Due to the magic of data, we can ascertain based on writing style which Justice most likely authored which unsigned opinion.
A recently published article in the Stanford Technology Law Review breaks it down:
Our work uses natural language processing to predict authorship of judicial opinions that are unsigned or whose attribution is disputed. Using a dataset of Supreme Court opinions with known authorship, we identify key words and phrases that can, to a high degree of accuracy, predict authorship. Thus, our method makes accessible an important class of cases heretofore inaccessible. For illustrative purposes, we explain our process as applied to the Obamacare decision, in which the authorship of a joint dissent was subject to significant popular speculation. We conclude with a chart predicting the author of every unsigned per curiam opinion during the Roberts Court.
So what about Obamacare? The article rebuts the (silly) thesis that Roberts authored both the majority and the dissent. The model shows that Roberts authored the majority opinion, and Kennedy and Scalia were the most-likely authors of the dissent.
Ultimately, the evidence is mixed as to whether both the majority opinion and the joint dissent were authored by the Chief Justice. Applying authorship attribution techniques, we aspire to determine quantitatively which of these hypotheses is more plausible. Our model assigns the highest probability to Justices Scalia and Kennedy, not Chief Justice Roberts, as the author of the dissenting opinion, which supports the “Crawford” theory of authorship.
Both MaxEnt-DF and MaxEnt-IG strongly predict Chief Justice Roberts for the majority opinion. For the joint dissent, the MaxEnt-DF model states that Justice Kennedy is the predicted author, but the probability distribution is not as peaked—Justice Scalia has the second-highest probability. Meanwhile, the MaxEnt-IG model is much more confident in Justice Scalia as the author of the joint dissent. Overall, these findings are sensible: Chief Justice Roberts signed the majority opinion, while Kennedy and Scalia are listed as authors of the joint dissent. Both models support the hypothesis that Kennedy and Scalia were authors and prime actors in writing the dissent, and refute the hypothesis that Roberts authored both opinions
The authors also broke it down by section of the opinion, though that result is “noisy” (it has Breyer as authoring parts of the dissent, which can’t be right). However, Scalia is the most-likely author of most of the dissent.
The study also found that “conservative” Justices are more likely to author a Per Curiam opinion:
Assuming these predictions are accurate, they are provocative. Justices commonly described as “conservative” are predicted authors of 45 out of the 65 per curiam opinions (69.2%). Justices commonly described as “conservativeswing” are predicted authors of 13 of the remaining 20 opinions—11 for Justice Kennedy and 2 for Justice O’Connor. Thus, conservative or conservative-swing justices are predicted authors of 58 out of the 65 per curiam opinions (89.2%). Justices commonly described as liberal are predicted authors of only 7 of the opinions (10.8%).
With the Court offering more and more PC opinions, this may be relevant.
The article offers some “insights on writing” style of the Justices based on an n-gram analysis:
For example, the term “consequently” appears in 99 different opinions in our training dataset; Justice Breyer wrote 79 of these opinions.
Some predictive n-grams begin with capitalized words, including “For one thing” (Breyer), “Notably,” (Ginsburg), and “The question is” (Kennedy). These correspond to words at the beginning of sentences, indicating that how different justices start sentences provides clues about authorship.
Some predictive n-grams include punctuation like commas and periods, including “reason stated, the” (Ginsburg), “the first place.” (Roberts), and “foregoing reasons,” (Thomas)
And here are the most commonly used one, two, and three-word phrases by each Justice:
To answer one of your questions, they were able to control for the different clerks, as there was only a slight adverse impact on the writing style from year-to-year.
H/T How Appealing