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On the mathematics behind the entropy diversification measure in strategic management

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  • David Booth
  • Stephane Booth

Abstract

On the face of it, one might wonder why a logarithmic function, entropy, is often chosen as a measure of concentration and/or diversification in economic and strategic management research. After all, say Acar and Troutt (2008), would not a linear one be easier to deal with? Such a function would map similar size intervals to similar size intervals making comparisons across different domain sets easier and more obvious. Such simplicity might be desirable if all other things are equal. We show here that all other things are not equal. In the case of measuring diversification, a simplistic view is trumped by the need for more complicated mathematical functions that can do the necessary measuring. The simple, e.g. linear measures, do not do the job. We show that on this basis entropy is the function of choice for diversification/concentration measurement. In particular, we show that: entropy is decomposable so that it gives a natural way to measure diversification/concentration; the popular Herfindahl measure is actually an approximation to the entropy.

Suggested Citation

  • David Booth & Stephane Booth, 2009. "On the mathematics behind the entropy diversification measure in strategic management," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 1(4), pages 532-540.
    • Handle: RePEc:ids:ijmore:v:1:y:2009:i:4:p:532-540
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    Cited by:

    1. Anjana Rajamani & Marieke van der Poel & Abe de Jong & Steven Ongena, 2017. "The International Diversification of Banks and the Value of Their Cross-Border M&A Advice," Management Science, INFORMS, vol. 63(7), pages 2211-2232, July.

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