Perhaps the most difficult aspect of constructing a multi-dimensional index is that of choosing weights for the components. This problem is often bypassed by adopting the ‘agnostic’ option of equal weights, as in the human development index. This is an annual ranking of countries produced by the United Nations Development Programme based on life expectancy, education, and per capita gross national income. These three dimensions are now aggregated multiplicatively. Whatever weights (exponents) are chosen for these dimensions, some nations will feel disadvantaged. To avoid the use of arbitrary weights, we propose for consideration a two-step approach: (1) find the most advantageous set of weights for each nation in turn, and regress the associated optimal scores on the underlying indicators to find a single weight set. This approach has the properties of non-subjectivity, fairness, and convenience. The result is that the highest weight is placed on the life expectancy dimension.