Measuring diversity

The present requirements on the (diversity) concept have made it mandatory to have a straightforward way
of measuring the very diversity in concrete situations or markets. This led to the search of indicators or
indexes to assess diversity. Supposing a suitably characterised context is given, basic elements for the
construction of such indexes are a well-defined set of objects, outcomes or types, say 1, 2, …, n, and an
associated frequency (or probability) distribution pi , 1 i n, i pi = 1.

A common mistake, still present in many studies and arguments, is to associate diversity with the sheer
multiplicity of types (variety), forgetting that their relative frequencies are also crucial for defining “the
amount of diversity” (balance). In spite of different options duly taking into account the two basic
constituents above, the Shannon-Wiener entropy index seems to be most favoured and, to many a number
of viewpoints, the best candidate. Indeed, since Shannon (1948), several proofs of optimality of the entropy
index have been produced. Its definition, as known, is:
HSW = - i pi lnpi ,