The Muon Rules

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This thread is the based on items developed in many threads on the Atlas Forum and except for erosity was initially codified by the Forum Redistricting Commission of 2014 to guide the submission and judging of plans for VA. The posts have been edited to reflect updates since that time. In that same spirit, I may make further edits based on comments and examples that arise.

Item 1. Choice of software and format. Plans shall be developed with Dave's Redistricting App using 2010 census data with Voting Age Population and City/Town lines enabled. For each district a plan shall list the Deviation (see item 7 for the definition), minority Voting Age Population (VAP) in percent for districts where it exceeds 25%, and the President 2008 results in percent. Plans must include a statewide map with City/Town lines off, and zoom views for areas where the division of counties is difficult to see from the statewide view with City/Town lines on. [Exceptions to the submission format may be granted by a majority vote of the commission.]

Item 2. Application of the Voting Rights Act. Each submitted plan must comply with the VRA. Section 2 of the VRA requires that minorities must have the opportunity to elect their candidate of choice. SCOTUS decisions have clarified that section 2 is mandated when a minority makes up at least 50%+1 of the VAP (or CVAP for Hispanics) in a compact area and there is evidence of racial bloc voting. The district does not need to have 50% of a minority to elect a candidate of choice if it can be shown that the minority is likely to prevail with a lower percentage. A district cannot be drawn where race is the predominant factor guiding the shape of the district.

Item 3. Criteria to evaluate plans - muon2's SPICE system. Plans shall be evaluated with five measures: two political measures, one demographic measure, and two geographic measures as follows.

Political measures

SKEW: a measure of the amount that a redistricting plan favors one party over another compared to the natural leanings of the state.

POLARIZATION: a measure of the number of districts that are uncompetitive for one of the major parties.

Demographic measures

INEQUALITY: a measure of the amount of population variance among districts.

Geographic measures

CHOP: a measure of the number of geographic communities of interest, such as political subdivisions, divided by separate districts.

EROSITY: a measure of the amount of irregularity of district boundaries based on the separation of connected population centers into different districts.

Use of measures

Measures are set up so that low scores are more desirable.

Item 3. Use of SPICE sores. Political measures (SKEW and POLARIZATION) may be used to judge between plans, but are not used to invalidate them. A plan is discarded if the INEQUALITY exceeds the maximum allowed by law. A combination of INEQUALITY, CHOP and EROSITY is used to eliminate plans according to one of the following methods. Multiple plans may be acceptable.

Item 3a. A plan is discarded if another plan has a lower CHOP while not increasing EROSITY. A plan is discarded if another plan has a lower EROSITY while not increasing CHOP. If two plans have equal CHOP and EROSITY, but differ on INEQUALITY the plan with higher INEQUALITY is discarded.

Item 3b. A plan is discarded if another plan has a lower CHOP+INEQUALITY while not increasing EROSITY. A plan is discarded if another plan has a lower EROSITY while not increasing the total CHOP+INEQUALITY.

These next two items will deal with the political measures for a plan. Under Item 3, they will only be used to guide the commission when they consider final plans, and can't be used to eliminate plans prior to the end of the submission period. First I will provide some definitions.

Definition: PVI. The Partisan Voting Index is based on the method developed by the Cook Political Report and widely used in assessing the political tendencies of congressional districts. It compares the Democratic share of the two-party vote in a state or a district to the Democratic share of the national presidential vote, averaged over the last two presidential elections. Shares are multiplied by 100 to get a percent, and expressed as D+x when positive and R+(-x) when negative.

Definitions: A highly competitive district has a PVI of 0 or 1 (-0.014 to +0.014) and statistically such districts have an even chance of being one by either district. A competitive district has a PVI of 2 through 5 (-0.054 to -0.015 and +0.015 to 0.054) and statistically such districts have an 3 out of 4 chance of being held by the favored party. An uncompetitive district has a PVI of 6 or greater for either party and has better than a 9 in 10 chance of being held by the favored party. This is based on congressional results during the preceding decade.

Definition: The expected delegation difference from a state with a known PVI is equal to 50%+2*PVI, so for example a D+5 state would be expected to have a delegation of 60% Democrats. Studies (e.g. Goeddert 2014) show that for every 1% shift in the national vote share there is an average shift by 2% in the number of congressional seats. Extending that to individual states, one can predict that in a 50-50 national election, a state delegation should have a Democratic fraction equal to 50% + 2*(state PVI). The percent difference between the Democratic and Republican fractions is then 4*(state PVI). The difference between the Democratic delegation size and the Republican delegation size should be 4*(state PVI/100)*(size of the delegation), where the division by 100 is to remove the percent.

Item 4: SKEW measures the partisan fairness of a plan. Count 0 for each highly competitive district, +1 for each competitive or uncompetitive Democratic district, and -1 for each competitive or uncompetitive Republican district. Take the total for all districts in the state and subtract the expected state delegation difference. Express a negative number as a positive number in favor of the Republicans. That positive number is the SKEW score, and lower numbers are closer to the ideal partisan fairness.

Item 5: POLARIZATION measures the competitiveness of a plan. Count 0 for each highly competitive district, 1 for each competitive district, and 2 for each uncompetitive district in a plan. The total for the whole state is the POLARIZATION score, and lower numbers indicate greater competitiveness.

Let's add to the discussion the I in SPICE: Inequality.

Definition: Quota. The quota is the total population of a state divided by the number of districts rounded to the nearest whole number.
Definition: Deviation. The deviation is the difference between the population of a district and the quota. Negative numbers indicate a district that has a population that is smaller than the quota.
Definition: Range. The range is the difference in population between the largest and smallest district in a plan.
Definition: Average Deviation. The average deviation is the average of the absolute values of the deviations for all districts in a plan.

Background: SCOTUS has set two different standards for districts. Legislative and local districts must be substantially equal and that has been interpreted to be a range not exceeding 10% of the quota. Congressional districts must be as equal as practicable, and for some time that was assumed to mean that only exact equality would do. However, the recent WV case makes it clear that a range of up to 1% of the quota is acceptable when driven by other neutral redistricting factors. Greater than 1% might also be acceptable, but 10% would presumably not be because that is set by a different standard. It's an evolving area in the law.

Item 6. All plans for congressional districts shall have a range not exceeding 1% of the quota. All other plans shall have a range not exceeding 10% of the quota except when otherwise limited by state law.

Background: Some time ago there were some threads that tried to optimize the population equality of districts with no county splits. The result of that exercise was the following graph.

Each square represents a state. New England states used towns instead of counties, and states with counties too large for a district assumed that a whole number of counties would nest inside the large county. The more counties available per district, the closer to equality one could achieve, and the relation is logarithmic in population. The green line represents the best fit to the data. Data for average deviation can be fit as well, but the result is not substantially different other than the scale factor that has the average deviation equal to about 1/4 the range.

The average state has about 72 counties and if one divides that number into 2, 3, 4, etc. districts then one can use the fit from the data in the graph to predict a likely range. That in turn can be built into a table.

Item 7. The INEQUALITY score for a plan is found by taking the range for a plan and comparing it to the table below.



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