The Loosemore–Hanby index measures disproportionality of electoral systems, how much the principle of one person, one vote is violated.[1] It computes the absolute difference between votes cast and seats obtained using the formula:
| LH= | 1 |
| 2 |
| n|v | |
| \sum | |
| i-s |
i|
vi
si
i
\Sigmaivi=\Sigmaisi=1
n
This index is minimized by the largest remainder (LR) 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.[3] 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.[4]
The LH index is related to the Schutz index of inequality, which is defined aswhere
ei
i
ai
\Delta
The complement of the LH index is called Party Total Representativity,[6] also called Rose index R. The Rose index is typically expressed in % and can be calculated by subtracting the LH index from 1:[7]
| R=1-LH=1- | 1 |
| 2 |
| n|v | |
| \sum | |
| i-s |
i|
This table uses the 2021 Dutch general election result.[8] The Netherlands uses a nationwide party list system, with seats allocated by the D'Hondt method. The low figure achieved through this calculation suggests the election was very proportional.
| VVD | 21.87 | 22.67 | 0.80 | ||
| D66 | 15.02 | 16.00 | 0.98 | ||
| PVV | 10.79 | 11.33 | 0.54 | ||
| CDA | 9.50 | 10.00 | 0.50 | ||
| SP | 5.98 | 6.00 | 0.02 | ||
| PvdA | 5.73 | 6.00 | 0.27 | ||
| GL | 5.16 | 5.33 | 0.17 | ||
| FvD | 5.02 | 5.33 | 0.31 | ||
| PvdD | 3.84 | 4.00 | 0.16 | ||
| CU | 3.37 | 3.33 | 0.04 | ||
| Volt | 2.42 | 2.00 | 0.42 | ||
| JA21 | 2.37 | 2.00 | 0.37 | ||
| SGP | 2.07 | 2.00 | 0.07 | ||
| DENK | 2.03 | 2.00 | 0.03 | ||
| 50+ | 1.02 | 0.67 | 0.35 | ||
| BBB | 1.00 | 0.67 | 0.33 | ||
| BIJ1 | 0.84 | 0.67 | 0.17 | ||
| Others | 1.97 | 0.00 | 1.97 | ||
| Total of absolute differences | 4.58 % | ||||
| Total / 2 | 2.29 % | ||||
The following table displays a calculation of the Rose Index by Nohlen of the most, or second most, recent legislative election in each European country prior to 2009. This calculation ranges from 0-100, with 100 being the most proportional score possible, and 0 the least. Parties which received less than 0.5% of the vote were not included.[9]
| Country | data-sort-type="number" | Rose Index |
|---|---|---|
| Albania | 46.6 | |
| Andorra | 89.1 | |
| Austria | 95.6 | |
| Belarus | N/A | |
| Belgium | 90.5 | |
| Bosnia and Herzegovina | 82.0 | |
| Bulgaria | 93.4 | |
| Croatia | 87.2 | |
| Cyprus | 96.1 | |
| Czechia | 91.1 | |
| Denmark | 99.0 | |
| Estonia | 94.0 | |
| Finland | 94.6 | |
| France | 77.4 | |
| Germany | 94.2 | |
| Great Britain | 80.0 | |
| Greece | 90.9 | |
| Hungary | N/A | |
| Iceland | 96.7 | |
| Ireland | 90.3 | |
| Italy | 95.1 | |
| Latvia | 89.7 | |
| Liechtenstein | 98.3 | |
| Lithuania | 91.5 | |
| Luxembourg | 95.5 | |
| Macedonia | N/A | |
| Malta | 98.0 | |
| Moldova | 83.6 | |
| Monaco | 68.8 | |
| Montenegro | N/A | |
| Netherlands | 96.7 | |
| Norway | 96.1 | |
| Poland | 53.3 | |
| Portugal | 91.5 | |
| Romania | N/A | |
| Russia | 70.0 | |
| San Marino | 98.5 | |
| Serbia | 90.8 | |
| Slovakia | 89.1 | |
| Slovenia | 90.1 | |
| Spain | 93.2 | |
| Sweden | 95.7 | |
| Switzerland | 96.2 | |
| Ukraine | 81.6 |