Efficiency Gaps as Variable-sized Districts

Efficiency gaps are functionally equivalent to malapportioned districts.

While what it means for a state to have a significant ‘efficiency gap’ can be hard to grasp conceptually, it is exactly the same as that state having malapportioned congressional districts which is against the law (PL94–171). Specifically, every set of similar-sized districts with variable winner surpluses is functionally equivalent to a set of variable-sized districts with similar winner surpluses.

These sets of districts have:

• The same total votes
• The same aggregate votes by party
• The same wins and losses by party
• The same number of wasted votes by party, and,
• The same efficiency gap

The new districts are of variable size though.

Example

I will illustrate this, using the 2016 congressional election in North Carolina as an example.

Exhibit 1 shows the votes and seats won by district. Republicans won 10 of 13 seats (76.9%), despite only getting 53.3% of the state-wide vote. The efficiency gap was 20.3% favoring Republicans.

Exhibit 1 — North Carolina 2016 Congressional Election Results (Actual)

The first step in generating the equivalent variable-sized districts is to remove the excess winning votes in each race. Exhibit 2 shows the process.

Exhibit 2 — Excess Winning Votes Removed

The total votes per district are reduced to the minimum number of votes required for the losing party to still have lost. Then the winning party’s votes in each race are adjusted accordingly. The losing party’s votes in each race remain the same. The winning party in each race still wins the race, but they now have zero wasted votes in that race.

The total votes and total votes by party are now less than they were. Using these new intermediate totals, you calculate how many total votes and votes by party you need to reallocate to match the original vote totals.

Exhibit 3 shows the process of reallocating the excess winning votes.

Exhibit 3 — Excess Winning Votes Reallocated

For each party, you reallocate their excess winning votes evenly across the races they won. Then you re-compute the vote totals by party and wasted votes by race.

As noted above, these new districts have:

• The same total votes
• The same aggregate votes by party
• The same wins and losses by party
• The same number of wasted votes by party, and,
• The same efficiency gap

The districts are of different sizes though. As Exhibit 3 shows, the variation in implied district size in this case varies almost 20%.

Conclusion

The threshold for allowable efficiency gaps should reflect the fact that they are just like malapportioned districts. I have argued in a previous article that I believe the threshold for variability should be low, like the standard for the populations of state legislative districts no more than 5–10%.

This is the seventh in a series of articles on redistricting and partisan gerrymandering.