Representation Equity Index

Traditional measures of an election’s fairness have focused on party proportionality: does the proportion of votes for party X match the proportion of seats party X is awarded? This is measured by the Gallagher Index, the Loosemore-Hanby Index, and others.

This paper proposes a complementary voter-centric measure, the Representation Equity Index (REIndex), which measures the fairness of an election as a whole from the voter’s perspective. It is built on a Representation Equity Score (REScore), which is assigned to each voter in the election. In a perfect world each voter would have a REScore of 1 and the election as a whole would have a REIndex of 0.

Of course, we do not live in a perfect world. We describe the application of Representation Equity to what we believe would be typical of real-world Canadian elections. Unfortunately, our current Single Member Plurality (sometimes called First-Past-The-Post) does not fare well. When other common electoral systems such as Alternative Vote, Single Transferable Vote, and Mixed Member Proportional1 are considered, the Representation Equity Index shows significant differences between them that are not revealed by the traditional party proportionality measures.

To see the simulations, click here. For the theoretical basis, read on.


  1. MMP hasn't actually been implemented yet. ↩︎