House Voting Solidarity,
the graphical version.
October 4, 2005
Update 10/9: I've realized there's a fly in the ointment. My formula for calculating party loyalty turns out to be a measure of partisan contentiousness. After doing a vote level analysis, I determined that there's too much of a reward for voting against the opposition as opposed to voting with your party. The graph remains valid in that light, but not strictly in terms of party loyalty. I'll post an updated graphic when I have the time to do so. Before I run out on calls this afternoon, I wanted to put up the latest graphical depiction of US House of Representatives' voting patterns. I'm sure you'll be every bit as excited about as I am. Self-directed sarcasm aside, it is kinda interesting. It depicts the less unified nature of Democratic party voting as well as demonstrating the effect of the Blue Dog Democrats in a grok-at-a-glance graphical format. (I love charts and graphs.)
Picture first, then more words.
Click the graphic for a larger version
I calculated voting solidarity statistics for each member and ordered them from least likely to cross party lines to most likely to do so. (That's pretty much the same ordering as the True Blue half of my original House analysis. The most Republican Democrats are data points on the right side.) I overlaid the Democratic area on the Republican one. Since there are more Republicans than Democrats, there's an area of red behind the blue. But because of the less unified nature of the Democrats, the fall-off rate of Democrats exposes a greater area of Republican dominance than would be seen just by their numeric superiority. I also calculated a projection of what the Democrats would look like if they voted with the partisan ratio of the Republicans.
WARNING: Geeky technical notes and methodology follow. Procede to the end if you want to find the earlier entries in the series.
I've specifically avoided numbers on the graph, because that projection of potential Democratic solidarity would in reality change the shape of the graph beyond anything I have the time, ability or analytical resources to calculate. (Hint: As fewer Democrats voted with Republicans, it raises the partisan quotient for Republicans as well.)
The way I calculated the partisan purity factor is as follows:
For each Representative, I calculated a value that represents the average of percentage of their party that voted the same way, minus the percentage of the other party that voted the same way. The rationale is that I get a single number that represents how "Republican" or "Democratic" an individual member is.
Here's the Democratic formula:
VoteQD = (Dyy+Dnn)/(Dyy+Dyn+Dny+Dnn) - (Ryy+Rnn)/(Ryy+Ryn+Rny+Rnn)
where Dyy equals the sum of yes votes by Democrats on measures where the Representative voted yes and Dyn is the sum of Democratic no votes on measures where the the Representative voted yes. (and etc.) So Dyy+Dnn is the sum of all votes cast by Democrats in agreement with with this party member. The four term denominators are the sum of all votes by their respective parties. Values range from 1.0 down to almost -1 (if you think about it, you can't quite get there.) The Republican version of the formula would reverse the order of the D and R sections. To completely normalize the values, I should have subtracted out the Representative's own votes, but it would amount to a rounding error smaller than observable in the chart and my brain was loosing cohesion by the time I figured this out. Don't put off dinner to do math....
The projection of the potential Democratic shortfall is a rather simple-minded interpolation that could be done quickly in a formula in Excel. It's really just a lookup function to grab the value of the closest Republican at the equivalent position in the rankings. A proper linear interpolation formula would have smoothed the roughness of the edges better. It's pretty close to reasonable, though and good enough for a freebie.
Well, that's it. I show you a cool graphic and then bore you with the gory details of math you never wanted to see. Ah... such are the travails of the scientific method. Always anti-climactic. And it gives an actual mathematician the opportunity to point out flaws in my math. :^)
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