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This is done by a proportional formula or method; for example, the Sainte-Laguë method – these are the same methods that may be used to allocate seats for geographic proportional representation (for example, how many seats each states gets in the US House of Representatives). Votes and seats often cannot be mathematically perfectly allocated ...
The Hare quota is often used to set electoral thresholds and to calculate apportionments under party-list proportional representation when using the largest remainder method. In such cases, the Hare quota gives unbiased apportionments that do not favor either large or small parties. [1]
Specifically, the Hare quota is unbiased in the number of seats it hands out, and so is more proportional than the Droop quota (which tends to give more seats to larger parties). The Hare suffers the disproportionality that it sometimes allocates a majority of seats to a party with less than a majority of votes in a district.
When apportioning seats in proportional representation, it is particularly important to avoid bias between large parties and small parties to avoid strategic voting. André Sainte-Laguë showed theoretically that the Sainte-Laguë method shows the lowest average bias in apportionment, [2] confirmed by different theoretical and empirical ways.
Compared to ideal proportional representation, the D'Hondt method reduces somewhat the political fragmentation for smaller electoral district sizes, [1] where it favors larger political parties over small parties. [2] The method was first described in 1792 by American Secretary of State and later President of the United States Thomas Jefferson.
In mathematics and political science, the quota rule describes a desired property of proportional apportionment methods. It says that the number of seats allocated to a party should be equal to their entitlement plus or minus one.
A party-list proportional representation electoral system allocates a share of the seats in a legislature to a political party in proportion to its share of the votes, a task which is mathematically equivalent to establishing a share of surplus votes to be transferred to a hopeful candidate based on the overall vote for an eliminated candidate.
An alternative formula was proposed by Grigorii Golosov in 2010. [9]= = + which is equivalent – if we only consider parties with at least one vote/seat – to = = + (/) Here, n is the number of parties, the square of each party's proportion of all votes or seats, and is the square of the largest party's proportion of all votes or seats.