I had this idea a while back, but I only got a chance to implement it the other day.
It is a fairly obvious idea - probably one of the first things you would think of doing. Indeed,
Keith Poole et. al. appear to do something pretty similar.
Details: Each point represents a US Senator in the 110th congress (2007-2008). Democrats are in Blue, Republicans in Red.
638 roll call votes were taken from the Congressional Record and
Principal Component Analysis was done to reduce it to 2 dimensions.
A few thoughts:
(0) It is pretty cool that the split between the parties is so clear. An impressive display for PCA to take hundreds of Yes, No votes and convert them into a "nice" picture.
(1) The Blue speck among all the Red is Senator Mark Warner of Virginia. Is he really that conservative? Is there any significance to the fact that Democrats seem much more tightly clustered?
(2) What do the axes represent? The horizontal axis is the principal one and seems to show the "left-right" divide. What about the vertical axis? What about the third and higher dimensions?
(3) Would some other
dimensionality reduction technique like
Multi-dimensional Scaling produce a drastically different picture? Other methods might make it easier to "weigh" votes by their importance.
(4) One could imagine building a nice 3-D interface on top of this that makes it easy to zoom into a sector of political space and study your senator more closely. That could come in handy at election time.
(5) One appeal of quantitative methods is that they can put a spotlight on some senators that you don't see on the news all the time like Mark Warner(VA) or Robert Menendez(NJ) or Frank Lautenberg(NJ) (in different rankings I did they ended up sticking out, yet I almost never hear them making waves in the national news). A politician could easily have a public perception at odds with their voting record.