The Seats-to-votes ratio,Niemi, Richard G. "Relationship between Votes and Seats: The Ultimate Question in Poltical Gerrymandering." UCLA L. Rev. 33 (1985): 185.
/ref> also known as the advantage ratio, is a measure of equal representation of voters. The equation for seats-to-votes ratio for a political party ''i'' is: :

\mathrm = S_i/V_i

, where

V_i

is fraction of votes and

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 "One man, one vote", or "one person, one vote", expresses the principle that individuals should have equal representation in voting. This slogan is used by advocates of political equality to refer to such electoral reforms as universal suffrage, ...

and relates to

proportional representation Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical (e.g. states, regions) and political divis ...

. Related is the votes-per-seat-won,General Election 2019: Turning votes into seats, Published Friday, 10 January, 2020, Roderick McInnes, UK Parliament, House of Commons Library
/ref> which is inverse to the seats-to-votes ratio.

Relation to disproportionality indices

The

Sainte-Laguë Index The Sainte-Laguë index (SLI) measures an election’s disproportionality, the adherence to the one person, one vote principle of equal representation. This index assumes if the fraction of voters matches the fraction of seats, then perfect propor ...

is a disproportionality index derived by applying the

Pearson's chi-squared test Pearson's chi-squared test (\chi^2) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g ...

to the seats-to-votes ratio.Goldenberg, Josh, and Stephen D. Fisher. "The Sainte-Laguë index of disproportionality and Dalton’s principle of transfers." Party Politics 25.2 (2019): 203-207.
/ref>

Relation to seat allocation methods

Different seat allocation methods such as

D'Hondt method The D'Hondt method, also called the Jefferson method or the greatest divisors method, is a method for allocating seats in parliaments among federal states, or in party-list proportional representation systems. It belongs to the class of highe ...

and Sainte-Laguë method differ in the seats-to-votes ratio for individual parties. The proportionality of seat allocation methods can be proven by calculating the seats-to-votes ratio.

Seats-to-votes ratio for D'Hondt method

The D'Hondt method approximates proportionality by minimizing the largest seats-to-votes ratio among all parties. The largest seats-to-votes ratio, which measures how over-represented the most over-represented party among all parties is:

\delta = \max_i a_i,

The D'Hondt method minimizes the largest seats-to-votes ratio by assigning the seats,

\delta^* = \min_ \max_i a_i,

where

\mathbf

is a seat allocation from the set of all allowed seat allocations

\mathcal

. The D'Hondt method splits the votes into exactly proportionally represented ones and residual ones, minimizing the overall amount of the residuals in the process. The overall fraction of residual votes is

\pi^* = 1 - \frac.

Notes

{{Reflist, 30em Electoral systems Psephology