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Electoral systems can be compared in respect to the extent of their
proportionality or disproportionality by
calculating one or more indexes that measure the gaps between the proportion
of votes and the proportion of seats received by all parties. The most
commonly used index is the index of disproportionality
developed by Michael Ghallagher. Ghallagher’s
index is computed in the following manner:
- The
percentage of seats received by each party (Si)
is subtracted from its percentage of votes (Vi)
and the differences are then squared.
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The squared differences are then summed and the total is divided by 2.
- The
square root is taken of the result.
By this measure, the smaller the ID, the more
proportional (i.e. less disproportional) the electoral system.
Conversely, the larger the larger the ID the less proportional the
system.
- Typical
PR systems thus have ID scores of less than 1.
- Non
PR systems with relatively low levels of disproportionality
score between 1 and 6. Those with modest levels between 7 and 12,
and those with very high levels in the upper teens or over 20.
- There
is no specified upper value of the Index of Disproportionality,
but scores rarely exceed those in the low to mid 20s.
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