Skew
Skew is a measure of how much a redistricting plan favors one party compared to the other. The measure assumes two major parties and uses the PVI to determine both the natural political inclination of the state as well as the political inclinations of each district based on their competitiveness.
1. Find the PVI for the state as a fraction (or divide the percent by 100) and multiply that by 4 times the number of districts. This is the expected excess in the delegation for the party in a neutral map. Count Republicans as a negative number.
2. Find the PVI's of the actual districts. Count 0 for each highly competitive district (PVI 0 or 1), +1 for all other Democratic districts, and -1 for all other Republican districts. The total is the expected excess in the delegation under the actual map.
3. Take the number from step 2 and subtract the number from step 1. Express a negative number as a positive number in favor of the Republicans. The resulting positive number is the SKEW score, and lower numbers are closer to the ideal partisan fairness.
For example consider the Congressional map for Pennsylvania in 2016. The official PVI for the whole state is based on the 2008 and 2012 elections and slightly favors the Democrats at +1.16%. Multiplying 0.0116 times 4 times 18 districts equals 0.835. This rounds off to +1 which is the expected advantage for the Democrats.
The PVI for the actual districts has 1 highly competitive district (PA-8), 5 districts for the Democrats (PA-1, PA-2, PA-13, PA-14, and PA-17), and the remaining 12 districts for the Republicans. The expected excess in the delegation is 5 - 12 = -7 which is an advantage for the Republicans.
Now take -7 and subtract +1 which gives -8. Since it's a negative number it reflects a plan skewed for the Republicans. The SKEW score for the plan is 8.
