It's Time to End Gerrymandering V: Partisan Symmetry Continued

We previously discussed the notion of partisan symmetry in our series on gerrymandering, as well as statistical tests based on concepts of skew and spread which can be used to detect gerrymandering when it occurs. Here we'll try to put all these concepts together into a single statistical test, which ultimately turns out to be a small modification of the skew test proposed by Sam Wang. We'll also discuss some of the limitations of the statistical testing approach we have employed, and how those limitations could be remedied through more sophisticated methods.

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It's Time to End Gerrymandering IV: Partisan Symmetry

Gerrymandering is the process of drawing legislative districts in order to manipulate election outcome. So far in this series, we have discussed the inherent disproportional nature of single winner elections, statistical tests that can be used to detect gerrymandering, and gave some initial consideration to how those tests might be manipulated. Here we will discuss a concept called partisan symmetry, which is important both from a legal and mathematical perspective.

As of yet, the supreme court has not accepted a standard for partisan gerrymandering that is legally actionable, although they have indicated that they are warm to accepting a standard based on partisan symmetry (link is a pdf). Partisan symmetry means that the election outcomes can be disproportionate, but the disproportionality should not only favor one party. Suppose that a given party wins 70% of seats with 60% of the vote. If in a hypothetical outcome with the same districting plan, 40% of the vote would have gotten that party 30% of seats, then the result can be considered symmetric even though it is not proportional. The hypothetical results can be constructed using a concept of a seats-votes curve, where the vote tallies are shifted by a uniform percentage in each district and the results recomputed. We used a similar concept for analyzing the electoral college results in the past three presidential election in a previous post. The legal argument against partisan asymmetry is that it violates the fourteenth amendment equal protection clause since the districting plan disadvantages citizens based on their political preferences. 

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It's Time to End Gerrymandering III: Safe Wins Continued

Gerrymandering is the practice of drawing legislative districts in order to deliberately manipulate election outcomes. So far in this series we have discussed how the winner take all voting system employed for electing congressional delegation does not typically result in a party winning seats in proportion to its overall level of support and how this can complicate analysis of gerrymandering. We also discussed how statistical tests can be used to identify when the redistricting party has engineered artificial safe wins, or wins by comfortable but not blowout margins, to maximize their share of seats.

In this post, we will follow with further discussion of statistical tests and introduce some additional measures that can be used to develop tests based on spread. The goal is to create tests based on well known statistics that detect gerrymandering but are simple enough to avoid the need for special software. This is easier said than done, since there is no one size fits all strategy to gerrymander a state and a test that is simple may not cover all cases. In addition, with computerized redistricting, once a statistical test is set as standard for a legally actionable threshold for striking down a district map, parties can attempt to develop strategies to increase their advantage while flying under the radar of the test. We will attempt to address this in by identifying gerrymandered voting patterns which would pass the statistical tests under consideration.

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It's Time to End Gerrymandering II: Safe Wins

Gerrymandering is the term used to describe deliberate manipulation of the electoral process by drawing non competitive districts for congressional and state assembly races. In the first post in this series, we discussed the concept of disproportionate outcomes, were the number of districts won by a party is out of proportion with their statewide level of support. Using district level data from the 2008, 2012, and 2016 presidential elections, we saw that proportional outcomes were very rare. Unfortunately, this is not enough to declare that we have uncovered gerrymandering because single winner elections tend not to lead to proportional representation, and even can lead to minority rule by chance.

Here we will attempt to separate chance outcomes from deliberate manipulation using statistical tests aimed at uncovering irregularities in the vote percentages of a state's districts. In particular, we are trying to uncover if the architects of the districting plan were trying to carve out safe wins for one party or the other. Safe wins are comfortable enough to limit or remove competition in the district, but gerrymanderers don't want to win by blowout margins either because this is inefficient. Safe wins provide the best tradeoff between eliminating competition and maximizing representation for the gerrymandering party.

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It's Time to End Gerrymandering I: Disproportionate Outcomes

Representative forms of government are supposed to operate on a simple principle: citizens choose which politicians makes up their government. Gerrymandering flips this on its head, and allows the government to choose which citizens make up their constituency. Politicians do this to eliminate competition in elections, removing the primary way for citizens to hold their representatives accountable. This is also done by political parties to boost their share of seats in congress and state assemblies relative to their share of votes. Over time, gerrymandering can even lead to single party rule. Once elections stop being competitive, citizens begin to see that joining the ruling party is a better strategy to getting their voice heard than attempting to oppose them. 

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