The Robin Hood Index (or Pietra ratio) is a measure of inequality in a resource distribution in a population. It indicates the amount of the resource that needs to be taken from more affluent areas and given to the less affluent areas in order to achieve an equal distribution (in effect, to rob from the rich to give to the poor).

Data collection:

(1) Separate population according to the amount of resource allocated and sort by ascending percentages.

(2) Divide population into tenths of the population

Decile |
Percentage of Total Resource |
Cumulative Sum of Total Resource |

0 |
0 |
0 |

1 (10%) |
x1 |
x1 |

2 (20%) |
x2 |
x1 + x2 |

3 (30%) |
x3 |
x1 + x2 + x3 |

4 (40%) |
x4 |
x1 + …+ x4 |

5 (50%) |
x5 |
x1 + …+ x5 |

6 (60%) |
x6 |
x1 + …+ x6 |

7 (70%) |
x7 |
x1 + …+ x7 |

8 (80%) |
x8 |
x1 + …+ x8 |

9 (90%) |
x9 |
x1 + …+ x9 |

10 (100%) |
x10 |
x1 + …+ x10 |

Method 1: From the Lorenz Curve

Step 1: Derive the equation for the Lorenz curve (see previous section).

Step 2: The height of the 45 degree line along the y-axis is the same as the value of the x-axis.

Step 3: Determine the y-value for the Lorenz curve for a given x value.

Step 4: The Robin Hood index is the maximum vertical distance between the Lorenz curve and the 45 degree line of equal resource allocation.

Robin Hood index =

= MAX((x value) – (y value for Lorenz function))

For the example in the Appendix of Kennedy et al (1996), this is 31.8%.

Method 2: By Percentages > 10%

Step 1: Identify the deciles with a percentage of resource allocation > 10%.

Step 2: Add together the percentages for these deciles.

Step 3: Subtract 10 * (number of deciles involved).

Robin Hood index (as a percent) =

= SUM(percentages for deciles > 10%) – (10% * (number of deciles summed))

Interpretation:

• minimum Robin Hood index: 0

• The greater the Robin Hood index, the more unequal the resource distribution.

• The index can be correlated with other health measures like mortality.