Units of Analysis and Rae's Fractionalization Index

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Abstract
This article examines the relationship between Rae's fractionalization index and the units of analysis on which it is based. It is shown that as one increases the size of the unit of analysis, the value of the index will increase. An exact mathematical relationship between the mean level of fractionalization for a given set of units and a fractionalization index based upon the aggregate voting totals for the units is established. This relationship shows that the aggregate fractionalization index overestimates the level of interparty competition in a system as measured by the mean level of fractionalization. U.S. congressional elections from 1824 to 1978 are used to indicate the importance of the overestimation by the aggregate fractionalization index.

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