Science Wednesday: The Inescapable Logic of Graphs

Yahoo News recently had an amazing graph analytics page (see our page on Sherlock, and this iSGTW article, for more on PSC’s recent activities in the field) concentrating on the voting records of U.S. senators. Specifically, how often they voted together. Here’s the embedded graph:

Note that the following is an honest attempt to look at the issue in a non-partisan way. (Impartiality, to my mind, is a myth; instead we should strive to be fair.)

The graph opens up at 65 percent — that is, every pair of senators who voted together 65 percent of the time in the 113th Congress is linked by a line (in the parlance, “vertices” linked by an “edge”). The gist of the article accompanying the graph is that the Democrats’ party unity is slipping, with more Dems breaking from the pack rather than voting in unison. That may well be, comparing the 113th to earlier Congresses. But it isn’t really what jumps out at me.

At 65 percent (note the slider at the top, which allows you to change the percentage), we see pretty solid party unity — the Dems are in a little ball, representing their voting solidarity, as are the Republicans. But we do see some interesting deviations.

Frank R. Lautenberg, a Dem from my home state of New Jersey, is a bit of a mystery. (You can identify the individuals by left-clicking on the little dots that represent them; annoyingly, if you want the greying and pull-down menu to go away once you’ve done that, there’s no “deselect” feature — you have to re-load the page.) He’s voted zero times with anybody at 65 percent. He doesn’t connect with anybody else until you slide the percentage down to 25 percent; apparently, he’s voting exceptionally independently. I haven’t really dug into his positions, but it’s interesting that the so-called independents — Angus King, I-ME, and Bernie Sanders, I-VT, track lock-step with the Dems.

Now Bernie is a socialist, so maybe it’s no surprise that he votes more with the not-quite-left-enough rather than with the right. King is a little more interesting, since Wikipedia says he justified caucusing with the Dems to his constituents as a practical matter of having more clout by being with the majority party — and that he’d caucus with the Republicans if that changed. His voting record seems to call that into question, even if he was absolutely sincere at the time.

It’s more subtle, but at 65 percent you can also detect two red dots that pull slightly away from the Republican pack, toward the Dems (though far closer to the Republicans). That’s Susan Collins, R-ME, and Lisa Murkowski, R-AK, two moderate Republicans sometimes called RINOs. Once again, the voting record tends to question that assignation, at least at this level of voting agreement.

Move the slider to 75 percent, and things start to get interesting. Now Joe Manchin, D-WV, starts to pull out by himself. Though he still has a tenuous connection with his party, his conservative-independent streak is starting to show.

At 80 percent, we see an interesting phenomenon — Collins and Murkowski are now off in their own little clique (the technical term for this phenomenon), voting with each other 80 percent of the time but nobody else that often.

This reminds me of a graph that Nick Nystrom showed me just before his interview with Bill Flanagan on Sherlock. The graph was based on the insulin response (for my sins, this was the topic of my dissertation). Cliques appeared on this one as well — little clusters of genes linked with each other but only connected with the main ball of interactions by a narrow isthmus. I sensed that this was biologically interesting, but it wasn’t until later that it hit me: These represented biological activities that the insulin response shares with that of other messengers — think glucagon, maybe, or epinephrine. Similarly, I think we can hypothesize that Collins and Murkowski, at the level of 80 percent, are sharing a political philosophy that, while connected with the GOP at a looser level of association, nevertheless is distinct and shared.

At 90 percent, we see the reason for my sort-of-dismissal at Yahoo’s contention that the Dems are fraying in a major way. At this level, Dems are starting to peel off, with some disconnected from their party and anybody else. This is the phenomenon the Yahoo analysts were noting; but you also have to look at the Republicans, who now form a crescent, spreading out in a kind of penumbra of the still-cohesive Democratic ball. It’s clearly still a party — but (again, at the 90-percent level of agreement) it’s a party only by the property of transitivity, and clearly has lost its cohesion.

These aren’t judgments — they’re observations, driven by graph analytics.

Now I will edge out onto the diving board, and make a prediction: The Republicans’ time out in the cold, much like the Democrats’ in the ’80s, won’t end until that crescent starts to coalesce into a ball. Or — though this wouldn’t be fun for either party — until the Dems spread out into their own crescent. I leave it to the reader to decide which would be best for the American public.

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