# 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

voting.diversity.shannon(groups)[source]

Calculate the Shannon index.

$\sum_{i=1}^n p_i \ln (p_i)$
Parameters

groups (list) – a list of integers representing populations of groups

voting.diversity.simpson(groups)[source]

Calculate the Simpson index.

$\sum_{i=1}^n p_i^2$
Parameters

groups (list) – a list of integers representing populations of groups