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I'm using the Census Shape files for state legislative district lines for 2008 and 2012. I want to create a measure that indicates how much these lines have changed between these two time periods (because of redistricting). At first, I thought the best approach was to calculate the percentage of overlap between the two different layers by each district. But, I'm not sure if that's the appropriate way to do it.

Is there a better measure that tells me how similar (or different), a 2012 district is to its 2008 counterpart?

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I don't think percentage overlap is a particularly useful measure, especially in the American West where districts may be sparsely populated and thus a large change in overlap may represent a small change in the voting population contained in the district. I would look for measures that do a better job of assessing the change in the voters in the district. Perhaps start with the block level census data and figure out how the census blocks are moved from one district to another, thus giving a measure of what percentage of voters were moved from one district to another. Depending on the reasons you are trying to do this assessment, you might dig even deeper and look at the change in racial composition of the districts, family income characteristics, etc.

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