diversity_aid {PolicyPortfolios}

Calculate portfolio diversity (Average Instrument Diversity)

Description

Function used to calculate the diversity of a portfolio (Average Instrument Diversity, AID). It is adapted from the idea of a Gini-Simpson diversity index. The measure can be interpreted as the average probability that picking two policy spaces from different Targets, they use a different Instrument.

Usage

diversity_aid(M)

Arguments

M

Matrix with two dimensions (Instrument, Target) containing absence (0) or presence (1) of policy intervention.

Value

A value of the portfolio diversity.

Details

\forall_{t=1..T}, \forall_{i=1..I} \sum_{c=1}^{C} \frac{c_{t,i} = c_{!t,!i}}{C}

where:

T are the targets covered by at least one policy instrument I are the instruments addressing at least one policy target C are the entirety of target-instrument-constellations

It is applied only to matrices, not to tidy objects in a proper policy portfolio. For a proper treatment using tidy data, use it through pp_measures().

References

Fernández-i-Marín, X., Knill, C. & Steinebach, Y. (2021). Studying Policy Design Quality in Comparative Perspective. _American Political Science Review_, online first.

Examples

data(consensus)
consensus %>%
  filter(Sector == "Environmental") %>%
  filter(Country %in% c("France", "United States")) %>%
  filter(Year %in% c(1976, 2005)) %>%
  pp_array() %>%
  apply(., c(1, 2, 3), diversity_aid) %>%
  as.vector() %>%
  round(digits = 3)
# 1976 (FR, US), 2005 (FR, US)