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Proportional representation: Difference between revisions
Merging the #Definition and #Measures sections, and creating a #Gallagher index section
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'''Proportional representation''' is a system used to elect a country's government. If a party wins over 50% of the vote, it wins over 50% of the seats and can form a government.
▲'''Proportional Representation''' ('''PR''') is a measure of the outcome of an election where there are multiple parties and multiple members are elected. It is one of many [[types of representation]] in a [[W:Representative government|representative government]].
In practice, the implementation involves ensuring that [[W:Political party|political parties]] in parliament or legislative assemblies receive a number of seats (approximately) proportional to the percentage of the vote they received by making use of a [[Partisan systems|partisan system]]. One system which achieves high levels of proportional representation is [[Party-list proportional representation|party-list proportional representation]]. Another kind of electoral system strives to achieve proportional representation, but without relying on the existence of political parties. A common example of this is the [[single transferable vote]] (STV). ▼
== Usage ==
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Countries which have systems that are similar or use semi-proportional representation include: [[Australia]], [[Germany]], [[Hungary]], [[India]], [[Republic of Ireland]], [[Italy]], [[Japan]], [[Mexico]], [[New Zealand]],[[Scotland]], [[Thailand]] and [[Wales]]. India is one of the most successful examples of a country with proportional representation.
== Measures ==▼
▲In practice, the implementation of "proportional representation" involves ensuring that [[W:Political party|political parties]] in parliament or legislative assemblies receive a number of seats (approximately) proportional to the percentage of the vote they received by making use of a [[Partisan systems|partisan system]]. One system which achieves high levels of proportional representation is [[
There are several metrics that are used to define proportionality of election methods explicitly.
▲== Measures ==
=== Gallagher index ===
[[W:Michael Gallagher (academic)|Michael Gallagher]], who created the index, referred to it as a "least squares index", inspired by the residual sum of squares used in the method of least squares. The index is therefore commonly abbreviated as "LSq" even though the measured allocation is not necessarily a least squares fit. The Gallagher index is computed by taking the [[W:Square root|square root]] of half the [[W:Summation|sum]] of the squares of the difference between percent of votes (<math>V_i</math>) and percent of seats (<math>S_i</math>) for each of the political parties (<math>i=1,\ldots,n</math>).
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The index weighs the deviations by their own value, creating a responsive index, ranging from 0 to 100. The larger the differences between the percentage of the votes and the percentage of seats summed over all parties, the larger the Gallagher index. The larger the index value, the larger the disproportionality, and vice versa. Michael Gallagher included "other" parties as a whole category, and [[Arend Lijphart]] modified it, excluding those parties. Unlike the well-known [[Loosemore–Hanby index]], the Gallagher index is less sensitive to small discrepancies.
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