# Farina: Calculates the Farina index In polrep: Calculate Political Representation Scores

## Description

Calculates the Farina index based on a population vector and a vector for the representatives

## Usage

 1 Farina(Z,R) 

## Arguments

 Z Population vector R Vector for the representatives

## Details

This calculated the Farina index as outlined in Kestelman 1999. It refers to a suggestion by J.E.G. Farina to use the cosine as a similarity index. Cosine similarity is not a proper metric, though.

Farina = \arccos(∑(Z*R)/(∑(Z^2)*∑(R^2))^{\frac{1}{2}})

The order of the groups in the population vector and the vector for the representatives needs to be the same. If there are groups A, B, C in the population, both vectors need to cover their proportion in the same order.

## Value

A single score given the population and representatives

Didier Ruedin

## References

Kestelman, P. 1999. 'Quantifying Representativity'. Voting Matters 10. http://www.votingmatters.org.uk/ISSUE10/P6.HTM.

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