# Three tests for practical evaluation of partisan gerrymandering.

 Author: Wang, Samuel S.-H. Position: II. Quantitatively Analyzing the Effects and Intents of Partisan Gerrymandering A. Analysis of Effects 3. National Districting Patterns Can Be Used to Identify a Natural Seats/Votes Relationship through Conclusion, with footnotes and tables, p. 1289-1321
1. National districting patterns can be used to identify a natural seats/votes relationship

Computer simulations can be used to ask a simple question: If a given state's popular House vote were split into differently composed districts carved from the same statewide voting population, what would its congressional delegation look like? The answer allows the definition of a range of seat outcomes that would arise naturally from districting standards that are extant at the time of the election in question.

It is possible to calculate each state's appropriate seat breakdown--in other words, how a congressional delegation would be constituted if its districts were not contorted to protect a political party or an incumbent. This is done by randomly selecting combinations of districts from around the United States that add up to the same statewide vote total for each party. Like a fantasy baseball team, a delegation put together this way is not constrained by the limits of geography. On a computer, it is possible to create millions of such unbiased delegations in short order. In this way, one can ask what would happen if a state had districts whose distribution of voting populations was typical of the pattern found in rest of the nation. (108) Because this approach uses existing districts, it uses as a baseline the asymmetries that are present nationwide. (109) Indeed, the average result of these simulations approximates a "natural" seats/votes relationship that can be defined with mathematical rigor and exactitude. In short, these simulations detect distortions in representativeness in one state, relative to the rest of the nation.

Using a standard ThinkPad Xl Carbon laptop computer equipped with the mathematical program MATLAB, simulation code (110) can perform one million simulations for a state in less than twenty seconds. Figure 2 shows one thousand such "simulated delegations" for the state of Pennsylvania, along with the actual outcome in gray. The solid curve defines a mathematically expected average seats/votes relationship.

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It is apparent that most possible redistrictings would have resulted in a more equitable congressional delegation. For outcomes with the same popular-vote split (50.7% Democratic, 49.3% Republican), one million simulations gave a median result of eight Democratic, ten Republican seats (an average of 8.5 Democratic seats). The actual outcome was five Democratic, thirteen Republican; however, only 0.2% of the simulations with the same popular vote (i.e., 50.7% Democratic) led to such a lopsided (or a more lopsided) split favoring Republicans.

Pennsylvania is known to have been targeted by the Republican State Legislative Committee's Redistricting Majority Project (REDMAP), a multiyear effort to facilitate and carry out aggressive redistricting after the 2010 census. (111) A similar computational analysis of all fifty states can be done to test if additional REDMAP states show statistical anomalies.

For all fifty states, Figure 3 is calculated using the vote outcomes of non-extreme states (shaded in light gray) to feed the simulations. (112) These results coincide strongly with targeted partisan redistricting efforts (113) and are highly unlikely to have arisen by chance. White shading indicates Republican Party control over redistricting, dark gray indicates Democratic Party control, and black indicates nonpartisan commission (AZ, Arizona) or a court-ordered map (TX, Texas). Out of ten states with extreme outcomes, eight favored the party that controlled the process, and none worked against the party in control. (114) Indeed, the extreme cases include all states with single-party control that have been mentioned on a redistricting watchlist published in 2011 by the Washington Post. (115)

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In Part II.B below, I develop an analysis of intent that again uses the zone-of-chance concept. There, as here, the standard deviation, sigma (a), will be used as a yardstick of deviations from the average expected outcome. As before, the general idea is that an average outcome only reflects one point in a range of outcomes, and the standard deviation is necessary to define a zone of chance. Generally speaking, for a bell-like curve, which these simulations approximately follow, a difference of 1.6 standard deviations or more occurs by chance in five percent of cases. Five percent is a common threshold for determining statistical significance. (116) The standard deviation is a handy and universal reference measure for detecting extreme outcomes, and it applies to all the analyses and tests in this Article. For convenience of notation in the tables that follow, I define the quantity Delta ([DELTA]) as the difference from average expectations, divided by sigma.

Table 1 shows states for which the partisan discrepancy was greater than one sigma in 2012. For comparison, discrepancies for the same states are shown for 2010 and 2014. Simulation-based values for sigma are given in the columns labeled "SD (sigma)." (117)

Five states showed deviations that were greater than one sigma and less than two sigma: Florida, Illinois, Indiana, Maryland, and Virginia. Six more states showed a deviation exceeding two sigma: Arizona, Michigan, North Carolina, Ohio, Pennsylvania, and Texas. Of these eleven states, REDMAP's redistricting efforts are known to have targeted five: Indiana and all four Republican-controlled states with two-sigma discrepancies, namely Michigan, North Carolina, Ohio, and Pennsylvania. (118) Of the remaining greater-than-two-sigma states, a fifth state, Texas, was redistricted by Republicans but showed a discrepancy favoring Democrats. (119) A sixth state, Arizona, was redistricted by an independent commission and favored Democrats. (120)

Of these six states, I briefly describe three cases of special interest: California, Texas, and Florida.

California. California is worth mentioning as a counterexample to the imbalanced states shown above. California was redistricted by an independent commission. (121) In 2012, the California House popular vote was 62% Democratic, resulting in 38 out of 53, or 72%, Democratic seats. (122) However, the average simulated delegation was also 72% Democratic. (123) Thus, election results in California exactly meet the expectations that arise from nationwide districting patterns.

Texas. Although the resampling simulations are a powerful and sensitive measure, the case of Texas demonstrates how examination of additional factors can be necessary. Before the 2012 election in Texas, a complex series of legal battles culminated in a court-ordered redistricting plan (124) and a congressional election outcome in which over 60% of Texas voters voted for Republicans, resulting in 24 Republican seats out of 36 total. (125) From a statistical standpoint, this was an underperformance for Republicans, who in a simulation would have won over 28 seats on average--a discrepancy of Delta = 2.3 times sigma, which is outside the zone of chance, and therefore a statistically significant deviation. One major factor contributing to this discrepancy was the presence of Hispanic majorities in 9 districts, (126) 6 of which elected Democratic congressmen. (127) These majority-minority districts, which have special status under the Voting Rights Act of 1965, reflect the growing Hispanic population in Texas, which as of the 2010 census constituted 38% of Texans. (128) Democrats won approximately 40% of the statewide two-party popular vote and won 12 out of 36 seats, or 33% of seats. (129) Because this change is in the direction of proportionality compared with typically occurring seats-votes curves, it is eu-proportional. The number of majority-minority districts (which usually favor Democrats) falls within the Gingles criteria. Thus, the final outcome in Texas in 2012 favored the partisan minority for mandated race-based reasons, and because it is eu-proportional, would not be grounds for further action.

Florida. In this case, where the value of Delta is between one and two, a similar but statistically stronger answer is given by a map-drawing approach. Chen and Rodden took a geographically intensive approach, drawing districts using automated rules of contiguity and community preservation, and implemented these rules thousands of times through detailed computer simulations. (130) They found that Florida's 2010 redistricting scheme was more favorable to Republicans than over 99% of their simulations, indicating that the Florida legislature applied an approach that led to a more partisan outcome than Chen and Rodden's rules would support. (131) Geographic considerations are among the principles of districting mandated by the Constitution of the State of Florida, which also allows for judicial review by the Florida Supreme Court. (132) In July 2015, that court replaced the map to comply with the state constitution. (133)

Nationwide, repairing the one-sigma and greater Republican-redistricted states (seven in all) would lead to an average swing of approximately twenty-eight seats (an average of 27.7) toward Democrats; repairing the two Democratic-redistricted states, Illinois and Maryland, would lead to an average swing of 5.7 seats toward Republicans. Therefore, based on these measures, Republican gains in 2012 from aggressive redistricting (28 seats) were nearly five times the advantages gained by Democrats from the same process (6 seats). This sharp asymmetry coincides with a period during which state legislative processes have come increasingly under single-party control. (134) Changes between decadal redistrictings favored Republicans, who controlled 13 state capitals in 2002, rising to 24 state capitals in 2012. (135) During that same interval, Democrats went from controlling 8 state capitals to controlling 13 state capitals. (136) Thus the potential for partisan control of districting has increased for both major parties, with a greater...