# Using interruptions to predict Supreme Court cases

If you wanted to know which way Justice Gorsuch was going to vote in the 2017 Term, you could have placed your bets with 86% accuracy by observing just one statistic from oral argument—how many times Gorsuch interrupted each side.

In the 2017 Term, Gorsuch heard 60 arguments and voted 40 times for the Petitioner and 19 times for the Respondent (Washington v. United States was affirmed by an equally divided Court, and by convention no individual justice votes are recorded). On average, he initiated 1.6 more interruptions during the Respondent’s time than during the Petitioner’s (a few of these interruptions were of other justices but most were of the advocate). But like Chicago’s annual average temperature of 49°, that number masks all the interesting variation. In those cases where Gorsuch voted for the Petitioner, he interrupted the Respondent an average 3.8 more times than the Petitioner. Conversely, when voting for the Respondent, he interrupted the Petitioner 3.1 more times on average.

One way to visualize this kind of data is with a histogram.

In the figure above, we have overlaid two different histograms of the interruption gap (interruptions of Petitioner minus those Respondent) for Gorsuch in the 2017 Term. The orange bars indicate the interruption gap in cases where the Justice voted for the Petitioner: it is clear that in the vast majority of these cases, Gorsuch interrupted less during the Petitioner’s time than Respondent’s. The blue bars show the interruption gap for the pro-Respondent cases. Here, in contrast, most of the weight of the figure is above zero—i.e. Gorsuch interrupted the Petitioner more often, though the shape of the blue distribution is flatter. We should note that because Gorsuch voted for the Petitioner twice as often as he voted for the Respondent (as the Court in general does), an orange bar represents twice as many cases as would a blue bar of the same height.

In the next figure, we further explore the distribution of Gorsuch’s interruption voting patterns through a boxplot.

Boxplots are cool (trust us!) but they require a little explaining. The “box” part of a boxplot indicates the range separating the top 25% of the data from the bottom 25% (the interquartile range); think of this as the space between the 25 and 75 yard lines on a football field. The vertical line segmenting this box is the median of the data. So, in the figure above, a quick comparison of the light blue pro-Respondent box with the orange pro-Petitioner box shows that there is no overlap between the middle 50% of each of these categories. What is more, the orange box is entirely to the left of zero on the interruption gap scale and the blue box is entirely to the right. The white space between the boxes tells you at a glance that 75% of cases in the orange category have a lower interruption gap than 75% of cases in the blue category. And thus, when Gorsuch interrupts one side more than the other, he is usually showing his hand and telegraphing which way he will vote.

The whiskers extending away from the boxes extend close to the extremes of the data: they indicate about how far the data extends before you get to true outliers (in a normal distribution, 0.7% of observations lie beyond the upper and lower limits). The fact that the whiskers cross the zero point confirms that although the interruption gap is a very strong predictor for Gorsuch, it is not infallible. In fact, in the 2017 Term, relying on the interruption gap to predict Gorsuch’s votes would have been misleading in just 7 cases.