Rank-Votes Graph

The first section you see when you choose the “Advanced” command in DRA 2020 shows a rank-vote graph for the map — a rich, visual way to characterize how fair & competitive the map is.

In a rank-vote graph, the y-axis represents Democratic vote share,¹ and the x-axis represents the rank order of the districts from lowest Democratic vote share (on the lower left) to the highest Democratic vote share (on the upper right).

The black horizontal rule is at 50% vote share. Hence, the red squares represent Republican wins (less than 50% Democratic vote), while the blue squares represent Democratic wins (more than 50% Democratic vote). As you move from left to right, the districts go from most Republican / least Democratic to most Democratic / least Republican. You can hover over a marker to see which district it represents and what the precise Democratic vote share is.

The beige region represents the core competitive range of 45–55% Democratic vote share. Ideally districts would fall in this range. In this example, none do.

With that context, there are five other features of interest:

• The horizontal black dash-dot line shows you the statewide Democratic vote share of the election composite (or election) that you’re using. In this example, it is 48.88%. You can hover over the line to see the value.
• The vertical black dash-dot line shows you the Democratic seat share that is equal to that statewide Democratic vote share. Ideally, the Democratic seat share would equal the statewide Democratic vote share — i.e., would be proportional — and the same would be true for Republicans. This would mean that all the districts to the right of this line would be blue while all the districts to the left would be red.
• The blue dashed line in the upper half represents the average Democratic win percentage. In this example, it is 69.15%. Again, you can hover over the line to see the value.
• The red dashed line in the bottom half represents the average Republican win percentage. Since the y-axis represents Democratic vote share, the line is drawn at 100% minus the average Republican win percentage. In this example, that is 42.37% (which corresponds to an average Republican win of 57.63%). The latter is what you see when you hover over this line. Ideally, the average Democratic and Republican win percentages should be equal.
• Finally, two black line segments meet at the white circle with black border. Ideally, these two line segments would be more-or-less on the same line. When the slopes of the two line segments differ though, they can create a visual hockey stick which indicates bias, meaning that one party’s voters have been “packed” into some districts. You can hover over the circle to see the angle that is called the declination. In this example, the value is 36.31°. The bigger the angle, the greater the bias.²

You can hover over the points to see what district they represent and what the vote share is. You can also press the camera icon to download the image.

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.

Footnotes

1. By convention, we express two-party vote shares as Democratic vote shares. Republican vote shares are simply one minus the Democratic share.
2. For more information about the declination measure, see Advanced Measures of Bias & Responsiveness.