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The Loosemore–Hanby index measures disproportionality of electoral systems, how much the principle of one person, one vote is violated. It computes the absolute difference between votes cast and seats obtained using the formula:
where v i {\displaystyle v_{i}} is the vote share and s i {\displaystyle s_{i}} the seat share of party i {\displaystyle i} such that Σ i v i = Σ i s i = 1 {\displaystyle \Sigma _{i}v_{i}=\Sigma _{i}s_{i}=1} ,and n {\displaystyle n} is the overall number of parties.
This index is minimized by the largest remainder method with the Hare quota. Any apportionment method that minimizes it will always apportion identically to LR-Hare. Other methods, including the widely used divisor methods such as the Webster/Sainte-Laguë method or the D'Hondt method minimize the Sainte-Laguë index instead.
The index is named after John Loosemore and Victor J. Hanby, who first published the formula in 1971 in a paper entitled "The Theoretical Limits of Maximum Distortion: Some Analytic Expressions for Electoral Systems". Along with Douglas W. Rae's, the formula is one of the two most cited disproportionality indices.Whereas the Rae index measures the average deviation, the Loosemore–Hanby index measures the total deviation. Michael Gallagher used least squares to develop the Gallagher index, which takes a middle ground between the Rae and Loosemore–Hanby indices.