# (Dis)proportionality Measures¶

The proportion module contains functions for measuring disproportionality in electoral systems.

voting.proportion.adjusted_loosemore_hanby(votes, seats, parties='votes')[source]

Calculate the adjusted Loosemore-Hanby index of disproportionality.

$N \sum_{i=1}^n |v_i - s_i|$

where N is $$\sum_{i=1}^n v_i$$ if parties == 'votes' or $$\sum_{i=1}^n s_i$$ if parties == 'seats'.

Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

• parties (str) – votes or seats to use to calculate the effective number of parties

voting.proportion.dhondt(votes, seats)[source]

Calculate the D’Hondt index of disproportionality.

$\max \frac{s_i}{v_i}$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.gallagher(votes, seats)[source]

Calculate the Gallagher index of disproportionality.

$\sqrt{\frac{1}{2} \sum_{i=1}^n (v_i - s_i)^2}$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.grofman(votes, seats, parties='votes')[source]

Calculate the Grofman index of disproportionality.

$N \sum_{i=1}^n |v_i - s_i|$

where N is $$\sum_{i=1}^n v_i^2$$ if parties == 'votes' or $$\sum_{i=1}^n s_i^2$$ if parties == 'seats'.

Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

• parties (str) – votes or seats to use to calculate the effective number of parties

voting.proportion.least_square(votes, seats)[source]

Calculate the least squares index of disproportionality.

$\sqrt{\sum_{i=1}^n (v_i - s_i)^2}$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.lijphart(votes, seats)[source]

Calculate the Lijphart index of disproportionality.

$\max | v_i - s_i |$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.loosemore_hanby(votes, seats)[source]

Calculate Loosemore-Hanby index of disproportionality.

$\frac{1}{2} \sum_{i=1}^n |v_i - s_i|$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.rae(votes, seats)[source]

Calculate Rae’s index of disproportionality.

$\frac{1}{n} \sum_{i=1}^n |v_i - s_i|$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.regression(votes, seats)[source]

Calculate the regression index of disproportionality.

$\frac{\sum_{i=1}^n v_i s_i}{\sum_{i=1}^n v_i^2}$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.rose(votes, seats)[source]

Calculate the Rose index of proportionality.

$100 - \frac{1}{2} \sum_{i=1}^n |v_i - s_i|$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts

voting.proportion.sainte_lague(votes, seats)[source]

Calculate the Sainte-Lague index of disproportionality.

$\sum_{i=1}^n \frac{(v_i - s_i)^2}{v_i}$
Parameters
• votes (list) – a list of vote counts

• seats (list) – a list of seat counts