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If anyone in a community speaks the same language, then P 1
= 1 and for the
speakers of other languages, P i
= 0. Thus the LDI of a completely monolingual
community is zero. If four languages are spoken by an equal number of people,
then P 1
= P 2
= P 3
= P 4
= 0.25 and the LDI can be calculated as LDI = 1 –
(0.25) 2 * 4 = 0.75. Thus a higher LDI means larger linguistic diversity and a
lower LDI means lower diversity.
The basic idea of LDI can be explained by the illustration in Figure 1. A square
of P i
means the probability that the i-th language speaker meets with a speaker of
the same language. And the sum of P i
squares represents the combined probability
of any speaker meeting with a speaker of the same language in the community.
Then the sum of P i
squares is subtracted from 1, indicating the probability that
any speaker will encounter different language speakers in a society. The darkcolored
areas of the square in Figure 1 correspond to this probability.
Figure 1. A graphic interpretation of LDI
Ethnologue provides a complete list of LDI data for each country or region,
together with population size and the number of indigenous and immigrant
languages. Based on this data 4 , Figure 2 was prepared to show how LDI changes
across countries and across continents. Each circle represents a country in this
chart. The circle’s size corresponds to the country’s population, and its vertical
axis represents the country’s LDI. The two large circles on the axis of Asia
correspond to India (LDI = 0.94) and China (LDI = 0.51).
4
Based on the Web version, an equivalent of the 16 th edition of Ethnologue.
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