Scores (Metrics)

These are the metrics (“scores”) calculated for a plan, when you run the scripts/score/SCORE.sh script. There is a PDF version of this page here.

Metrics fall into one of several categories:

• General – population deviation
• Partisan – measures of partisan bias (fairness) & competitiveness (responsiveness)
• Minority – measures of the opportunity for minority representation
• Compactness – measures of compactness
• Splitting – measures of county-district splitting

For each of these categories, there are plan-level scores (CSV) and by-district measurements (JSONL). Note: The first value in each by-district list is the total for the state. The values 1-N are the values for the individual districts.

General

There is one general metric:

• population_deviation – The population deviation of the plan.

Partisan

The measures of partisan bias (next) and competitiveness & responsiveness (following) are described in some detail in Advanced Measures of Bias & Responsiveness. Many use fractional seat probabilities.

• estimated_vote_pct – The Democratic two-party vote share.

These are the plan-level partisan bias metrics:

• fptp_seats – The estimated number of Democratic seats using “first past the post” (FPTP), all-or-nothing accounting.
• efficiency_gap_wasted_votes – The efficiency gap calculated using the wasted votes formula. Smaller absolute value is better. Positive values favor Republicans; negative values favor Democrats.
• efficiency_gap_statewide – The efficiency gap calculated using the statewide formula and FPTP accounting.
• efficiency_gap – The efficiency gap calculated using the statewide formula and fractional seat probabilities.

• estimated_seats – The estimated number of fractional Democratic seats.
• pr_deviation – The deviation from pr_seats. Smaller is better, and zero is perfect.
• disproportionality – estimated_vote_pct minus estimated_seats as a percentage of the number of districts.
• seats_bias (αₛ) – The seats bias at 50% Democratic vote share.
• votes_bias (αᵥ) – The votes bias at 50% Democratic vote share.
• geometric_seats_bias (β) – The seats bias at the statewide Democratic vote share, not 50% (aka “partisan bias”).
• declination (δ) – The declination angle (in degrees), calculated using fractional seats and votes. Smaller is better.
• mean_median_statewide – The statewide Democratic two-party vote share minus the median Democratic two-party district vote share.
• mean_median_average_district – The mean Democratic two-party district vote share minus the median Democratic two-party district vote share.
• turnout_bias (TO) – The difference between the statewide Democratic vote share and the average their average district vote share.
• lopsided_outcomes (LO) – The difference between the average two-party vote shares for the Democratic and Republican wins.
• proportionality – DRA’s propoprtionality rating. Integers [0-100], where bigger is better.

There are two by-district aggregates:

• dem_by_district – The number of Democratic votes by district.
• tot_by_district – The total two-party (Democratic & Republican) votes by district.

These are the competitiveness & responsiveness metrics:

• competitive_district_count – The number of districts that fall into the 45-55% Democratic/Republican range.
• average_margin – The average margin of victory. Smaller is better.

• competitive_districts – The estimated number of competitive districts, using fractional seat probabilities. Bigger is better.
• responsiveness (ρ) – The slope of the seats-votes curve at the statewide Democratic vote share.
• responsive_districts – The likely number of responsive districts, using fractional seat probabilities.
• overall_responsiveness (R) – An overall measure of responsiveness which you can think of as a winner’s bonus.
• competitiveness – DRA’s competitiveness rating. Integers [0-100], where bigger is better.

Minority

These are measures of the opportunity for minority representation. See also the measures in the ‘global’ category below.

• mmd_black – The count of Black-alone majority-minority districts (MMD).
• mmd_hispanic – The count of Hispanic-alone majority-minority districts (MMD).
• mmd_coalition – The count of Black & Hispanic-together coalition districts (MMD).

• opportunity_districts – The estimated number of single race or ethnicity minority opportunity districts, using fractional seat probabilities (and DRA’s method). Note: This revised metric means does not clip below the 37% threshold (like DRA does). Hence, the results are more continuous.
• proportional_opportunities – The proportional number of single race or ethnicity minority opportunity districts, based on statewide VAP.
• coalition_districts – The estimated number of all-minorities-together coalition districts, using fractional seat probabilities (and DRA’s method). Note: This revised metric means does not clip below the 37% threshold (like DRA does). Hence, the results are more continuous.
• proportional_coalitions – The proportional number of all-minorities-together coalition districts, based on statewide VAP.
• minority – DRA’s minority opportunity rating. Integers [0-100], where bigger is better. Note: This revised metric means does not clip below the 37% threshold (like DRA does). Hence, the results are more continuous.

There are mostly self-explanatory by-district aggregates for each VAP category:

• total_vap
• white_vap
• black_vap
• hispanic_vap
• asian_vap
• pacific_vap
• native_vap
• minority_vap – The total VAP minus white VAP, i.e., all minorities combined.

Compactness

The measures of compactness:

• cut_score – The number of edges between nodes (precincts) in the contiguity graph that are cut (cross district boundaries). A measure of compactness using discrete geometry. Smaller is better.
• reock – The average Reock measure of compactnes for the districts. Bigger is better.
• polsby_popper – The average Polsby-Popper measure of compactness for the districts. Bigger is better.

• spanning_tree_score – The spanning tree scrore. Another measure of compactness using discrete geometry. Bigger is better.
• population_compactness – The population compactness of the map. Lower is more energy compact. Smaller is better.
• compactness – DRA’s compactness rating. Integers [0-100], where bigger is better.

There are two sets of by-district aggregates for compactness. First abstracts of district shapes from which Reock & Polsby-Popper can be computed efficiently:

• area
• diameter
• perimeter

and the by-district measurements of them:

• reock
• polsby_popper

Splitting

These are measures of county-district splitting:

The county and district splitting measures are described in Measuring County & District Splitting.

• counties_split – The number of counties split across districts. Smaller is better.
• county_splits – The number of times counties are split, e.g, a county may be split more than once. Smaller is better.

• county_splitting – A measure of the degree of county splitting. Smaller is better, and 1.0 (no splitting) is the best.
• district_splitting – A measure of the degree of district splitting. Smaller is better, and 1.0 (no splitting) is the best.
• splitting – DRA’s county-district splitting rating. Integers [0-100], where bigger is better.