Difference-Splitting Voting: Middle-Ground Votes at the U.S. Supreme Court

Abstract

The Supreme Court has recently delivered big wins for conservatives on issues such as guns, abortion, and campaign finance. In many well-known cases in the Court’s history, however, various justices have cast votes that split the difference between conservative and liberal positions. This paper develops the first systematic measure of “difference-splitting votes” at the Supreme Court and considers what predicts this voting behavior. I find that these votes have declined as the Court’s docket has shrunk. Not all justices are inclined to cast these votes: justices who are more conscientious and less extreme are more likely to engage in difference-splitting. Justices are also more likely to cast these votes in salient cases. By understanding these votes, we can learn more about how jurists craft nuanced legal outcomes and the ways justices can send signals to other actors through their voting behavior.

Keywords

Supreme Court difference-splitting ideology case salience judicial personality

In a pair of affirmative action cases arising out of Michigan in 2003, Justices O’Connor and Breyer voted to strike down the undergraduate affirmative action program (Gratz) but uphold the one at the law school (Grutter).¹ And in a pair of cases decided in 2005, Breyer voted that a display of the Ten Commandments at the Texas State Capitol was consistent with the Establishment Clause (Van Orden v. Perry),² but those at Kentucky courthouses were not (McCreary County v. ACLU).³ Scholars and jurists have noticed the importance of these “split-the-difference” votes (e.g, Klarman, 2014; Wilkinson, 2006), but empirical researchers have not yet measured the prevalence of this phenomenon over time or systematically considered its causes.

This paper develops a new strategy for defining and measuring difference-splitting votes in order to consider how this form of Supreme Court voting has changed over time and what factors predict its emergence. Such voting behavior that grants victories both to conservative and liberal positions in closely related disputes have long been a feature of the Court’s jurisprudence. For example, on the same day that the Court announced new constitutional limits on police lineups (Wade and Gilbert),⁴ it also kept those limits from applying retroactively (Stovall),⁵ sharply limiting the pool of people who might benefit from the ruling (Powe, 2000, pp. 403-4, 425-29). Chief Justice Warren, Justice Clark, and Justice Brennan were in the majority for all three decisions. However, in recent years, these kinds of votes have seemed to be few and far between. As the modern Court has issued conservative rulings across a wide array of topics, rarely are these rulings paired with partial victories for litigants advancing liberal positions. While Grutter and Gratz led to some justices voting for a middle-ground outcome, no justices did so in the recent affirmative action case SFFA v. Harvard, even though it combined cases from Harvard and UNC and thus in principle could have allowed for such middle-ground votes.⁶ Yet such votes have not disappeared altogether—as seen in a pair of 2022 rulings regarding vaccination requirements during the Covid-19 pandemic.⁷

I find that these difference-splitting votes have indeed declined over time, but that this is largely driven by the Court taking fewer cases that present the opportunity for justices to cast them. This decline in “difference-splitting opportunities” is strongly correlated with the passage of the Case Selections Act of 1988, the Court’s overall declining caseload, and increasing ideological polarization at the Court. Conditional on the Court taking cases that allow for the casting of difference-splitting votes, justices who are more ideologically moderate, more conscientious, and more qualified are more likely to cast these votes, although I find little evidence that a justice’s institutional position affects this behavior. This voting behavior is also more likely in more salient cases (Clark et al., 2015) and by justices early in their careers. Taken together, this paper defines and measures an important understudied phenomenon in judicial politics and provides the first theoretical explanation for and empirical test of its determinants.

This voting behavior is potentially deeply connected to many aspects of judicial politics. First, the decline of these difference-splitting votes over time helps demonstrate the consequences of the Court’s increasing polarization (Bonica & Sen, 2021; Clark, 2009a; Devins & Baum, 2017) and greater docket control (Heise et al., 2020; Owens & Simon, 2012). Second, these also involve taking a middle-of-the-road position on a particular issue (Lindquist et al., 2007), rather than having a voting record that averages out as moderate across issue areas. Not all justices whose voting behavior appears “moderate” will necessarily be inclined to take these middle-ground positions; previous literature has suggested that judicial behavior can vary based on personality traits as well as ideology (Black et al., 2020; Hall, 2018) and that justices may exhibit different behavior when they fill a specialized institutional role (the Chief Justice) or find themselves in a pivotal ideological position on the Court (being a median or “swing” justice) (e.g., Badas, 2021; Baum & Devins, 2010; Enns & Wohlfarth, 2013; Johnson, 2018; Mark & Zilis, 2019). Third, these votes illuminate how case salience (Clark et al., 2015; Strother, 2019; Unah & Hancock, 2006) might affect judicial decision-making on a dimension previously not considered by the literature. Finally, the study of the crafting of these middle-ground positions also helps shed light on how the Court creates its legal doctrine (e.g., Lax, 2011) and when the Court chooses to give guidance to lower courts on complex legal questions (e.g., Beim & Rader, 2019; Masood et al., 2019).

In defining and studying this phenomenon, I bring together legal scholarship about the concept of “split-the-difference jurisprudence” (Wilkinson, 2006) with the tools of political science. Understanding this concept of “difference-splitting voting” provides a new lens for observers of American law to understand judicial behavior in some high-profile decisions, and distinguishing between this behavior and general ideological moderation may be helpful for legal practitioners thinking about how to craft their arguments. Furthermore, this more sophisticated way of thinking about judicial voting is not limited to the United States; scholars of comparative judicial behavior can consider whether the frequency of this voting is associated with other cross-national variations in judicial behavior, such as the prevalence of attitudinal voting (Solberg & Waltenburg, 2024). This work, focused on the United States Supreme Court, provides the first theoretical account and the first presentation of descriptive data and empirical analyses about a phenomenon in judicial behavior with potentially broad applications.

1. Difference-Splitting Voting at the Supreme Court

Grutter/Gratz and Van Orden/McCreary County provide paradigmatic examples of difference-splitting votes: by taking two cases that both implicate the same issue, justices can chop up the policy space in a finer-grained way, demonstrating how the legal standard they are applying can lead to one result with one fact pattern and another result with a different fact pattern. So doing, the Court (if the difference-splitting position is victorious) sends a strong signal to outside actors about the bounds of its doctrine—and, perhaps not incidentally, about the Court’s own conscientiousness and reasonableness in not treating all cases alike. The ability of difference-splitting votes to mark significant doctrinal moments can become apparent as soon as multiple cases on the same topic have cert petitions granted in short succession: for example, when the Court granted cert in Gregg v. Georgia and the other cases presenting post-Furman death penalty statutes, “it seemed that the Court was sending a signal to all concerned that it was intent in dealing with capital punishment in its totality” because of “the wide array of laws and facts involved in the cases” (Epstein & Kobylka, 1992, p. 100). Indeed, that several justices chose to split the difference in Gregg and the other 1976 death penalty cases delineated the bounds of death penalty jurisprudence in a way that could help predict subsequent cases for years after (George & Epstein, 1992).

Yet while Grutter/Gratz, Van Orden/McCreary County, and the July 2, 1976 death penalty decisions provide very clear examples of difference-splitting voting, this behavior is not limited to votes across cases with separate captions. Within a single case caption when multiple cert petitions are granted, such middle-ground positions are also possible. Consider the famous approach of Chief Justice Roberts to NFIB v. Sebelius,⁸ upholding the individual mandate as a tax (but not as a regulation of interstate commerce) and invalidating the conditioning of existing Medicaid funds as an incentive to make states expand the Medicaid program. Since there were multiple cert petitions consolidated under a single case caption, Roberts could craft a decision that handed each side a partial victory.

To capture all these paradigmatic scenarios, I define a difference-splitting vote for the purposes of this paper as either (a) one where a justice votes liberally in one case and conservatively on another case that is handed down on the same day and involves the same substantive policy question, or (b) where a justice votes both conservatively and liberally within the same case caption on the same policy issue when the case consolidates multiple docket numbers into one caption. To avoid linguistic repetition, I will also call the position taken by a difference-splitting vote a “middle-ground position.”⁹ This encompasses situations like Gratz/Grutter, where the difference-splitting is across cases, and NFIB v. Sebelius, where it is within a single case caption that consolidated several docket numbers (bringing before the Court, inter alia, the challenge to the individual mandate and the challenge to the Medicaid expansion from petitions by different litigants from a single case below). Note that this includes not only cases that are formally consolidated, but those that are informally “grouped” or are “companion cases” (Kowiak, 2022; Wasby, 2021); that is, released on the same day but with different case captions.¹⁰

Thus, a difference-splitting vote in this sense is the result of two choices: the creation of the difference-splitting opportunity, by joining together the disposition of cases in this way or consolidating cases, and the subsequent decision by a justice about whether to split-the-difference across these votes or not. That first choice, to bundle certain cases or questions together, most likely occurred at the cert stage or when deciding to set cases for oral argument. This paper focuses primarily on measuring and explaining the second choice—why justices cast difference-splitting votes given that there is the opportunity to do so—but I also consider the factors that might affect the first choice of whether to create difference-splitting opportunities at all.

By creating a new measure of difference-splitting voting, we are able to study a phenomenon that traditional codings of judicial voting are unable to capture. Studies of judicial voting frequently conceptualize the dependent variable as whether the vote is “liberal” or “conservative,” as in the Supreme Court Database (Spaeth et al., 2024). Binary outcome variables of judicial voting, sometimes aggregated by term and/or justice, form the backbone of a vast array of scholarship. For example, such codings can be used to validate judicial ideology measures (e.g., Bonica et al., 2017; Epstein & Mershon, 1996; Segal & Cover, 1989), demonstrate voting differences by political party (e.g., Pinello, 1999; Sunstein et al., 2006), evaluate what predicts ideological voting (e.g., Bartels, 2011; Unah & Hancock, 2006), consider correlations between public liberalism and judicial voting (e.g., Casillas et al., 2011; Epstein & Martin, 2010; Johnson & Strother, 2021), and much more. Despite various theoretical and empirical problems with the use of such a binary coding (e.g., Harvey & Woodruff, 2013; Ho & Quinn, 2010), these variables are widely used in empirical studies of judicial behavior.

Yet a “liberal vote” measure does not fully capture what is going on in situations like Grutter/Gratz. A “difference-splitting vote” is different from a conventional liberal or conservative vote, not only in terms of ideological valence, but also in other important ways. Most notably, difference-splitting votes have the potential to send signals to outside actors more effectively than other types of votes. They are ostentatious signals of a justice’s, and perhaps the Court’s moderation and conscientiousness. This may be helpful for a justice’s reputation. An example of such reputational benefits comes from Van Orden v. Perry, one of a pair of cases about the public display of the Ten Commandments. When the Harvard Law Review published a series of “Essays in Honor of Stephen G. Breyer,” two of them singled out Van Orden for praise (Fallon, 2014; Klarman, 2014). Klarman (2014, p. 452) called the opinion “a laudable act of judicial statesmanship” that “acknowledges political reality and makes a wise concession to the force of public opinion.”¹¹ Of course, any potential benefit to judicial reputation is speculative, as reputation is difficult to measure, much less what we would really want: justices’ perceived benefits to reputation ex ante when choosing among different courses of decisions. And, justices have different audiences (Baum, 2006); some justices will be more interested in cultivating a moderate reputation than others. Nevertheless, Judge J. Harvie Wilkinson likely expresses what most judges would believe about the reputational consequences of these votes: difference-splitting appears moderate, and “[m]oderation is a trait that the public admires in the judiciary” since it may be seen as reflecting a “proper judicial temperament” (Wilkinson, 2006, p. 1981); furthermore, splitting the difference can allow judges to embrace middle-ground positions that are consistent with public opinion (Wilkinson, 2006, p. 1982).

Further, by their very nature, these votes highlight how far a justice is willing to go on a particular issue: that is, the vote highlights that a justice will go as far as uphold a claim with respect to litigant A, but not for litigant B, or with respect to one question in a case but not another related question. Thus, difference-splitting votes can also provide a signal to future litigants and lower court judges that a justice is unwilling to move policy any further on a particular issue. Think about Grutter/Gratz: The distinction between a points-based system and “plus factors” is small. To rule for one litigant and against another suggests that O’Connor and Breyer had found what they believed was the constitutionally significant line between acceptable and unacceptable affirmative action programs, leaving relatively little uncertainty to outside actors about what is or isn’t allowed.¹² Indeed, the Supreme Court did not take another case involving affirmative action in higher education (Fisher I¹³) until O’Connor had left the bench. A contrary decision in Grutter “would have clarified very little” as “[o]ver time, there would be new circuit conflicts and increasing pressure for the Court to issue a more decisive opinion” (Devins, 2003, pp. 378-79). This was true in Gregg and the related death penalty cases too, even though “[o]n one level, the Court’s opinions …were …confusing and varied,” because the votes sent a “signal” that “mandatory [death penalty] laws were ‘out’ and guided discretion was ‘in’ ” (Epstein & Kobylka, 1992, p. 114). In general, the consideration of more cases at once, such as through consolidation and summary decisions, can help the Supreme Court indicate to lower courts that its precedents ought to be interpreted broadly rather than narrowly (Masood et al., 2019).

1.1. Difference-Splitting Votes and Other Phenomena

This phenomenon of difference-splitting voting needs to be distinguished from others that may coincide with this voting behavior but that are conceptually distinct and might not be driven by the same theoretical factors. First, justices may engage in bargaining (e.g., Epstein & Knight, 1998; Lax & Cameron, 2007; Maltzman et al., 2000) or deliberation (Haire et al., 2013), and this may lead to justices compromising over the language of the case’s controlling opinion. While the difference-splitting votes in Gratz/Grutter may indeed partially result from a bargaining process, they need not. A single justice may choose to take a voting position with a liberal outcome in one case and a conservative outcome in another case without bargaining with his or her colleagues at all. Thus, difference-splitting voting can, but not need not, emerge from bargaining.

Nor is the decision to split-the-difference necessarily the same calculus as the decision to write separately. While justices often use a separate opinion to explain why they are treating two cases differently from each other—consider, for example, Breyer’s opinion in Van Orden v. Perry—there are many possible rationales for writing separately, of which distinguishing a related case is only one. Furthermore, justices can cast these difference-splitting votes without explaining their reasoning if they choose to do so; the concept is fundamentally about voting, not opinion content.¹⁴

2. Why Cast Difference-Splitting Votes?

I argue that there are three sets of factors that may influence the casting of difference-splitting votes. First, some justices may be more likely to vote this way than others. Second, some types of cases may provide greater opportunities or incentives for justices to split the difference. Finally, changes to the Court’s docket over time likely have affected the opportunities to cast these votes.

2.1. Justice-Specific Factors

Justices who are ideologically moderate should be inclined to split the difference, as ideology is a strong predictor of Supreme Court voting behavior more generally (e.g., Segal & Spaeth, 2002). Justices who have ideal points in the middle of a one-dimensional policy space are more likely in general to find themselves casting a mix of liberal and conservative votes, since for these justices small movements in case cutpoints are more likely to translate into changed dispositional votes. The example of O’Connor in Grutter/Gratz appears to fit in this mold.¹⁵ These justices may also see their role as splitting the difference between the positions of those at the ideological poles, whatever those positions may be (Kennedy, 1996, pp. 795-96). In contrast, more ideologically extreme justices may be more likely to believe that “there are differences on fundamental things that really can’t be compromised […] [s]o it’s not like you are going to split the difference” (Stuart & Dickinson, 2024).¹⁶ However, while these middle-ground positions are almost certainly the result of moderation, the moderation is of a certain sort: if justices have some conservative views and some liberal views, which might average out to moderation in their overall voting record, we shouldn’t expect within-issue difference-splitting votes. The difference between true moderation and having a mix of liberal and conservative views has been a focus of study in the mass public (e.g., Broockman, 2016; Fowler et al., 2023), but it has implications for the study of elite actors such as Supreme Court justices as well. Consider Justice Gorsuch. He is generally very conservative, but tends to vote in a liberal direction in cases involving Native American tribes and some criminal issues.¹⁷ Imagine that fifty percent of the Court’s docket were on those issues. Then Gorsuch would appear quite moderate. Now imagine another justice who had moderate views on all issues, both the ones on which Gorsuch is conservative and those on which he is liberal. That justice would be more likely to cast difference-splitting votes than Gorsuch, although that justice’s average voting record may look similar. Importantly, this distinction has implications for the development of legal doctrine. This hypothetical justice would not vote to change public policy nearly as much as Gorsuch, as this justice would be more happy with the status quo. Our measures of ideology that summarize voting behavior may not fully capture the difference between these two kinds of moderation.

While the theoretical basis for expecting ideology to matter is very strong, recent research suggests that we should consider a broader set of justice motivations and that these motivations may be tied to personality (Epstein & Knight, 2013; Hall, 2018). In particular, empirical work shows that the Big Five personality trait of conscientiousness (see generally McCrae & Costa, 2008) “influences every aspect of judicial behavior” (Black et al., 2020, p. 6), including opinion writing and voting. This makes good sense, as conscientiousness should lead justices to expend more effort on their work (Hall, 2018, p. 21); someone who is conscientious is “dutiful, deliberate, driven, persistent, self-assured, or hardworking” (Black et al., 2020, p. 22), and in the legal realm, this is associated with greater time in opinion writing, “opinions with greater breadth, opinions that are more cognitively complex, longer opinions,” and greater respect for precedent (Black et al., 2020, p. 9). This greater respect for precedent reflects a broader expectation that conscientious judges should be more desirous of following legal constraints even when they may conflict with policy goals (Hall, 2018, p. 22). Difference-splitting voting involves treating two cases on the same topic differently, even though they were considered by the Court in close proximity and are being presented to the legal world and public together. It takes less cognitive effort to decide that two closely related cases should have the same general outcome, as this does not require a deep dive into the specifics of each case; since we already know that conscientious justices put more time and effort into their opinion writing, we should expect that they will also put more time and effort into deciding whether to split the difference on closely related cases, even if they are not the opinion author. Splitting the difference also often involves a careful application of existing precedent to the facts of related cases: often it involves taking an existing legal principle and explaining why it leads to one outcome in one case, but distinguishing its application in another case, because of the relevant change in the facts. Of course, there are both theoretical and practical reasons to think that conscientiousness may not be a big factor: the theoretical argument for conscientiousness mattering depends, in part, on justices taking legal factors seriously; to the extent that behavior in these cases is purely ideological, there may be no additional predictive power of personality traits. Furthermore, the theoretical argument for conscientiousness mattering depends on the cases being genuinely on related topics, and the justice then taking the time to distinguish them; if the measurement strategy for difference-splitting voting is overly broad and capturing votes that are not closely related, then ideology should still matter—moderate justices will still build up moderate voting records, even across disparate cases—but conscientiousness likely will not.¹⁸

Similarly, I expect more highly qualified justices (Cameron et al., 1990) to split the difference more often. Interestingly, qualifications are uncorrelated with conscientiousness (Black et al., 2020, p. 52); nevertheless, we should expect that more qualified justices will also be more diligent and more inclined to follow legal norms, even if their measured personality is not especially conscientious. It is thus important also to include this variable in the model. It is less clear how judicial tenure should affect this behavior; on the one hand, aging may lead the justices to default to heuristics and treat cases with less individual attention (Black et al., 2024), and more experienced justices may have firmer prior beliefs when approaching new cases; on the other hand, it may take experience for justices to learn how to spot the small details that might justify distinguishing two closely related cases. Given that it is possible that age and experience may affect this behavior while being correlated with other covariates—in particular, we know that justices who are more conscientious also tend to serve longer (Black et al., 2020, p. 52)—it is important to include judicial tenure in the model as a control variable.

These difference-splitting votes may also in part stem from a strategic decision to present a justice’s position as middle-of-the-road for reputational reasons. Justices with greater institutional power such as the median justice or the Chief may be especially concerned with the reputation of the Court and may want to cast difference-splitting votes in order to make the Court appear more middle-of-the-road.¹⁹ Scholarship has shown how the median justice and the Chief Justice often behave differently from other justices or have outsize influence (e.g., Badas, 2021; Baum & Devins, 2010; Enns & Wohlfarth, 2013; Johnson, 2018; Mark & Zilis, 2019), with a particular focus on how these justices respond to outside actors. Of course, not all medians are equally powerful (Epstein & Jacobi, 2008), and the median justice is likely to be ideologically moderate as well, so disentangling the influences of these two variables is tricky.²⁰ Moderates may be inclined to middle-ground outcomes regardless of their institutional position, while status as the median may only make a difference for the relatively more extreme median justices.

2.2. Case-Specific Factors

Features of the cases involved are also likely to matter. As Strother (2019, p. 133) notes, many scholars have argued that “justices’ desire to maintain their reserve of diffuse institutional support, along with their fear of nonimplementation of their decisions, causes them to alter their behavior (votes) under some conditions” of case salience, but there is no agreement in the literature about when this operates: in salient cases (Hall, 2014), in non-salient cases (Casillas et al., 2011), or not at all (Johnson & Strother, 2021). On the one hand, to the extent that justices view difference-splitting votes as a way to build their reputations with outside actors, these reputational benefits are likely difficult to achieve in non-salient cases. On the other hand, highly salient cases may be those where justices have firmer views and thus may be less inclined toward difference-splitting. If other covariates, such as issue area, are able to pick up on the firmness of a justice’s ideological views, it may be that the reputational benefits of difference-splitting in salient cases will dominate.

2.3. Temporal Factors

As the Court’s mandatory docket has shrunk, particularly following the Case Selections Act of 1988, and the Court has been more jealous of its cert grants (e.g., Heise et al., 2020; Owens & Simon, 2012; O’Brien, 1997), we should expect difference-splitting opportunities to decline as well. And as polarization has increased (Bonica & Sen, 2021; Devins & Baum, 2017), middle-ground outcomes may become harder to reach, or justices may be less interested in forging the opportunities to reach such outcomes as fewer justices are inclined to split the difference between liberal and conservative positions. These factors suggest that difference-splitting voting should decline over time, especially following 1988.

3. Measurement of Difference-Splitting Votes

In order to measure difference-splitting, we need first to make the unit of the analysis the vote by a justice within a Difference-splitting opportunity rather than the vote in a case, since the dependent variable needs to capture this phenomenon of splitting-the-difference across cases as in Grutter/Gratz. To obtain Difference-splitting opportunities, we start with any case with multiple docket entries in the Supreme Court Database (Spaeth et al., 2024) or any group of cases with different captions where (a) the “issue” as defined by the Supreme Court Database is the same,²¹ (b) the decision date is the same, and (c) where oral argument had previously been held on the same week, to avoid pairing cases where the opinions happen to fall on the same day but where the justices likely thought of the cases as unrelated.²² Thus, the unit of analysis is the bundle of decision-date–oral argument week–issue, which I will refer to as “date-issue” for short. When there is more than one vote per justice in this bundle, either because there was more than one case that shared an issue, decision date, and oral argument week (e.g., Grutter/Gratz) or because within a single case citation more than one question was voted upon,²³ we have a Difference-splitting opportunity. In these Difference-splitting opportunities, it is possible for justices to cast a vote in a liberal direction and another vote in a conservative direction.

Thus, I operationalize Difference-splitting vote to refer to any time that a justice casts both a liberal and a conservative vote within a Difference-splitting opportunity. In the example of Grutter/Gratz, O’Connor and Breyer are coded as 1 for Difference-splitting vote while the other justices are coded as 0. In NFIB v. Sebelius, Roberts, Breyer, and Kagan are coded as 1 and the others are coded as 0. Note that a Difference-splitting opportunity is an date-issue combination where the casting of such a difference-splitting vote is possible, whether or not a justice actually does so. For example, in Roe v. Wade²⁴ and Doe v. Bolton,²⁵ it was conceptually possible to strike down the Texas abortion law but uphold Georgia’s law, even though the justices who struck down one were the same as those who struck down the other (Klarman, 2014, p. 453). Thus, the bundle of Roe and Doe is included in the set of difference-splitting opportunities, but all justices are coded as 0 for Difference-splitting vote. In general, I rely on the codings from the Supreme Court Database in order to have a consistent coding of “liberal” and “conservative” across cases. However, since the Database may sometimes misidentify what was in fact the more liberal or conservative position in political terms (e.g., Epstein et al., 2013; Harvey & Woodruff, 2013), I engage in minor manual checking of some codings that appear the most potentially problematic; see Section B in the Online Appendix for more details.

Taken together, this process covers the 1946–2023 Terms and generates 10,137 votes in 1,126 difference-splitting opportunities. In the regression models predicting Difference-splitting vote, we cover the 1955–2008 Terms, with 7,648 votes in 849 difference-splitting opportunities. The decline stems from the lack of coverage of the full timeline for the measure of case salience, a theoretically important predictor.

3.1. Difference-Splitting Votes over Time

Figure 1 shows how the Court’s decisions in what cases to take and which opinions to release together has affected the possibility of these difference-splitting votes over time. The left panel presents the counts, while the right panel presents the proportion. The denominator is the total number of date-issue combinations out of all cases.²⁶ The numerator is the number of date-issue combinations where each justice has more than one vote in the Database, either because there was more than one case that date or because the date had more than one vote tallied on that issue. I label these situations as difference-splitting opportunities, as in principle justices could engage in this difference-splitting voting behavior in these cases. This does not mean, however, that any justices actually did cast such votes; this merely shows the share of date-issues where such voting behavior was possible.

Figure 1.

The potential for difference-splitting votes over time

What we see in Figure 1 is that the opportunities to cast these difference-splitting votes have been falling over time, especially in the post-Case Selections Act period; this mostly appears to be about the overall decline in the Court’s docket, although until quite recently the proportion of Difference-splitting opportunities out of all date-issue combinations had been on the decline as well. Since the number of Difference-splitting opportunities is likely the outcome of a strategic choice about which cases to take and how to pair them together in decision days, this suggests a secular decrease in the Court’s interest in issuing these types of decisions.

Even within the universe of difference-splitting opportunities, most justices do not cast difference-splitting votes. Figure 2 shows the share of actual difference-splitting votes cast, out of the difference-splitting opportunities identified in Figure 1; the unit of analysis is a justice’s vote (1 for a difference-splitting vote or 0 otherwise; counts in the left panel and the proportion in the right panel). We see that even when the Court creates Difference-splitting opportunities through consolidating cases or taking up cases in short succession on the same issue, most of the time the justices do not actually cast difference-splitting votes. Furthermore, we see a decline over time in the count of such votes in Figure 2, driven by the overall decline in Difference-splitting opportunities; however, in the right panel, we see that the share of these votes, out of opportunities to cast them, has perhaps grown in very recent years–although the left panel shows that the raw number of those votes is low. Putting the two figures together, we see that not only have difference-splitting opportunities declined, but actual difference-splitting votes have declined as well. What once was a somewhat common feature of the Court’s decision-making is close to disappearing, likely because of broader changes in the Court’s docket around the time of the Case Selection Act.

Figure 2.

Actual difference-splitting votes over time, as a share of difference-splitting opportunities

Figure 3 shows the estimates by Chief Justiceship from the Warren Court onward for each justice’s Difference-Splitting Propensity. This is the proportion of difference-splitting votes the justice cast out of the justice’s difference-splitting opportunities, with 95% Wilson score confidence intervals (Agresti & Coull, 1998; Wilson, 1927).²⁷ In each panel the overall mean proportion (0.09) is plotted as a dashed line in order to make over-time comparisons more visually apparent.

Figure 3.

Difference-splitting propensity by justice and Chief Justiceship, proportions with Wilson score confidence intervals. Overall average proportion across the whole dataset plotted with dashed lines

Two patterns stand out. First, most obviously, justices who served earlier tend to have higher scores. Several justices during the Warren Court have scores above the overall mean, while the Rehnquist court has several justices below the mean. The Burger and Roberts Courts look more average, but with more spread during the Roberts Court.

Second, “swing justices” and moderates tend to rank highly on Difference-Splitting Propensity, after taking into account the general time trend noted above. Several of the highest-ranking justices in their eras, such as Frankfurter, Stewart, Powell, O’Connor, and Kennedy, are precisely those one would expect. (Yet, this is not uniformly true: Byron White and Sandra Day O’Connor have middling scores in the Burger Court.) Many of the justices who score low on this metric are those farthest from the ideological center. The Chief Justices do not stand out as having particularly high or low scores, and Rehnquist’s score (insignificantly) declines from being an Associate Justice to being Chief.

4. What Predicts Difference-Splitting Opportunities and Votes?

The descriptive statistics show that the frequency of difference-splitting opportunities and difference-splitting votes have changed over time, and the justices vary in their propensity to cast difference-splitting votes. I now turn to regression models to test the theoretical arguments developed above.

4.1. Predicting Difference-Splitting Opportunities

I begin by considering what predicts the emergence of difference-splitting opportunities. Table 1 tests the key factors that may predict the emergence of difference-splitting opportunities by Term, using a linear model. Caseload is the number of cases before the Court in a given Term, which we would expect to have a strong relationship with difference-splitting opportunities—the fewer the cases, fewer the chances to decide related cases together. After Case Selections Act considers whether a case is from the 1988 Term or later, following Owens and Simon (2012) and Heise et al. (2020); if greater docket control leads the justices to choose not to create difference-splitting opportunities, this should be a negative predictor even after considering Caseload. Other variables control for the ideological environment, both outside and within the Court. Court curbing bills, t-1 represents the political environment surrounding the Court, employing court-curbing data from Ura and Wohlfarth (2022).²⁸ Court polarization follows the approach of Clark (2009a), using Martin-Quinn scores to calculate a polarization statistic for each Term. We may expect a more hostile Congress, an institution with an important relationship to the Court (see generally Rivero & Key, 2024) to push the Court toward taking cases that may lead to more modest ideological victories. In contrast, a more polarized Court may be more interested in taking cases that will lead to a clear ideological victory for the dominant faction on the bench and less interested in taking cases that will allow for nuanced, middle-ground positions.

Table 1.

Predicting Difference-Splitting Opportunities by Year, OLS Model

	Difference-splitting opportunities
Caseload	0.11*** (0.02)
After Case Selections Act	−3.95** (1.61)
Court polarization	−1.06** (0.52)
Court curbing bills, t-1	−4.95 (3.50)
Constant	2.51 (3.30)
N	71
Adjusted R²	0.74

*p < .1; **p < .05; ***p < .01

We find that these variables are jointly strong predictors of the emergence of difference-splitting opportunities. Furthermore, Caseload, After Case Selections Act, and Court polarization are all significant and in the expected direction. As the Court’s caseload declined, its docket control was increased by Congress, and it has become more polarized, Difference-splitting opportunities has decreased. We do not see evidence, however, that this is driven by court-curbing threats.

4.2. Predicting Difference-Splitting Votes

Now that we have seen which factors predict the emergency of Difference-splitting opportunities, I now present logistic regression models of difference-splitting voting to test my hypotheses about what predicts these votes, given the presence of an opportunity to cast such a vote. I use two main sets of predictors. First, I employ important case-level variables. Importantly, I use L.C. mixed directionality, an indicator for whether the lower court directionality (taken from the SCDB) for the cases in the Difference-splitting opportunity was all liberal or all conservative (L.C. mixed directionality = 0) or mixed (L.C. mixed directionality = 1). Taking a bundle of cases where the lower courts ruled in ideoligically split directions should strongly predict difference-splitting voting at the Supreme Court. I also include whether the difference-splitting opportunity was across Multiple case captions and the interaction of L.C. mixed × Multiple captions. Of greater theoretical import, I include a pre-decision measure of case salience (Clark et al., 2015), binning cases into High salience (top third of salience estimates in the data), Medium salience (middle third), and Low salience (bottom third), reflecting disagreements in the literature about when case salience affects judicial behavior and whether this relationship is potentially nonlinear (e.g., Casillas et al., 2011; Hall, 2014; Johnson & Strother, 2021).²⁹ I also include issue area fixed effects to take into account the broad topic of each case. Term fixed effects hold constant temporal factors that may affect this voting.

Second, I employ variables at the justice-level. Measures of the Big Five personality traits test whether non-strategic personality factors such as conscientiousness predict difference-splitting behavior, as measured by Black et al. (2020), using written material from the justices before they were confirmed to generate Big Five personality trait estimates. The justice’s Qualifications score is taken from newspaper data pre-confirmation (Cameron et al., 1990; Epstein et al., 2022). ln(Time on bench) controls for how long a justice has served. Ideological extremity is the absolute value of the justice’s Bailey (Bailey, 2013, 2021),³⁰ Martin and Quinn (2002), or Segal-Cover (Segal & Cover, 1989) scores,³¹ scaled to have a standard deviation of 1 for comparability across models. In addition, I include an indicator for whether a justice is the Chief. Standard errors are clustered by difference-splitting opportunity.³²

Table 2 presents the results. Across all models in the table, L.C. mixed directionality is a strong predictor of difference-splitting voting, as one would expect; similarly, cases with multiple captions (suggesting greater factual distinction than consolidated cases) have more such voting. We also see that both Moderate salience and High salience cases evince more difference-splitting voting than Low salience cases (the baseline category). This is especially notable given that these models already contain issue area fixed effects, which capture the broad topic of the case. The salience result suggests that the justices may be attempting to build their reputations for middle-of-the-road jurisprudence strategically in those cases that are most likely to generate public attention, or that these are the cases to which the justices devote particular time and energy, leading to more carefully drawn doctrinal lines.

Table 2.

Logistic Regressions Predicting Difference-Splitting Votes as a Function of Case-Level and Justice-Level Factors. Data From the 1955–2008 Terms

	Difference-splitting vote
	Bailey	MQ	Segal-cover
	(1)	(2)	(3)
L.C. mixed directionality	1.30*** (0.35)	1.30*** (0.35)	1.30*** (0.35)
Multiple case captions	2.48*** (0.27)	2.48*** (0.27)	2.48*** (0.27)
L.C. mixed × Multiple captions	−1.46*** (0.41)	−1.46*** (0.41)	−1.46*** (0.41)
Medium salience case	0.47* (0.25)	0.47* (0.25)	0.47* (0.25)
High salience case	0.47* (0.24)	0.47* (0.24)	0.47** (0.24)
Openness	0.05* (0.03)	0.05 (0.03)	0.08** (0.03)
Conscientiousness	0.15*** (0.05)	0.15*** (0.05)	0.22*** (0.06)
Extraversion	−0.08* (0.05)	−0.06 (0.05)	−0.17*** (0.06)
Agreeableness	0.01 (0.04)	0.03 (0.04)	0.02 (0.04)
Neuroticism	0.04 (0.04)	0.06 (0.04)	0.05 (0.04)
Qualifications	0.44** (0.18)	0.47*** (0.18)	0.70*** (0.19)
ln (Time on bench)	−0.10** (0.04)	−0.10** (0.04)	−0.12*** (0.04)
Ideological extremity	−0.15*** (0.04)	−0.13*** (0.05)	−0.17*** (0.05)
Chief Justice	−0.07 (0.12)	−0.11 (0.12)	−0.18 (0.12)
Constant	−3.27*** (0.62)	−3.36*** (0.62)	−3.31*** (0.62)
Opportunity-Clustered SEs	✓	✓	✓
Issue Area FEs	✓	✓	✓
Term FEs	✓	✓	✓
AIC	4048.15	4051.02	4047.52
N	7,648	7,648	7,648

*p < .1; **p < .05; ***p < .01

Considering the justice-level coefficients, we find a consistent positive coefficient on Conscientiousness, consistent with theoretical expectations. Similarly, Qualifications is positively related to difference-splitting voting. Agreeableness and neuroticism appear unrelated to these votes; in some models, openness positively predicts difference-splitting voting and extraversion negatively predicts it.³³ ln(Time on bench) is a strong negative predictor across all three models—as justices serve longer, they are less likely to engage in difference-splitting voting. Not surprisingly, there is a substantial negative relationship between Ideological extremity and difference-splitting voting, no matter how ideological extremity is measured: more extreme justices are less likely to cast difference-splitting votes, given a difference-splitting opportunity. Chief Justice status is generally imprecisely estimated, and, contrary to theoretical expectations, has a negative sign.

Taken together, we see that justice ideology, qualifications, and conscientiousness predict difference-splitting voting. In addition, difference-splitting voting is less common in low salience cases, consistent with the view that these votes are partly intended to send signals to lower courts and other outside actors; low salience cases may not be seen as important enough to put in the effort to send such signals. Figure 4 presents predicted probabilities for different values of these variables, keeping other variables at their observed values (see Hanmer & Kalkan, 2013);³⁴ given the different scales of these variables, this helps clarify their relative importance. While no one factor dominates, we see meaningful variation in the predicted probability of casting a difference-splitting vote across values of these key variables.

Figure 4.

Predicted probabilities of casting a difference-splitting vote by key covariates

4.2.1. Robustness

In the Appendix, I consider several alternative analyses. First, the main models do not distinguish between median status and judicial extremity (which are, of course, correlated); in Table C.1, I estimate models that include an interaction between where a justice is currently the median (estimated using either Bailey or Martin-Quinn scores) and the justice’s ideological extremity. This tests the theoretical expectation that more extreme medians should be more likely to cast these votes; while the interaction term is positive, is it insignificant. Second, Table C.2 estimates linear fixed models, starting with an analogue to Model 1 of Table 2 and then also including issue fixed effects (instead of issue area fixed effects) and justice fixed effects. We see substantively similar results to what is in the main text. Table C.3 replaces the term fixed effects with term-level covariates; these covariates are not predictive, unlike when predicting difference-splitting opportunities, but the other variables change little. Table C.4 limits the sample to those cases where there was at least one justice split the difference and at least one justice did not, to take into account the possibility that some of the unanimous cases may reflect facts that were very hard to distinguish or legal claims that were logically hard to separate; most coefficients of interest are somewhat larger in this smaller sample, except we no longer see significant coefficients for High salience cases. Table C.5 includes a measure of case complexity;³⁵ while this measure is unavailable for all cases and thus is not included in the main models, the coefficient is positive, as one would expect, but not significant. Finally, Tables C.6 and C.7 exclude the salience measure in order to consider a broader time frame; Table C.6 has the same starting point as the main models (1955 Term) but stretches to the 2016 Term, the last term with complete personality measures; the results are similar to the main text. Table C.7 goes back further, to the 1946 Term (for models with Martin-Quinn and Segal-Cover scores) or the 1950 Term (Bailey scores); here, conscientiousness is no longer a significant predictor in the Bailey score model (although it remains positive), suggesting that there may be heterogeneity in the effect of personality on this voting over time, perhaps reflecting the different types of cases the justices were hearing prior to the Warren Court.

Finally, I consider how much my results are driven by my definition of a difference-splitting opportunity. First, I expand the definition to add in any circumstance where a justice casts both a liberal and conservative vote within the same case, as defined by the Database, even if the case did not have multiple docket numbers. That is, this includes cases whether there was a single petition granted but where the Database records multiple votes; while this does not This substantially increases the sample size for the models, but leads to little substantive changes in the results (see Table C.8), although Medium salience case is no longer statistically significant. Second, I consider how the results differ when allowing a difference-splitting vote to be cast across cases that are handed down on different days,³⁶ expanding to week (Table C.9), month (Table C.10), and term (Table C.11). The results when expanding to week are, unsurprisingly, very similar. When expanding to the month and term level, we no longer see any predictive power for Conscientiousness in most models, and High salience case is no longer significant in the term-level models. Medium salience case, Qualifications, and Ideological extremity remain significant predictors.³⁷

5. Discussion

This paper has developed a measurement strategy for difference-splitting votes, cataloged the frequency of those votes over time, and considered what leads justices to cast these votes. As the Court’s docket has shrunk and the Court has become more polarized, the Court has become less likely to bundle cases in a way that makes such difference-splitting voting. And while much of this voting behavior by individual justices may be a result of ideological moderation, other factors such as justice personality and case salience are also important. This paper has presented the first comprehensive theoretical and empirical account of this voting behavior in the context of the United States Supreme Court; future researchers can consider how this behavior manifests in other courts and whether its determinants vary depending on the institution under study.

What is the probable fate of difference-splitting votes in the future? On the one hand, the Court has fewer moderates and we have seen a secular decline in difference-splitting votes as a function of declining difference-splitting opportunities. The justices of today have generally been less inclined to split the difference than justices of the past, on account of this decline in difference-splitting opportunities. Nevertheless, to the extent that there are reputational benefits to casting difference-splitting votes, we likely will continue see some of these votes in the future in the salient cases from justices near the ideological center, as we saw in Biden v. Missouri and NFIB v. OSHA.

I have hypothesized that these decisions are driven by the desire to send signals to outside actors such as the public or lower courts. If that is the case, there are two further implications that deserve future study. First, judicial interest in crafting difference-splitting opportunities or casting difference-splitting votes likely exhibits substantial heterogeneity across cases. The reputational value of appearing middle-of-the-road is probably much higher on affirmative action than on an obscure tax issue. On the flip side, the obscure tax issue may be particularly important to resolve for the lower courts, if it has generated a lot of confusion. While controlling for the issue area in the case can help control for these phenomena, further exploration of these case- or issue-specific factors may shed light on this.

Second, how do these outside actors respond to the signals that the justices send when they craft these decisions? Is the Court actually successful in generating legal clarity or improving the Court’s reputation? If so, does this depend on the legal principles used in the case (e.g., Krewson & Owens, 2023; Rivero & Stone, 2025)? Measuring how these votes affect public evaluations of the Court’s legitimacy and attitudes toward the Court and the justices is an important topic for further research.

Finally, this paper considered what predicts difference-splitting voting given the presence of a difference-splitting opportunity. But, as we’ve seen, difference-splitting opportunities themselves have fallen precipitously, largely as a result of the Court’s declining overall caseload and growing ideological polarization. Future research can illuminate why the Court has given itself fewer opportunities to cast difference-splitting votes, despite their potential benefits to the Court’s reputation and institutional power.

Supplemental Material

Supplemental Material - Difference-Splitting Voting: Middle-Ground Votes at the U.S. Supreme Court

Supplemental Material for Difference-Splitting Voting: Middle-Ground Votes at the U.S. Supreme Court by Albert H. Rivero in Journal of Law & Empirical Analysis.

Footnotes

Acknowledgments

I thank JBrandon Duck-Mayr, Brett Parker, and attendees of the 2023 Annual Meeting of the Midwest Political Science Association and the University of Virginia American Politics Seminar for helpful comments

ORCID iD

Albert H. Rivero

Ethical Considerations

There are no human participants in this article and informed consent is not required.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The author will make publicly available all data and code necessary to replicate the analyses of the paper upon publication on Dataverse.*

Supplemental Material

Supplemental material for this article is available online.

Notes

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