Seats-Votes Curve

When you go to the Advanced tab in DRA 2020, you can see a seats-votes curve for the map — a powerful way to understand how biased & responsive the map is.

By default, both the inferred Democratic curve (blue) and the corresponding Republican curve (red) are shown. You can turn off the Republican curve with a toggle on the right.

The diagram highlights several items to help you with your analysis:

• Cross hairs — To help you register whether the Democratic vote share and corresponding seat shares are more or less than 50%, the diagram has solid black horizontal and vertical rules at 50%. This creates four “quadrants.” In the upper right, Democratic vote & seat shares are greater than 50%. In the lower left, the Democratic vote & seat shares are less than 50% — alternatively, the Republican vote & seat shares are greater than 50%.
• Center point of symmetry — A symmetric seats-votes curve will pass through the (vote % = 50%, seat % = 50%) point where half the votes wins half the seats. This point is shown with a black circle.
• Statewide vote share — This is shown with vertical rule with a dashdot pattern.
• Zone of uncertainty — The light gray region that brackets the statewide vote share shows the approximate average uncertainty of the inferred seats–votes curve.
• Line of proportionality — The dotted 45° line shows where the seat share is equal to the vote share.
• EG=0 — The dashed line with a slope of two shows where the efficiency gap (EG) is zero.

The curve is pre-zoomed into the area that encompasses the center point of symmetry and the statewide vote share and inferred seat share (where the statewide vote share vertical rule intersects the blue Democratic curve). You can manually zoom the curve, if necessary.

A seats–votes curve graphically illustrates five important measures of bias:

• Seats bias (αₛ) — The line segment from the black circle to the black square shows the seats bias at 50% Democratic vote share. This is the fraction of seats less than (or greater than) half that Democrats win with half the votes.
• Votes bias (αᵥ)— The line segment from the black circle to the black diamond shows the votes bias at 50% Democratic seat share. This is the fraction of votes more than (or less than) half that Democrats need to win half the seats.
• Partisan bias (β) — This is half the difference between the inferred Republican and Democratic seat shares at the statewide Democratic vote share, i.e., half the vertical distance between the red and blue curves.
• Global symmetry (GS) — This measures a combination of seats and votes bias. It is the total area between the Democratic (blue) and Republican (red) curves.
• Geographic seats — A white star with black outline shows estimated number of fractional Democratic seats implied by political geography.

All of these measures are discussed in more detail in Advanced Measures of Bias & Responsiveness.

You can hover over the curve at any point to see what the (vote %, seat %) values. You can press the camera icon to download the image or use the zoom controls to inspect a portion of the curve more closely. You can also zoom by drag selecting the region that you want to expand.

Methodology

To estimate the partisan characteristics of a map, we use:

• A composite of statewide elections, and
• Fractional seat probabilities instead of all-or-nothing accounting, except as noted.