Diversity measures¶
The diversity
module provides functions for measuring the diversity
among quantities of groups in a population.
The quantity \(p_i\) represents the proportion of the population belonging to group \(i\).
-
voting.diversity.
berger_parker
(groups)[source]¶ Calculate the Berger-Parker index.
\[max(p_i)\]- Parameters
group (list) – a list of integers representing populations of groups
-
voting.diversity.
general
(groups, q=1)[source]¶ Calculate the general diversity index.
\[\left( \sum_{i=1}^n p_i^q \right) ^ {1/(1-q)}\]- Parameters
groups (list) – a list of integers representing populations of groups
q (float) – weight value
-
voting.diversity.
gini_simpson
(groups)[source]¶ Calculate the Gini-Simpson index.
\[1 - \sum_{i=1}^n p_i^2\]- Parameters
group (list) – a list of integers representing populations of groups
-
voting.diversity.
golosov
(groups)[source]¶ Calculate the effective number of parties using Golosov.
\[\sum_{i=1}^n \frac{p_i}{p_i + p_1^2 - p_i^2}\]where \(p_1\) is the largest proportion.
- Parameters
group (list) – a list of integers representing populations of a group
-
voting.diversity.
inverse_simpson
(groups)[source]¶ Calculate the Inverse-Simpson index.
\[\frac{1}{\sum_{i=1}^n p_i^2}\]- Parameters
group (list) – a list of integers representing populations of groups
-
voting.diversity.
laakso_taagepera
(groups)[source]¶ Calculate the effective number of parties using Laakso-Taagepera.
\[\frac{1}{\sum_{i=1}^n p_i^2}\]- Parameters
group (list) – a list of integers representing populations of groups
-
voting.diversity.
renyi
(groups, q=0)[source]¶ Calculate the Renyi entropy.
\[\frac{1}{1-q} \ln \left( \sum_{i=1}^n p_i ^ q \right)\]- Parameters
groups (list) – a list of integers representing populations of groups
q (float) – weight value