(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