ordering the Supreme Court justices

Today I put nine people in order -- and it wasn't a baseball team.
I came across the following table, which gives the percentage of the time that each pair of justices of the U.S. Supreme Court agreed with each other in non-unanimous decisions:

	Thomas	Scalia	Roberts	Alito	Kennedy	Breyer	Souter	Ginsburg	Stevens
Thomas	100	75	65	62	51	22	23	23	11
Scalia	75	100	79	67	38	30	38	33	19
Roberts	65	79	100	83	74	44	47	38	21
Alito	62	67	83	100	77	47	40	38	27
Kennedy	51	38	74	77	100	57	57	49	38
Breyer	22	30	44	47	57	100	70	68	37
Souter	23	38	47	40	57	70	100	77	57
Ginsburg	23	33	38	38	49	68	77	100	73
Stevens	11	19	21	27	38	37	57	73	100

I came across the data in the Philadelphia Inquirer (June 29, 2007, page A14); the table lists as its source the Supreme Court Institute at the Georgetown University Law Center. It's a version of the table on p. 18 of that institute's October Term 2006 overview (although, rather inexplicably, some of the numbers are different between the two tables!)
The table above, though, is sorted in a conservative-to-liberal order derived from the alignment data. As I originally saw the table, the justices were in the order Roberts, Stevens, Scalia, Kennedy, Souter, Thomas, Ginsburg, Breyer, Alito. This is the Chief Justice followed by the eight Associate Justices in the order in which they were appointed.
These nine people are basically just names to me -- and in fact, some of them aren't even that. I hadn't heard of some of these people until today. Anyway, here's how I did the sorting: Thomas and Stevens agree with each other least often, so one assumes they have the largest ideological difference; put them first and ninth in the order. Scalia is the justice who's most likely to agree with Thomas, so put him second; similarly Ginsburg is mostly likely to agree with Steens, so put her 8th. Roberts is most likely to agree with Scalia of the five justices who have yet to be picked, so put him third. Alito and Roberts are the two justices who are most likely to agree with each other, so clearly they should be next to each other in this ordering; put Alito fourth. Thus, we so far have
Thomas, Scalia, Roberts, Alito, ?, ?, ?, Ginsburg, Stevens.
(Note that the people on the left here are more conservative than the ones on the right, the reverse of what you'd expect from the usual use of "left" and "right" as "liberal" and "conservative".) We still have to position Kennedy, Souter, and Breyer. At this point I created the following table:

	Ginsburg	Stevens
Kennedy	49	74
Souter	77	57
Breyer	68	57

It's a tough call, but I figured that since Souter is the most likely to agree with Ginsburg, they should be next to each other; thus Souter gets the seventh slot. So now we have to put Kennedy and Breyer in order. Thomas, Scalia, Roberts, and Alito were all more likely to agree with Kennedy than with Breyer; Souter, Ginsburg, and Stevens were all more likely to agree with Breyer than with Kennedy. On this basis, Kennedy gets the fifth slot, Souter the 6th, which gives the order you can read off the first row of the big table which opened this post.
What surprised me is how coherent the assignment ended up being. If you look at the table above, for the most part each row or column increases smoothly to 100 and then decreases smoothly. (The coloring marks the exceptions; each pair of adjacent entries that's in the same color is a pair in the "wrong" order.) Furthermore, if you switch the order of any two adjacent justices you create more exceptions; this is clearly at least a local minimum. What this basically says is that the current court is one-dimensional; on most cases you can probably draw a line between two people in the ordering I gave and all the "yes" votes will be on one side, all the "no" votes on the other. (I may check this at some future date.)
I'm kind of curious if this could be done for, say, the Senate, although since the Senate has a hundred members and I'd have to compile the data myself I'm not going to do it. This took maybe ten or twenty minutes once I had the table, and was an amusing break from what I was working on this morning; doing it for the Senate would be actual work.
What's more, this ordering is in order with what the Supreme Court Institute has to say in the narrative parts of their report. Kennedy was in the majority in all 22 5-4 decisions the court made this term. They call Scalia a "conservative pole", though, which doesn't line up with my data.
Also, it would probably be possible to incorporate past justices into this ordering, if they'd overlapped with enough of the current justices that where they fell in the ordering was obvious. But I doubt that it's possible to rank all 110 justices this way; for one thing, our left-right distinction is different from the one that's existed at various points in history. And even if "left" and "right" had carried the same meaning over the last two hundred years, we wouldn't be able to compare every pair of justices -- just those that had overlapped -- and extending that sort of partial order to a total order is hard.