Monday, January 30, 2006

A pattern analysis of the second Rehnquist US Supreme Court

That's the title of a paper by applied mathematician Lawrence Sirovich at the Mt Sinai School of Medicine in New York, published online on June 23, 2003. in the Proceedings of the National Academy of Sciences. It has already been the subject of a NYTimes article (four bucks or Times Select required).

[Note: I originally wrote this article in June 2003, just after the article was released. I think it would be interesting to do a similar analysis in the next few months on Judge Roberts and later Scalito.]

Its abstract : The second Rehnquist Court has remained unchanged in composition for 8 years, resulting in a large temporally stable database. This paper reports on a mathematically objective analysis of this ensemble of rulings aimed at extracting key patterns and latent information. Although the rulings of a nine-justice Court require representation in nine dimensions, smaller spaces describe the Court's actions; e.g., a 2D subspace describes the margins of all decisions, and use of Shannon information shows that the Court acts as if composed of 4.68 ideal justices. Comparison is also made with the 1959-1961 and 1967-1969 Warren Courts. Both Warren Courts have
remarkable parallels with the Rehnquist Court. In each instance, we present an optimal mapping of
the justices between the Courts, which underscores the similarity in the workings of seemingly dissimilar courts.

The full paper is available at the same site, but you'll need a subscription to get it. I'm lucky since I work at institution that subscribes to it, and thus have got and read the full paper. Sirovich's analysis is specifically devoid of any judicial/psychological/game-theoretic analysis. He deals with a simplified form of the process, where each judge says yes/no on the whole decision and the majority vote is the final opinion. As he admits, this does not take into account that a justice can vote differently on different parts of the whole case, but we have to start somewhere. Excluding such cases of split votes, an absent justice, lack of public information on who voted which way, and other ambiguities limits the analysis to 468 cases, about 70% of all decisions by the Supreme Court from 1994 to 2002/3.

Sirovich uses Singular Value Decomposition (SVD) analysis to find the two most important factor in making a decision. SVD is a tool for summarization, not prediction (in this case at least), i.e. it does not lend itself immediately to a method of predicting Supreme Court decisions beforehand. It turns out that nearly half (47%) of the court's decisions are unanimous (no-brainers perhaps?), and the first Sirovich dimension corresponds to this.

Kennedy +0.36
O'Connor +0.36
Souter +0.35
Rehnquist +0.35
Breyer +0.34
Ginsburg +0.33
Thomas +0.32
Scalia +0.31
Stevens +0.26

The second dimension is more interesting, being represented by the following weights :

Thomas +0.41
Scalia +0.40
Rehnquist +0.30
Kennedy +0.17
O'Connor +0.10
Souter -0.31
Breyer -0.33
Ginsburg -0.37
Stevens -0.45

Sirovich is careful not to draw any conclusions from his data that could be viewed as political. However, he has provided enough data for others to interpret, as we do here.

The weights of the second dimension correspond to the general perception of judges as liberal/conservative. Quoting from a CNN article of 10 July 2001, "Conventional wisdom divides the current Justices of the United States Supreme Court into three camps. First, there are the staunchly conservative Justices: Chief Justice William Rehnquist and Justices Antonin Scalia and Clarence Thomas. Second, there are the moderately conservative "swing" Justices, Sandra Day O'Connor and Anthony Kennedy. Finally, there are the moderately liberal Justices: John Paul Stevens, David Souter, Ruth Bader Ginsburg, and Stephen Breyer."

This is summarized in the table below (note the order), which has a few other details as well.

Judge Public perception Appointed
Thomas very conservative 1991 (Bush Sr)
Scalia very conservative 1986 (Reagan)
Rehnquist very conservative 1972 (Nixon)
Kennedy consersative 1988 (Reagan)
O'Connor conservative 1981 (Reagan)
Souter liberal 1990 (Bush Sr)
Breyer liberal 1994 (Clinton)
Ginsburg liberal 1993 (Clinton)
Stevens liberal 1975 (Ford)

Sirovich's analysis finds that nearly all cases are summarizable by these two dimensions. Of course, SVD analysis focuses on trends, not subtleties. To continue the quote from Dorf's article, "These categories broadly describe the Justices' political views. Yet political ideology does not neatly translate into judicial philosophy, as was apparent in a number of the most interesting cases the Supreme Court decided over the past year. Indeed, were it not for the long shadow cast by Bush v. Gore, the 2000-2001 term of the U.S. Supreme Court might well be remembered for the unusually large number of cases in which "conservative" Justices voted for "liberal" outcomes and vice-versa."

Sirovich's article goes on to compare the current Supreme Court with the Warren Courts of the 1960s, and finds more similarities than have generally been supposed to exist. We do not go into the details of that, except to say that it is an example of something one needs a quantitative tool like SVD to be able to do.

The article has many other interesting statistics, some of which are listed below. Keep in mind that these are for the 70% (= 468) of all cases that the analysis can deal with.

  • While 47% (220) of cases were unanimous, the next most likely voting outcome, accounting for 10% (45) of all cases, was the 5-4 decision with Thomas, Scalia, Rehnquist, Kennedy and O'Connor forming the majority, as in Bush vs Gore 2000.
  • Of the 15% (72) cases involving a 5-4 majority, 45 had the conservative majority mentioned in the previous point, 18 had the Breyer-Ginsburg-O'Connor-Souter-Stevens majority and 9 had the Breyer-Ginsburg-Kennedy-Souter-Stevens majority. The swinginess value of O'Connor and Kennedy is obvious.
  • The most likely judges to agree are Scalia and Thomas (>93% of the time), followed by Ginsburg and Souter (>90% of the time).
  • Of the 33 cases where only one judge has dissented, Stevens has been the dissenter 21 times. Rehnquist, Scalia and Thomas have each been sole dissenter 3 times and Breyer, Ginsburg, Kennedy and O'Connor once each. Souter has never been the sole dissenter.
  • There are 2(9-1)=256 possible voting patterns (where each person votes 'agrees with majority' or 'disagrees with majority'). However, only 12 of these account for over 80% (377) of all cases, and only 30 of them occurred more than once.

Sirovich got much of his data from and, and recommends The Oxford Guide to United States Supreme Court Decisions (Oxford Univ Press, 1999) and The Oxford Companion to the Supreme Court of the United States (OUP, 1992), both edited by Kermit Hall, as valuable guides for non-lawyers such as himself.

Tuesday, January 24, 2006

Searching for the WWW

What happens when you search for "www" using different search engines?

Google sends you to Yahoo. [link] So does A9. [link]

MSN sends you to Slashdot, [link]

Yahoo sends you to the W3 Consortium [WWW Consortium] but when I tried it earlier four hours ago it sent me to hotmail.

Saturday, January 07, 2006


We've just heard (belatedly) about this really nice Java Applet called LiveGraphics3d that comes from the Mathematica-using math community. It seems relatively simple to use, is well documented, and while it has limitations, it could still be very useful for displaying things like cosmic ray showers, galaxy simulations, and results of machine learning algorithms. What's quite amazing is that you can define lines and surfaces using equations. It can handle at least a few thousand points quite well, too.

Martin Kraus, the creator, has some nice examples of impossible objects :

Tuesday, December 27, 2005

AIDS statistics

IndexMundi also has some excellent drawing capabilities; for instance, the screenshot below shows the countries with the highest reported rates of AIDS... the top eight countries are in Southern Africa.

In a few cases, it's not clear if the basic numbers are correct - for instance, this graph shows Zimbabwe having 1.8 people living with AIDS - that's because Zimbabwe reports people dying of AIDS rather than living with AIDS.


Miguel Barrientos' IndexMundi allows you to plot correlations of several values... [IM Blog]

Migration and GDP per capita - slightly positive, indicating that wealthier countries have higher immigration rates (some interesting cause/effect arguments here)

Richer countries have lower infant mortality rates and have higher life expectancy and lower fertility and higher literacy and may not be getting richer(!) and lower unemployment and lower industrial production growth rate (!)

Sunday, December 25, 2005

The Mystery of the Disappearing Teaspoons

Megan Lim and other Melbourne researchers have produced a definite contender for a future IgNobel prize in the form of their five-month study on "the displacement of Camellia sinensis spathulatus" a.k.a. teaspoons. They report their results in a light-hearted holiday issue of the British Medical Journal.

They discreetly labeled 70 teaspoons, placed in tearooms around their institute (of 140 people) and observed, every week over five months, which ones were left. The result was that "56 (80%) of the 70 teaspoons disappeared during the study." Also, "the rate of loss was not influenced by the teaspoons' value" as shown in the picture below (which is from their research paper and which will probably get me into trouble with the journal for copyright breach).

Actually, looking at the graph above, expensive teaspoons did disappear more quickly initially, so we will clearly require further studies to verify their conclusion.

They go on further to note that "the half life of the teaspoons was 81 days" - that means that it takes about 2.5-3 months for half the teaspoons to disappear. However, this differs depending on how many people have access to the spoons - "The half life of teaspoons in communal tearooms (42 days) was significantly shorter than for those in rooms associated with particular research groups (77 days)."

The BMJ also allows people to respond to the study; one reader (Philip Colquitt) provides a good reason for why this kind of study is of great importance:

... if whole nations can be invaded by other nations, on the pretext of the existence of weapons of mass destruction[WMD], which WMD disappear without rational explanation, this suggests that primates(homo sapiens) may well be on the right track in trying to master spoon detection before going on to the more advanced stuff.

Articles about this. (Link to Google News)

Sunday, November 27, 2005

The Perfect Paper Plane

The Guardian reports on How to make the perfect paper plane - this Flash shows how to make the Leeds Avenger, the best designed plane at this week's British Flying Dead Trees Championships. Note that it got beaten by a simpler model called the Spruce Moose, as Martin Wainwright reports that :

"... In the best tradition of British inventions, this [the Avenger] repeatedly went into terminal nose dives in spite of complex flaps and tucks which had earned the judges' admiration..."

I also like the line describing other entries in the contest:

"...Other designers increasingly opted for desperately novel throwing techniques, last minute flap additions and in one case what looked like prayers...

The winning entry lasted 6.5 seconds before it met a well, but even otherwise it would have had trouble staying afloat the additional 20 seconds required to break the world record.