cosfun: Calculates the cosine measure

In polrep: Calculate Political Representation Scores

Calculates the cosine measure

Description

Calculates the cosine measure based on a population vector and a vector for the representatives

Usage

cosfun(Z,R)

Arguments

Z	Population vector
R	Vector for the representatives

Details

Calculates the cosine of a vector of voters and a vector for the representatives. These are the cosine proportionality scores presented by Koppel and Diskin (2009). Given are the '1-cos' values, which are not proper metrics (they do not have the triangle inequality property).

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.

cosunf = 1-(\sum(Z * R)/(\sum(Z^2) * \sum(R^2))^{\frac{1}{2}})

Other implementations can be found in the 'cosine.similarity' function of the package 'tcR', and the 'cosine' function of the package 'lsa'.

Value

A single score given the population and representatives

Author(s)

Didier Ruedin

References

Koppel, M., and A. Diskin. (2009) Measuring disproportionality, volatility and malapportionment: axiomatization and solutions. Social Choice and Welfare 33, no. 2: 281-286.

See Also

Farina

polrep documentation built on Jan. 5, 2024, 3:01 a.m.