We measure country welfare by an index number calculated from welfare components like GDP per capita and expected length of life. We rank countries from high to low welfare using such estimated welfare indices. In such calculation the chosen welfare components, the procedures used to normalize them, and the weight structure are important. Changing the components, the normalization procedures, or the weight structure change the welfare indices and it may in the next step also alter the rank order. In this paper, I present information about the importance of the weight structure, and the normalization procedure, taking the welfare components as given. I draw one million random weight structures and from the welfare indices that follow I extract the rank order for each structure. The result of this procedure is a rank order distribution for each country. In this paper, I present the rank order distribution for some countries. For example: According to the human development index Sweden is ranked at 7th place. With random weights Sweden is ranked as high as fifth place in 5.1 per cent of the cases, and as low as 14th in 13.6 per cent of the cases, with the mean rank equal to 9.8.