How can we enumerate the polarization of a party system, or the polarization of opinions? Polarization exists when the population are divided in their opinions. If we measure these opinions on an ordered scale (as is common place), we’re looking at peaks in two non-adjacent positions. An ideal type would be 50% for an issue, and 50% against it.
The opposite ideal type can help us formulate what we mean by polarization. If all positions are equally popular, we cannot really speak of polarization, but it is not the logical opposite. The opposite of polarization is agreement: everyone has the same position on an issue.
To enumerate polarization, we can work backwards from Cees van der Eijk‘s (2001) measure of agreement: inverting it. I’ve written up a few functions to do this in R.
Van der Eijk, C. 2001. “Measuring agreement in ordered rating scales.” Quality and Quantity 35(3): 325-341.
Didier Ruedin 
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