The LoosemoreâHanby 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:
,
where
is the vote share and
the seat share of party
such that ,
and is the overall number of parties.
[2]
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 LoosemoreâHanby index measures the total deviation. Michael Gallagher used least squares to develop the Gallagher index, which takes a middle ground between the Rae and LoosemoreâHanby indices. [4]
The LH index is related to the Schutz index of inequality, which is defined as
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]
.
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.
Party | Vote Share (%) | Seat Share (%) | Absolute Difference (%) | |
---|---|---|---|---|
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 | Rose Index |
---|---|
Albania | 46.6 [a] |
Andorra | 89.1 [b] |
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 |
The LoosemoreâHanby 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:
,
where
is the vote share and
the seat share of party
such that ,
and is the overall number of parties.
[2]
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 LoosemoreâHanby index measures the total deviation. Michael Gallagher used least squares to develop the Gallagher index, which takes a middle ground between the Rae and LoosemoreâHanby indices. [4]
The LH index is related to the Schutz index of inequality, which is defined as
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]
.
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.
Party | Vote Share (%) | Seat Share (%) | Absolute Difference (%) | |
---|---|---|---|---|
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 | Rose Index |
---|---|
Albania | 46.6 [a] |
Andorra | 89.1 [b] |
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 |