Using Network Analysis To Gauge The Justices’ Relative Importance In Oral Arguments
This analysis underscores that influence within judicial discourse is more multifaceted than meets the eye.
Anecdotes and research support the notion that oral arguments do not often influence case outcomes. Chief Justice John Roberts said as much in an interview with Bryan Garner for the Scribes Journal in 2010: “The oral argument is the tip of the iceberg — the most visible part of the process — but the briefs are more important.” In fact, a series of studies including my own work points to the justices generally asking more questions to the parties they eventually vote against on the merits which corroborates the point that the justices often know the way they will vote based on concerns they have with the opposing side’s position by the point of oral argument.
Once again, Chief Justice Roberts elaborated on this point. This time in response to Garner’s question:
“When you approach an oral argument as a judge, to what extent do you have a tentative vote in mind? Is there a kind of rebuttable presumption”?
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Roberts replied:
“It really varies on the case. Some cases seem clear. You look at the briefs, and you’re just not persuaded by one side, and you are by another, so you do go in with kind of . . . I’m kind of leaning this way. Usually, you’ve got concerns. I’m leaning this way, but I need a better answer to this problem…So even when you’re tentatively leaning, you have issues that you want to raise that give the other side a chance to sway you.”
In the same set of interviews, Justice Scalia pointed to why attorneys should still value oral arguments:
“…one of the benefits of oral argument — you can put things in perspective the way a brief can’t. Say, ‘Your Honor, we have five points in the brief, but you know, what we think is the most important, what this case really comes down to . . .’ and then boom! Hit your big point. And I’ll think, ‘Oh, yeah, I read your brief last week, and all I remember from it is that lengthy point three, but that’s not the one that you want to talk about.’”
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While oral arguments may not often sway justices’ final votes, they hold significant value in other respects. These sessions allow justices to clarify the legal issues, test the strengths and weaknesses of both sides, and signal which arguments they find compelling or problematic. This process frames the conversation in ways that can affect how parties refine their positions and how cases are understood by the public. Litigating attorneys, through these exchanges, often gain a clearer sense of where each justice’s concerns lie, shaping their strategies both in the current case and in future litigation.
Even if votes are often predetermined, a justice’s influence during argument can steer the conversation, frame legal questions, and potentially impact the policy outcomes or legal frameworks that emerge from a case.
Maybe it is time to rethink the value of oral arguments as something more than impacting the justices’ votes. In past, I and others have focused on the idea that one of the main goals of oral arguments is dominating the speaking time available as a means to share ideas and prevent other justices from talking. Ultimately though, the justices that speak the most on the current Court tend to be in the Court’s majority least frequently. Given the disconnect between majority votes and speaking time, what other ways can we measure the justices’ influences in oral arguments? The answers are supplied by looking at oral arguments since Justice Jackson joined the Court at the beginning of the 2022 Supreme Court Term and moving through the first week of oral arguments during this 2024 Term.
The Tools
Imagine a group of people at a dinner party. Some people speak frequently, while others contribute less but often respond to certain individuals. As the night progresses, you might notice patterns—certain voices dominate, others are echoed or referenced, and some people are frequently the focus of the group’s attention. Even if you weren’t listening to the content of what was being said, you could still gather insights about the dynamics at play: who leads the conversation, who influences others, and who helps connect different parts of the group. These interactions can tell us a lot about the relationships within the group, even if the content of the discussion is unknown.
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This is much like what network analysis does in a more formal context. In the case of Supreme Court oral arguments, network analysis helps us map out and understand the complex interactions between justices and attorneys. By tracking who speaks when, who references whom, and how much space in the conversation each participant occupies, we can construct a network of these interactions. To build this network, data is collected from transcripts (thanks to R code supplied by Jake Truscott’s SCOTUSText)—each utterance is logged, along with who spoke it and who they were responding to or referencing. This data was then analyzed to uncover patterns of influence, centrality, and participation, much like observing the dinner party conversation from a broader, structural perspective.
The value of network analysis lies in its ability to highlight the underlying structure of interactions that may not be immediately apparent from simply reading the text of a transcript. By focusing on who is influencing or directing the conversation, and how often participants engage with one another, network analysis provides a lens for understanding the dynamics of oral arguments beyond individual statements. It also offers insights into the court’s decision-making process, even if that influence isn’t reflected in the final vote.
The network graphs are constructed by treating each justice as a “node” (a point in the graph) and each interaction between them as an “edge” (a line connecting nodes). For example, if one justice speaks after another or references them, a line is drawn between their nodes. The strength of these connections is weighted in these analyses by factors like how many times they speak in sequence or how many words they contribute. The resulting graph shows not just individual behavior but the relational structure of the court, revealing who is central to the conversation and how ideas flow between the justices. The graph below shows an utterance (turn taking) network chart of the justices from arguments with justices and attorneys mapped based on their interactions.
Measures
The analysis below looks at three different measures based on utterances, word counts, and references to other justices during oral arguments. To assess a justice’s importance during oral arguments lies in the ability to capture multiple dimensions of influence that raw word counts alone cannot. Utterance centrality, which considers the relationship between the current and previous speaker based on who speaks when, reveals how integrated a justice’s speech is within the conversational flow, highlighting their role in maintaining or shifting the dialogue. This metric emphasizes the justice’s connection to the broader exchange of ideas rather than just the volume of their speech.
Word count centrality, while also looking at speaker pairs, adds a quantitative dimension by weighting each speaker’s contribution based on the number of words spoken. This highlights the depth or elaboration of a justice’s participation. It shows not only who speaks but how much they contribute substantively in terms of word volume, providing insight into how much space they take up in the conversation. A justice might dominate discussions even if they don’t speak frequently, simply through more extensive interventions when they do.
References
Reference centrality shifts the focus from speech quantity to the relational influence a justice has by being referenced by others. It reflects the extent to which their ideas or arguments are considered important or persuasive by their peers. A high reference centrality suggests that other justices find their points critical enough to revisit, indicating their indirect influence through the prominence of their contributions in others’ reasoning. Here is the network map of the justices’ references to each other where node and edge sizes relate to a justices’ importance in this network and the importance of their interaction with the other justices.
The centrality measure used in this article is eigenvector centrality which is a measure of how important each justice is in a network based on who they are connected to in a manner similar to the dinner party example above. To calculate the eigenvector centrality for the justices based on their interactions, I organized the data to focus on the exchanges between justices looking at which justices referenced other justices in their oral argument speech.
The eigenvector centrality scores for the justices revealed a distinct hierarchy of influence. Justice Alito emerged as the most central figure with a score of 1, indicating his prominent position within the referencing network. Following him, Justice Gorsuch (0.857) and Justice Sotomayor (0.873) demonstrated significant influence, reflecting their active engagement in referencing discussions. Justice Kagan (0.809), along with Justices Barrett and Jackson, both at 0.826, also exhibited noteworthy levels of connectivity and reference interactions.
In contrast, Chief Justice Roberts, with a centrality score of 0.256, stood out as the least influential in terms of referencing, suggesting that he is less frequently cited by his peers. This discrepancy illustrates the value of eigenvector centrality, as it reveals insights that individual reference counts alone may obscure. For instance, while Justice Barrett had the highest individual reference count with 42 references to Justice Alito, this does not fully capture the interconnectedness that eigenvector centrality provides. Her centrality score of 0.826 reflects a more intricate role in the referencing dynamics compared to the sheer volume of references.
Overall, the use of eigenvector centrality in this analysis offers a more comprehensive understanding of the influence and interactions among justices. It highlights not only who is referenced the most but also identifies the justices whose references are most consequential within the judicial discourse.
The limitation of relying solely on individual reference counts, however, becomes evident when considering the nuances of judicial influence. For instance, a justice may have a high reference count but may not be cited by justices who hold significant sway in the judicial discourse. Conversely, a justice with fewer references may be more frequently cited by the most influential members of the court, thereby elevating their centrality and importance in the network.
Utterances
For the other two network measures I tracked how many times each justice spoke and with whom they interacted, specifically looking at the speaker in each row and the speaker in the row directly above it. I eliminated the attorneys’ remarks from these graphs so that the sequence of speaking only focused on the justices’ speech. I also removed any utterances of Chief Justice Roberts of fewer than five words thereby eliminating instances where he calls on other justices to give them an additional turn during arguments. After counting the interactions, I created a table that represented how many times each justice interacted with another justice. The next measure looks at utterance or turn-taking patterns.
The results reveal the eigenvector centrality scores for each justice, highlighting their relative importance based on the interaction patterns. Justice Gorsuch has the highest score of 1, indicating that he is at the center of the interaction network among the justices. Justice Jackson follows with a centrality score of 0.462, suggesting that while she is not as central as Justice Gorsuch, she still plays an important role in the network. Chief Justice Roberts and Justice Sotomayor have scores of 0.291 and 0.294, respectively, placing them in a moderately central position within the network. Justice Thomas has the lowest score at 0.041, implicating his minimal influence in this network.
Word Counts
Lastly, word count centrality results are generated based on the number of words spoken by each justice during their interactions. This measure reflects not only the individual contributions of the justices but also how these contributions relate to one another in the context of the discussion.
In the analysis, each justice’s utterances are once again paired with those of the previous speaker. The word count of the current speaker’s utterance is summed for all interactions with their preceding speaker, which allows the establishment of directed connections between speakers based on their contributions.
The word count centrality results for the justices reflect their levels of influence during discussions, based on the number of words they contributed in comparison to one another. Utilizing the eigenvector centrality algorithm on this graph, the analysis identified Justice Jackson as having the highest word count centrality value of 1, indicating a dominant role in the discourse. Other justices, such as Chief Justice Roberts and Justice Kagan, also displayed significant centrality values of 0.961 and 0.950, respectively.
Conclusion
While according to Chief Justice Roberts, oral arguments may not be as important as briefs, the interaction of the three centrality measures used in this analysis—word count centrality, utterance centrality, and reference centrality—provides a nuanced understanding of the justices’ relative influence during oral arguments. Justice Jackson exhibits the highest word count centrality, indicating a prominent presence in the discussions. Justice Alito shows high reference centrality, signifying that, despite a lower volume of spoken contributions, he is frequently cited by others, suggesting a role in shaping the discourse without necessarily leading it. In contrast, Justice Thomas has lower scores across all measures, indicating a relatively reduced presence in the interactions. These findings illustrate a complex landscape of influence among the justices, where verbal contributions, their relevance to ongoing discussions, and the frequency with which justices are referenced interact to define their relative standing in oral arguments. This analysis underscores that influence within judicial discourse is more multifaceted than meets the eye.
Adam Feldman runs the litigation consulting company Optimized Legal Solutions LLC. For more information write Adam at [email protected]. Find him on Twitter: @AdamSFeldman.
