Richie Lionell points us to this interactive visualization of votes of U.S. Senators.

It’s attractive. My big problem is that nothing is conveyed by the positions of the points along the circles. Thus, that cute image of the points moving around is a bit misleading. Maybe someone has a suggestion of how to do this better?

Here’s my thought: Forget the circular display. Instead of a radius-and-angle display, use an x-y display, in which the y-axis represents distance from the focal senator (thus, the y-axis in my proposed graph will play the same role as the radial axis in the display above), and the x-axis is a traditional left-right display (so that liberal Democrats are on the left and conservative Republicans are on the right). This will convey more information while still including the valuable message of the graph above, showing distance from the focal senator.

In addition, the graph is compact enough that you can show several senators at once, by just showing several small displays on a single page. That would be much better than the existing system which can only allow you to see one senator’s image at a time, and reduces me, as a user, to a confusing sort of mental accounting, comparing various images in my head.

The above recommendations follow the general principle of thinking of graphs as comparisons.

**P.S.** Alberto Cairo took up the challenge:

I think Cairo’s visualization is much better than Lionell’s, as it conveys additional information and does not distract with that meaningless angular axis. More than that, Lionell’s graph has the problem that it puts the senator in question at the center. But that’s not right. Some senators are on the right, and some are on the left, and that’s important. Putting each senator as if he or she is in the center, that’s misleading.

The only problem I have with Cairo’s graph is that I have no idea what is the “similarity score.” A similarity score of 80, that says what?

Yes makes sense. I find many graphs pretty lame nevertheless.

I would think a standard correlation matrix heatmap would be ideal for this. (One of billions of examples here.) For any pair of senators, the intersection of their row/column gives their correlation. One could group Democrat and Republican senators together along each axis. Of course, there’s nothing “interactive” about this, but there doesn’t really need to be, since all the information is presentable at once.

There are a few alternative visualisations here: http://www.stat.columbia.edu/~jakulin/Politics/

I like the cluster representation. If one really wants to use two dimensions, PCA and MDS at least do give some meaning to the relative situation of points.