Why is geometric mean better suited for the HDI than the arithmetic mean?
Unlike the old HDI, the HDI introduced in the 2010 HDR is based on the geometric mean and it takes into account differences in achievement across dimensions. Poor performance in any dimension is now directly reflected in the new HDI, which captures how well a country’s performance is across the three dimensions. That is to say, a low achievement in one dimension is not anymore linearly compensated for by high achievement in another dimension. The geometric mean reduces the level of substitutability between dimensions and at the same time ensures that a 1% decline in index of say life expectancy at birth has the same impact on the HDI as a 1% decline in education or income index. Thus, as a basis for comparisons of achievements, this method is also more respectful of the intrinsic differences across the dimensions than a simple average.