In a perfectly homogeneous nation-state, in which one ethno-national group has 100 percent of the population, HHi = 1. If the state has an extremely polyethnic character in which every ethno-national group is vanishingly small, i.e., where each person represents their own ethno-national group, the HHi tends toward 0. The method of measurement used for this index allows each group's share of the population to "determine its own weight," so its share is multiplied by its own share.
In the case of Belgium, let us agree that the most salient definition of ethno-national groups is linguistic. In 1976, Flemings made up 59 percent of the population, Walloons 39.3 percent and Germans 0.64 percent. Of the total population, therefore, the Flemings had a fractional share of .59, Walloons .393 and Germans .0064.
Using the HHi index, a group's weighted share is determined by its own weight, i.e., in the case of the Flemings, by multiplying .59 by .59 = .348. Correspondingly, the share of Walloons is .393 x .393 = .153. The share of Germans is (.0064) = .00004096.
So, without imposing any arbitrary cutoff points, the political importance of the Belgian Germans is going to be discounted by this measure, which will conform to all but the most ardent Germanophiles' intuitions.
The result of adding up these weighted values of all
these ethnic components provides our Herfindahl-Hirschman
concentration index:
HHi = 
p 2I
where p I is the fractional share of the i-th
ethno-national group and stands for summation over
all components. In the Belgian case in 1976, the HHi was
therefore .501 when we reduce to three decimal places.
What we shall call the effective number of ethno-national
groups (ENENg) is defined as the reciprocal of the HHi
index:
ENENg = 1/HHi = 1/ p 2I
Given our Belgian data, the ENENg = 1/.501 = 1.996, or 2, if we round off. The somewhat elaborate procedure adopted to calculate the effective number of ethno-national groups in Belgium conforms to our intuitions about this case: there are two effective ethno-national groups.