Quality & Quantity 38: 51–74, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
Selecting Indexes of Electoral Proportionality:
General Properties and Relationships
GALINA BORISYUK, COLIN RALLINGS and MICHAEL THRASHER
Local Government Chronicle Elections Centre, Department of Politics, University of Plymouth,
Drake Circus, Plymouth PL4 8AA, UK
Abstract. Measuring the proportionality of outcomes in terms of each party’s vote and seat shares is
an important task in electoral analysis. Various indexes have been designed that provide a summary
statistic of electoral proportionality/disproportionality. Claims and counter-claims have been made
regarding the strengths and weaknesses of particular indexes. Important consequences follow from
this methodological pluralism. First, it is not always clear which index has been employed when par-
ticular electoral outcomes are discussed. Second, recent additions to the list of indexes have not been
thoroughly scrutinised and appraised. Third, the lack of knowledge about the general relationship
between indexes means that observations might be different had a different index been used. This
article seeks to identify and clarify the particular properties of different indexes of proportionality.
Relatively new, and largely untested, indexes of proportionality are examined and some unusual
and potentially damaging properties are identiﬁed. We also compare different measures of dispro-
portionality in an effort to specify some general properties of the inter-relationships between them.
Understanding the particular patterns of electoral competition and vote distributions that affect the
relationship between these measures should enable users to anticipate the consequences of preferring
one index over others.
Key words: proportionality indices, electoral outcome, electoral disproportionality, statistical
measures, votes, seats, wasted votes.
One of the most important ways of evaluating an electoral system is to measure the
relationship between each party’s vote and seat shares. When seat shares equate
with vote shares the outcome is said to be proportional. When seat and vote shares
fail to equate the system leads to disproportionality. But, as Gallagher (1991: 33)
has noted, “once the notion of disproportionality is raised, we move away from an
absolute standard to a relative one” and, therefore, the search is on for some meas-
ure that can capture the level of disproportionality. In fact, electoral analysts have
developed different indexes for measuring the proportionality/disproportionality of
any election result and disagreement still persists over the most appropriate index
to use (Gallagher, 1991; Cox and Shugart, 1991; Monroe, 1994; Pennisi, 1998).
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