COI Splitting

When you click on the Advanced tab there is now a Community Splitting section. This tool lets you analyze the degree to which communities of interest (COI) are split by the districts in a map.

To analyze the degree to which the COI maps associated with your map are split, simply press the Analyze button. Note: Maps that aren’t COI and overlays that aren’t maps per se, i.e., geojson overlays, are ignored. We need the map details for the analysis.

You will then see a table with two metrics calculated for each COI. These metrics are described in a forthcoming paper in Stanford Journal of Civil Rights and Civil Liberties.¹

• Effective Splits Index — The index provides a weighted measure of the number of splitting events. For a community that is split into equal halves by population, the effective number of splits is one. For a community that is divided into two parts, one with 90% of its population and one with 10% of its population, the index yields 0.22 effective splits. A result more than 0.5 effective splits may be regarded as a substantial split. In short, “effective splits” deem an unevenly split community as being less split than an equally split one. The ideal value is zero — no splits.
• Uncertainty of Membership — This measure characterizes how many bits of information² are needed to specify how a community is divided up. If a COI is split into two halves of equal population, there is 1 bit of uncertainty about which district a resident belongs to. If the community is unequally split, the amount of uncertainty is smaller. This definition matches the idea that a highly uneven split of a COI should be counted less than an even split. Effectively, this corresponds to the amount of uncertainty a resident of a COI experiences when attempting to guess what district they reside in. Uncertainty of greater than 0.5 bit may be considered substantial. The ideal value is zero — no uncertainty.

The following table shows you some example splits and the corresponding results for these two measures, where uncertainty is the number of bits.

Because this is a somewhat expensive piece of analysis, we don’t run it automatically — you have to press Analyze, like you do for Demographic Voting Analysis.

Footnotes

1. See Turning Communities Of Interest Into A Rigorous Standard For Fair Districting (Wang et al, forthcoming).
2. You may recognize this from Information theory a la Claude Shannon.