THE JUSTICES don black robes, sit impassively during State of the Union addresses and steer clear of Twitter for a reason: the Supreme Court is supposed to be a dispassionate tribunal untainted by politics or emotion. In 2016, a study by Ryan Black and three fellow political scientists found that Supreme Court justices frown on emotionally charged language in legal briefs. Words like “glorious” and “outrageous” seldom persuade, the researchers found; measured language more often wins the day. An aversion to over-the-top language from lawyers’ pens does not mean the justices conduct themselves with robotic stoicism, however. A new paper shows that it may be possible to predict the outcome of a case by listening carefully to the pitch of the justices’ voices during oral arguments.

When justices question a lawyer at a higher-than-usual pitch, that lawyer's side is likely to lose, say Ryan Enos and Maya Sen of Harvard and Bryce Dietrich of the University of Iowa. The three political scientists claim that justices “telegraph their preferences during oral arguments” with their “subconscious vocal inflections”. The pitch of judges’ voices conveys more about their eventual votes than “legal, political and textual information”. 

Their claim is based on more than 3,000 hours of audio recordings of Supreme Court oral arguments between 1982 and 2014, encompassing 146,335 statements by 18 justices. Using speech-analysis software, Ms Sen and Messrs Dietrich and Enos analysed the ups and downs of justices’ voices and looked for pitch discrepancies between utterances to the opposing sides’ lawyers. Their hunch, before crunching the numbers, was that “a justice who is more emotionally activated when speaking towards an attorney will be more likely to vote against that attorney”.   

That’s just what the study found. 56% of the justices’ votes could be predicted on the basis of pitch difference. All the vocal data put together correctly predicted 66.55% of case outcomes, or about two of every three Supreme Court rulings. That number is impressive compared with the success of other empirical measures intended to predict how the Supreme Court will decide cases. An influential metric developed by Daniel Katz, Michael Bommarito and Josh Blackman using 95 variables—including the legal issue at stake, the month the argument took place and why the justices agreed to hear the case—correctly predicted the same universe of cases only 64.76% of the time.

Ms Sen and her colleagues emphasise that the words justices say are not the only indicator of how they might vote; inarticulate and “implicit signals” are important clues as well. But the researchers are not sure how to explain the findings. They speculate that justices may “actively rely on their emotions in reaching important decisions”, but this seems backwards. Raising one’s voice to a higher register when sparring with the eventual loser isn’t necessarily a sign a justice relies on her emotions. It’s more likely to indicate that she has emotions connected to her view of the law and gets exercised when encountering ideas she disagrees with during hearings. It does not appear particularly surprising that judges’ views ring through when they speak.

Still, the phenomenon is more pronounced for some jurists than it is for others. For Justice Clarence Thomas, who has spoken up during only one hearing since February 2006, the model has no predictive power. And for justices like Stephen Breyer, who maintain an even tone no matter which lawyer stands at the podium, the model is less predictive. Ms Sen points out that Justices Ruth Bader Ginsburg, Elena Kagan and Anthony Kennedy show some of the starkest differences in pitch when addressing one side or the other, making their participation in oral arguments particularly ripe for analysis.

Since the swing vote of Justice Kennedy is often the question mark in closely watched cases—as in this year’s gerrymandering and gay rights disputes—the 81-year-old’s propensity to vary the frequency of his voice (subconsciously, we assume) may be particularly telling. Ms Sen and colleagues note that when Justice Kennedy speaks at a frequency 22.31Hz higher than his normal pitch toward the petitioner (the appealing party) and 22.31Hz lower than usual toward the respondent, he votes for the petitioner only 43% of the time. When he keeps an even tone in his questioning of both sides, that figure is 58%. 

That remarkable 15-point gap may provide a hint about the outcome in two of the most closely watched cases of the year: Masterpiece Cakeshop v Colorado Civil Rights Commission, involving a Christian baker’s plea for a right not to make a gay-wedding cake, and Gill v Whitford, a challenge to a Republican-drawn partisan gerrymander in Wisconsin. At your correspondent’s request, Ms Sen and Mr Dietrich took a look at the timbre of Justice Kennedy’s voice in the Masterpiece Cakeshop and Gill oral arguments held in the autumn. The cake case, Mr Dietrich says, is “too close to call” as Justice Kennedy's pitch was only slightly higher than usual when questioning the lawyers for Colorado. But the results for Gill were consistent with The Economist’s guess when we covered the hearing in October 2017. Justice Kennedy asked no questions of the challengers that day and lilted noticeably in his many questions to the state, raising his pitch 26.32 Hz over his usual tone. The swing justice sounds ready, for the first time in the court’s history, to impose limits on partisan redistricting. We'll hear whether that prediction is sound by the end of June 2018.