Metrics

The following sections describe each metric and how they are calculated.

Modularity:

A communitiy is a group of people that have more in common with each other, on average, than they do with people from another group. Redistricting groups people across geographic space, and therefore can either split communities or keep them intact. Redistricting laws in many states have explicit preferences for redistricting plans that follow existing boundaries, such as county lines, which implicitly encourages communities to be kept intact. Frequently, in legal challenges to gerrymandered districts, split municipalities are shown as evidence that natural communities were split in order to gain partisan advantage.

Communities of interest and majority-minority districts are two explicit ways of keeping particular communities intact, and both function by keeping groups of people with common policy concerns in a single district. For communities of interest, people from such a group self identify and advocate for being kept in a single interest so that they can elect a representative that will represent their particular interests. Majority-minority districts are similar, though they are required by the Voting Rights Act so as to not "improperly dilute minorities voting power."

None of these community formations, however, attempt to maintain communities across all districts. Framed as an optimization problem, we might ask how we could make districts such that we maintain as many communities as possible within each district, such that we minimize community splitting across all districts. While optimization is redistricting is notoriously difficult, we attempt here to show at least what a range of possibilities might look like if such a metric were incorporated into redistricting law.

For such an optimization, we need both a formula for defining community strength, and a measurement to use in that formula. For the measurement, we employ human mobility flows from Safegraph. The mobility flows consist of anomymized cellphone counts that have moved from one census block group to another during a given time span. To quantify community strength, we use modularity, which is freqeuntly used in community detection research. Modularity here is defined as the sum of district intra flow divided by the sum of district inter flows, where intra flows are mobility flows originating in one district and ending in that same district, while inter flows are mobility flows originating in one district and ending in another. By summing across all districts to calculate modularity, we can get a sense of how the districting plan, as a whole, keeps communties intact.

Efficiency Gap

"[The efficiency gap] represents the difference between the parties’ respective wasted votes in an election—where a vote is wasted if it is cast (1) for a losing cadidate, or (2) for a winning candidate but in excess of what she needed to prevail. Large numbers of votes commonly are cast for losing candidates as a result of the time-honored gerrymandering technique of “cracking.” Likewise, excessive votes often are cast for winning candidates thanks to the equally age-old mechanism of “packing.” The efficiency gap essentially aggregates all of a district plan’s cracking and packing choices into a single, tidy number." (Stephanopoulos, McGhee, 2015). For more reading on the efficiency gap, you can visit ballotpedia.

To demonstrate how gerrymandering uses both packing and cracking to change election outcomes, we present the following example from the Washington Post: In this example, the Purple and Green parties are competing to win seats in 5 equal-population districts, and votes for a given party a represented by icons of the same color. The Green party receives 20/50 votes, yet is able to win 3/5 seats due to how the districts were arranged.

To achieve this outcome, Purple voters are "packed" into two districts such they was "waste" votes in those districts, as they receive many more votes than simple majorrity required to win those two districts. Conversely, almost no Green votes are "wasted" on competing for those two districts - instead, the Green votes are largely concentrated in the upper three districts. In those same districts, the Green party is able to narrowly win all three elections, since the purple voters were "cracked" such they are a narrow minority in the upper three districts.

Compactness

Compactness is metric that is used in redistricting to help guard against gerrymandering. Compactness can be defined geometrically in many ways, but the general idea in redistricting is to avoid long, odd shapes that demonstrate intent to unnaturally split communities in such as way as to crack and pack districts. For more specifics on compactness, you can refer to ballotpedia. Here, we use the Polsby-Popper definition of compactness, which essentially compares the area and perimeter of a district. The range of values of this metric is from 0 to 1, where 0 is the least compact and 1 is the most compact (the district is circular).

Metadata

The following table describes the attributes used in the plots and interactive maps. Demographic and voting data was acquired from Maptitude.