here, we show that this approach was marred by an oversight, namely the issue of the ordering of variables along the axes. In order to avoid this problem, we propose the use of a new mathematical approach involving a Hypercube Graph, which we call magic hypercube, which produces the same index, regardless the ordering of the variables. An application of the new concept is offered using economic data from Brazil and Chile.