The seats-to-votes ratio,[1] also known as the advantage ratio,[2] is a measure of equal representation of voters. The equation for seats-to-votes ratio for a political party i is:
where v i {\displaystyle \mathrm {v_{i}} } is fraction of votes and s i {\displaystyle s_{i}} is fraction of seats.
In the case both seats and votes are represented as fractions or percentages, then every voter has equal representation if the seats-to-votes ratio is 1. The principle of equal representation is expressed in slogan one man, one vote and relates to proportional representation.
Related is the votes-per-seat-won,[3] which is inverse to the seats-to-votes ratio.
The Sainte-Laguë Index is a disproportionality index derived by applying the Pearson's chi-squared test to the seats-to-votes ratio,[4] the Gallagher index has a similar formula.
Different apportionment methods such as Sainte-Laguë method and D'Hondt method differ in the seats-to-votes ratio for individual parties.
The Sainte-Laguë method optimizes the seats-to-votes ratio among all parties i {\displaystyle i} with the least squares approach. The difference of the seats-to-votes ratio and the ideal seats-to-votes ratio for each party is squared, weighted according to the vote share of each party and summed up:
It was shown[2] that this error is minimized by the Sainte-Laguë method.
The D'Hondt method approximates proportionality by minimizing the largest seats-to-votes ratio among all parties.[2] The largest seats-to-votes ratio, which measures how over-represented the most over-represented party among all parties is:
The D'Hondt method minimizes the largest seats-to-votes ratio by assigning the seats,[5]
where s {\displaystyle \mathbf {s} } is a seat allocation from the set of all allowed seat allocations S {\displaystyle {\mathcal {S}}} .
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