Judges on collegial, multimember courts decide cases in small groups, and the case outcomes often vary from those we would anticipate if a judge was acting alone (see Cross and Tiller Reference Cross and Tiller1998; Kim Reference Kim2009). In these small-group settings, individual judges’ votes often differ based on the identity of the other judges hearing a particular case. This phenomenon has been dubbed “panel effects.” Scholars have noted their presence in terms of judges’ partisanship (e.g., Cross and Tiller Reference Cross and Tiller1998; Sunstein et al. Reference Sunstein, Schkade, Ellman and Sawicki2006; Beim and Kastellec Reference Beim and Kastellec2014), gender (e.g., Farhang and Wawro Reference Farhang and Wawro2004; Peresie Reference Peresie2005; Boyd, Epstein, and Martin Reference Boyd, Epstein and Martin2010), and race (e.g., Cox and Miles Reference Cox and Miles2008; Kastellec Reference Kastellec2013).
Panel effects are substantively important. For example, Sunstein, Schkade, and Ellman (Reference Sunstein, Schkade and Ellman2004) note that Republican judges vote to uphold an affirmative action program only 37% of the time when sitting on a unified panel, but they vote to uphold such a program 49% of the time when they hold a panel majority but there is also one Democratic appointee sitting on the panel with them. Thus, so-called counterjudges—the Democratic judge in this example—can be successful in spite of being outnumbered.
When are counterjudges outnumbered but not outvoted? Existing explanations for panel effects can generally be organized into three categories. First, explanations focused on acquiescence suggest that panel effects occur because judges defer to other panel members (and, by extension, suppress their dissenting views) in order to lower their workload and avoid raising the ire of other panel members (e.g., Fischman Reference Fischman2015). Second, deliberative explanations suggest that panel members do not suppress their disagreement; rather, their dialogue leads to genuine consensus (e.g., Edwards Reference Edwards2003). Finally, strategic explanations suggest that panel effects result from judges’ attention to external actors. Judges vote strategically to dodge review by a higher court (e.g., Cross and Tiller Reference Cross and Tiller1998).Footnote 1
These explanations have generally been developed and tested individually (but see Kim Reference Kim2009; Fischman Reference Fischman2015). This is due, in large part, to numerous data and methodological limitations that make it difficult to disentangle these competing explanations. As a result, while there can be little doubt that panel effects exist, our understanding of why counterjudges win remains murky.Footnote 2 The complexity of the problem indicates that further research should be done considering the various theorized mechanisms together, as well as considering the problem from different angles, such as focusing on the elements related to counterjudge success.
To this end, we derive indicators of each theory of panel effects and present a test of competing explanations. By capturing the varying position of the counterjudge vis-à-vis her fellow panel members, we can parse the factors that are associated with counterjudge success. To do so, we rely on a data set of published search and seizure opinions decided in the US courts of appeals from 1953 to 2010 and focus on the dynamics between panel majorities and counterjudges on split panels. Search and seizure cases provide the opportunity to consider panel effects in the types of cases that court of appeals judges spend a fair amount of their time deciding (see Klein Reference Klein2002, 68). Our results provide some evidence for all three explanations playing some role in counterjudge success, but the evidence most consistently supports the importance of strategy.
The results have important implications for our understanding of both appellate decision making and group decision making more broadly, as well as helping set the stage for further research. First, while most studies try to document whether panel effects exist (e.g., Sunstein et al. Reference Sunstein, Schkade, Ellman and Sawicki2006; Boyd et al. Reference Boyd, Epstein and Martin2010), we examine the circumstances under which outcomes favor the partisan minority. Our results demonstrate the importance of the judicial hierarchy, especially the ideological configuration at its three levels, in shaping counterjudge success. Second, these findings reveal that rules regarding panel assignment and life tenure affect both the decisions that court of appeals panels make and the likelihood of decisions that vary from the ideological preferences of panel majorities. As legislative bodies begin to devote more scrutiny to the procedures and operation of appellate courts, our findings have scholarly as well as practical implications. Third, policies of all types are formulated by small groups. By illuminating the factors that lead policy-making bodies to make unexpected decisions, our results have implications for understanding group decision making beyond courthouse walls. Finally, this work highlights the importance of continuing to investigate the mechanisms behind panel effects, which appear to be complex, nuanced, and multifaceted. Additional work probing the extent to which the three dominant theories of group decision making account for the outcomes we observe should be done to leverage various aspects of such decisions while accounting for issue-specific considerations.
The Nature and Size of Panel Effects
Three-judge panels establish the vast majority of law in the US courts of appeals. Judges’ panel assignments rotate regularly, changing the three-judge groupings that decide cases (Levy Reference Levy2017). Sometimes a judge will sit with two like-minded colleagues, while other cases are resolved by panel members who have heterogeneous ideological preferences. Panels are assigned administratively, and judges do not get to choose the members of their panel, reducing concerns about endogeneity between panel assignment practices and observed outcomes. Together, the use of panels to resolve cases and the administrative assignment of judges to panels create variation in the groups of judges that resolve cases. And this variation matters. Scholars have frequently documented panel effects in judicial decision making. Panels resolve cases by majority rule, yet empirical results consistently reveal patterns at odds with what the median voter theorem would predict (Kastellec Reference Kastellec2007). A single judge can affect both case outcomes and opinion content (Hinkle Reference Hinkle2017).
These effects are substantively important in size. Sunstein et al. (Reference Sunstein, Schkade, Ellman and Sawicki2006), for example, examine the presence of panel effects based on judicial partisanship in 23 issue areas.Footnote 3 Across all issue areas, panels with a Republican counterjudge resolved 10% fewer cases in a liberal direction than panels comprising three Democrats. The effects for a Democratic counterjudge were smaller, with 5% more cases resolved in a liberal direction when a single Democrat was on a three-judge panel compared to an all-Republican panel. Epstein, Landes, and Posner (Reference Epstein, Landes and Posner2013) update these data to 2008. They report that the presence of a Democratic counterjudge decreases the probability of a conservative vote by 0.06; the presence of a Republican counterjudge increases that probability by 0.08. That the presence of a counterjudge can affect the outcome of between 1 in 10 and 1 in 20 cases suggests that panel effects play an important role in the development of American jurisprudence.
Both Sunstein et al. (Reference Sunstein, Schkade, Ellman and Sawicki2006) and Epstein et al. (Reference Epstein, Landes and Posner2013) note that the presence and magnitude of panel effects vary by issue area. While some of the issues in Sunstein et al.’s study, such as affirmative action, sex and race discrimination, and First Amendment cases, have marked panel effects, other issues, like abortion, takings, and federalism cases, yield no statistically significant panel effects. This is not an isolated finding; many studies report results that vary widely by issue (e.g., Boyd et al. Reference Boyd, Epstein and Martin2010).
Panel effects emerge along characteristics other than partisanship in certain types of cases, as well. First, in a recent and rigorous article, Boyd et al. (Reference Boyd, Epstein and Martin2010) examine the presence of panel effects by gender. They find the probability that a male judge votes for a sex discrimination plaintiff increases between 12% and 14% when there is a female judge on the panel. However, they find no analogous effects in the other 12 issue areas they analyze. They attribute this unique effect to an informational advantage available to panels with a female judge; when deciding cases in areas like sex discrimination, a female judge on a panel provides additional information to its other members that can sway their votes. Second, in another leading article, Kastellec (Reference Kastellec2013) examines the effect of a counterjudge on the propensity of nonblack colleagues to uphold affirmative action programs from 1971 to 2008. He finds that the probability that a nonblack judge will vote to uphold an affirmative action program increases from about 50% when sitting with two nonblack colleagues to about 80% when there is a black judge on the panel. Thus, the effects of a female or black counterjudge seem to be greater than those involving judicial partisanship. However, these effects are seemingly present only in the sliver of the caseload directly implicating the counterjudge’s identity.
Explanations for Panel Effects
Scholars have offered three major explanations for the presence of panel effects. First, panel effects might result from acquiescence: judges feel pressured to produce unanimous decisions, perhaps owing to a norm of consensus (e.g., Goldman Reference Goldman1968; Posner Reference Posner2008; Epstein, Landes, and Posner Reference Epstein, Landes and Posner2011; Fischman Reference Fischman2011). As a result, even a judge who disagrees with the majority outcome in a case may suppress her dissent to preserve the air of unanimity. Under this explanation, a norm of consensus leads to dissent aversion. The benefits of avoiding a dissent are magnified by the costs associated with dissenting, including the time and effort required for opinion writing and the harm to collegiality (see Howard Reference Howard1981; Cross and Tiller Reference Cross and Tiller1998; Caminker Reference Caminker1999; Cameron, Segal, and Songer Reference Cameron, Segal and Songer2000; Kastellec Reference Kastellec2007; Posner Reference Posner2008; Carrubba and Clark Reference Carrubba and Clark2012; Epstein et al. Reference Epstein, Landes and Posner2013) and the court’s legitimacy (see Atkins and Green Reference Atkins and Green1976; Ginsburg Reference Ginsburg1990; Farhang and Wawro Reference Farhang and Wawro2004; Hettinger, Lindquist, and Martinek Reference Hettinger, Lindquist and Martinek2006; Kim Reference Kim2009). Relatedly, Sunstein et al. (Reference Sunstein, Schkade, Ellman and Sawicki2006, 15, citing Asch 1984) note psychological research indicating that conformity pressures can arise because an individual determines that “it is not worthwhile to dissent in public.” Regardless of the source, scholars asserting an acquiescent mechanism for panel effects focus on internal pressures within the panel.
While acquiescent explanations generally focus on the pressures faced by a potential dissenter, a norm of consensus could also affect the behavior of panel majorities (see Epstein et al. Reference Epstein, Landes and Posner2013, 192–93; cf. Kim Reference Kim2009). First, dissents increase the costs for majorities because they must expend time and effort to respond to counterarguments (see Corley and Ward Reference Corley and Ward2012) and change the issues discussed (Rice Reference Rice2017; see also De Mesquita and Stephenson Reference Mesquita, Bueno and Stephenson2002; Lax Reference Lax2007; Posner Reference Posner2008; Epstein et al. Reference Epstein, Landes and Posner2013). As a result, majorities may, under some circumstances, be willing to make some significant accommodations regarding an opinion to avoid a dissent.Footnote 4 Second, when the members of the panel majority have less intense preferences about the outcome of a case, pressures to avoid dissent may result in panel effects (Epstein et al. Reference Epstein, Landes and Posner2011). Finally, a norm of consensus aimed at maintaining legitimacy should influence majorities as well as minorities; all judges have an incentive to keep their institution in the public’s esteem (Rasmusen Reference Rasmusen1994).
Second, scholars argue that deliberation among judges can alter outcomes (Edwards Reference Edwards1998, Reference Edwards2003; Caminker Reference Caminker1999; Wald Reference Wald1999; Kim Reference Kim2009; Spitzer and Talley Reference Spitzer and Talley2013). Generally, these deliberative accounts focus on the role of the exchange of information and posit that panel effects result from the good-faith dialogue fostered by the variety in perspectives on a diverse panel.Footnote 5 Boyd et al. (Reference Boyd, Epstein and Martin2010), for example, suggest that gender-based panel effects occur in sex discrimination cases because female judges provide valuable information to their male colleagues that changes their views and is absent on all-male panels. In another vein, Spitzer and Talley (Reference Spitzer and Talley2013) offer a model of panel effects that focuses on the unique pressure felt by a judge in the minority to collect and disseminate information that supports her position. In short, deliberative approaches theorize that panel effects result from judges changing their minds in the presence of new information and perspectives (Edwards Reference Edwards1998).
Finally, scholars have offered a third strategic explanation: panel effects result from majorities capitulating to counterjudges to avoid external review by the circuit sitting en banc or the Supreme Court (Cross and Tiller Reference Cross and Tiller1998; Kastellec Reference Kastellec2011; Beim, Hirsch, and Kastellec Reference Beim, Hirsch and Kastellec2014, Reference Beim, Hirsch and Kastellec2016). When dissent makes review more likely, panel majorities are more likely to take steps to prevent a dissent from being written, perhaps leading the panel majority to capitulate to the counterjudge (Hazelton, Hinkle, and Jeon Reference Hazelton, Hinkle and Seon Jeon2016). The most prominent strategic theory—whistleblower theory—suggests that majorities may decide cases in ways that are at odds with their ideological preferences when the panel includes a counterjudge who is ideologically aligned with a reviewing court and could use a dissent to signal noncompliance to that court (Cross and Tiller Reference Cross and Tiller1998; Kim Reference Kim2009; Kastellec Reference Kastellec2011; Beim et al. Reference Beim, Hirsch and Kastellec2014, Reference Beim, Hirsch and Kastellec2016).
There have been a few previous studies that considered competing theories of panel effects (Atkins Reference Atkins1973; Kim Reference Kim2009; Fischman Reference Fischman2015), although none of these studies offered measures of acquiescent, deliberative, and strategic influences together. Many questions remain regarding the role each type of effect plays in shaping outcomes (see Kim Reference Kim2009; Fischman Reference Fischman2015). Our goal is to examine the effect that indicators of each theory have on the probability that a counterjudge is successful.
Measuring the Mechanisms
Acquiescence
Acquiescence theories implicate future interactions among judges: if you upset your colleague by violating a norm of consensus, it is likely to make further exchanges with that colleague, whether they be social or professional, more difficult. The more the panel majority anticipates having to work with a counterjudge in the future, the more utility they receive from complying with the norm of consensus. This idea relates favorably to the influence of anticipated future interactions in game theory (see, e.g., Heide and Miner Reference Heide and Miner1992).
Total future interactions are a function of (a) how long the counterjudge remains on the bench and (b) how often two judges interact. As a judge considers whether to bow to the wishes of a counterjudge, he does not definitively know how long that judge will remain his colleague and on how many future panels they will serve together. But the two judges do know each other’s age, which is strongly predictive of when a circuit judge will leave the bench.Footnote 6 As counterjudges get older, their success rate may diminish as their colleagues begin to increasingly anticipate their departure from the bench.Footnote 7 Additionally, a counterjudge who has already taken on senior status may pose less of a concern since senior judges are generally excluded from en banc cases and may take on reduced caseloads.
The second factor—how often judges interact—is, in part, a function of geographic location and circuit size in combination with the three-judge panel structure. Judges are likely to anticipate more exchanges with a judge when they serve in a small circuit because they are more likely to sit with each other on panels. All circuits resolve cases in three-judge panels, but judges in smaller circuits have a higher probability of sitting with a particular colleague on any given panel. The probability of sitting with another judge on a panel is not a linear relationship with panel size but can be estimated using combinatorics.Footnote 8 For example, a judge in a 6-person circuit will sit with each other colleague in an estimated 40% of cases. That number drops to 22% in a 10-person circuit and 15% in a circuit with 14 judges.
Geographic location also affects the frequency of interaction between two judges. Unlike judges on the US Supreme Court or most state high courts, judges in most of the US courts of appeals are geographically dispersed during the majority of their work, only coming together at various times throughout the year to hear oral argument. Figure 1 shows the geographic dispersion of the home chambers of such judges at one particular point in time, 2010 (the most recent year in our data), as well as the variation in the number of judges in each city.Footnote 9 When the judges in the panel majority have their primary chambers in the same city (which typically also means the same building) as the counterjudge, they may naturally anticipate a greater number of future interactions. Conversely, judges may expect very little in the way of future dealings with a counterjudge sitting by designation from either another circuit or a district court.
Location of US courts of appeals chambers in 2010.

Deliberation
Deliberative theories emphasize the interactions generated by judges’ relationships with one another and the unique information each judge brings to the table. Deliberative panel effects are therefore based on judges’ present interactions, past interactions, and expertise. First, just as with future interaction, the total amount of past interaction is a function of the number of years over which two judges interact and the frequency of interaction during that time. The longer two judges have served together, the more likely they are to have met each other, served on administrative committees together, and decided cases on panels together. Judges with higher levels of past contact are more likely to know each other’s perspectives and preferences, enhancing their ability to make persuasive arguments in the course of deliberations (see Edwards Reference Edwards2003; Baum Reference Baum2006; Hazelton, Hinkle, and Nelson Reference Hazelton, Hinkle and Nelson2017). Fortunately, unlike the years of anticipated future interaction, counting the number of years judges have served together on the circuit in the past is straightforward.Footnote 10
Frequency of past interaction also affects the ability of judges to deliberate effectively. Judges from smaller circuits have served on a greater proportion of past panels with each of their colleagues, giving them increased opportunities to learn what types of arguments are likely to persuade their circuit colleagues. Likewise, the presence of two judges in the same city affects deliberative power. Judges who see each other often—even in social settings—build relationships and learn about their colleagues’ likes and dislikes in ways that can be helpful when they deliberate (see, e.g., Lee et al. Reference Lee, Leung, Lo, Xiong and Wu2011). Moreover, close physical proximity creates opportunities to discuss a case in person, enhancing a case’s deliberative environment.Footnote 11 Cohen (Reference Cohen2002, 157) quotes a Ninth Circuit judge: “I think that if you are in proximity to the other judges, I think it does encourage a bit more of an interaction… . I think, frankly, on working through a point, it is very helpful to sit down with one other judge if there is a sticking point on a case—particularly if the difference is between two judges—to go into the other judge’s chambers, sit down, and try to work through it.” While there are certainly limits on face-to-face deliberation,Footnote 12 Cohen’s interviewee ties close physical proximity directly to an enhanced deliberative environment.
Counterjudges’ status and information may also influence their deliberative success. Judges sitting by designation may not be as effective at persuading their panel colleagues as a result of either not knowing them as well or not being held in as high esteem. In particular, district judges sitting by designation may be at a particular disadvantage in terms of persuasive ability compared to circuit judges from another circuit because district judges do not have regular experience judging in a collegial environment.
The literature on race- and gender-based panel effects often points to the unique perspective, information, and experiences a lone woman or minority member can bring to a panel deciding a matter in which such characteristics are salient (see, e.g., Boyd et al. Reference Boyd, Epstein and Martin2010; Kastellec Reference Kastellec2013). A similar account applies in terms of an ideologically defined counterjudge. If panel effects are driven by the counterjudge’s role in deliberation, then judges who have unique information or experience to bring to the table should have a larger influence. A counterjudge with relevant professional experience may have information and a perspective that gives her a more persuasive voice. Within the legal profession, law school prestige is very influential (see Redding Reference Redding2003). This influence can be seen in the selection of judges (see Slotnick, Goldman, and Schiavoni Reference Slotnick, Goldman and Schiavoni2015). Such prestige is likely associated with graduate quality but may also reflect bias and networks. Klein and Morrisroe (Reference Klein and Morrisroe1999) identify 25 of the most prestigious and influential circuit judges from 1989 to 1991. More than two-thirds of the judges on that list attended elite law schools, a credential possessed by less than half of circuit judges across the board. Thus, there is reason to believe that a counterjudge with an elite law school pedigree may exert greater influence.
Overall, experience on the bench should also play a role in deliberative effectiveness. There is evidence that new judges behave differently from more experienced judges and may defer to those judges with more experience (e.g., Hettinger, Lindquist, and Martinek Reference Hettinger, Lindquist and Martinek2003). Thus, relative experience may influence outcomes. When counterjudges have served on the circuit longer than any other panel member, that experience should lend them greater influence over deliberations.Footnote 13 Conversely, when counterjudges are the least experienced members of the panel, they should have the least influence over deliberations.
Disentangling deliberative panel effects from those caused by acquiescence is difficult. Our strategy for this task hinges on distinguishing between anticipated future interactions on the one hand and past and current interactions and expertise on the other. This is admittedly complicated by the reality that some of the indicators we examine simultaneously reflect both theories. For example, judges from the same city have interacted more in the past, can discuss a given case more readily, and anticipate interacting more in the future. Similarly, judges with a higher probability of future panel service generally anticipate more future interactions, but they are also likely to have more past interactions. Finally, consider those counterjudges sitting by designation. These judges may have less influence over deliberations because other judges are less willing to listen to a judge from another court, or the panel majority may be less worried about the norm of consensus when dealing with a judge they do not anticipate working with in the future.
Strategy
According to strategic explanations, majorities capitulate to counterjudges because they anticipate review by higher courts. The desire to avoid review (and potential reversal) leads members of panel majorities to succumb to the counterjudge’s preferences in those situations in which acting ideologically is most likely to trigger review (Kim Reference Kim2009; Kastellec Reference Kastellec2011). Further review is more likely when a panel majority is ideologically distant from the reviewing court (e.g., Black and Owens Reference Black and Owens2009; Beim et al. Reference Beim, Hirsch and Kastellec2016). Under these conditions, the presence of a dissenting opinion increases the probability of review even more (George Reference George1999; Black and Owens Reference Black and Owens2009; Beim et al. Reference Beim, Hirsch and Kastellec2016). As a result, a strategic panel majority will be more likely to defer to the counterjudge as the panel majority becomes more distant from either potential reviewing court (the full circuit en banc or the Supreme Court).
We extend previous tests of the strategic explanation for panel effects by taking the full judicial hierarchy into account. While strategic explanations suggest that panel majorities try to reduce the probability of review, a dissenting opinion is not the only factor that affects that likelihood. In their seminal work on agenda setting in the Supreme Court, Tanenhaus et al. (Reference Tanenhaus, Schick, Muraskin, Rosen and Schubert1963) argue that any type of dissensus in the lower courts, including a reversal of the trial court, increases the probability of review. More recent work has parsed the effects of lower court reversal and dissent, showing that both factors predict both justices’ votes on certiorari petitions (Black and Owens Reference Black and Owens2009; Black and Boyd Reference Black and Boyd2010, Reference Black and Boyd2013) and the cases placed on the discuss list (Caldeira and Wright Reference Caldeira and Wright1990). Likewise, George (Reference George1999) shows that both reversal and dissent also significantly increase the probability of the full circuit granting en banc review. This puts counterjudges who are ideologically aligned with the lower court ruling in a particularly strong position. If they do not obtain their desired result, not only may they trigger a higher probability of review by writing a dissent, but the fact that the majority reversed the lower court would increase the probability of review even more.
However, an important caveat is required when exploring the advantage a counterjudge gets from being aligned with the lower court ruling. Circuit courts generally tend to affirm cases for a variety of procedural and institutional reasons (e.g., Kim Reference Kim2009). Even when the lower court ruling is liberal, a conservative circuit panel is more likely than not to affirm that ruling regardless of the presence of a counterjudge. Therefore, we must carefully distinguish between the background tendency to affirm and strategic ceding to a counterjudge who is aligned with the lower court by the majority members of a split panel. To do so, we focus on the interaction between the distance to the potential reviewing courts and the counterjudge’s alignment with the lower court. If panel majorities respond more dramatically to the position of the potential reviewing court when counterjudges are aligned with the lower court ruling compared to when they are not aligned, that difference between effect sizes reflects the strategic impact of the lower court ruling. Table 1 summarizes each of our indicators, the theory (or theories) with which they are associated, and our directional expectations for their relationship between the indicator and the counterjudge’s success.
Summary of Hypotheses

Note.—Hypothesized impact of each indicator on the probability that the case outcome will reflect the counterjudge’s (CJ) ideology. SCOTUS = Supreme Court of the United States.
Data and Research Design
The US courts of appeals resolve a prodigious number of cases each year. We utilize a database of all published Fourth Amendment search and seizure opinions from 1953 to 2010.Footnote 14 This topic incorporates a discrete set of legal issues that are routinely raised in litigation within the context of both civil and criminal cases. Of course, the decision to examine a single issue area across several decades raises important research design considerations. A single-issue study has many benefits: it reduces case heterogeneity, limits the number of cases to a reasonable amount of data collection, and increases variation in factors that change over time. Because of variation in legal methodologies and circumstances, analyzing judicial decision making within issue areas can be particularly important in understanding the forces at play (see Friedman and Martin Reference Friedman, Martin and Gardner Geyh2011). At the same time, any single-issue study necessarily raises concerns about generalizability.
We selected search and seizure cases for a number of reasons. First, these cases are considered bread-and-butter cases for court of appeals judges (see Klein Reference Klein2002, 68); the familiarity of circuit judges with these types of cases helps reduce potential confounding factors related to specialized areas of law or unfamiliar types of cases.Footnote 15 At the same time, this ubiquity reduces the amount of specialized expertise any counterjudge can bring to the table. Second, search and seizure cases present a rigorous test case for probing panel effects. Existing studies have suggested that partisan panel effects are not particularly prominent in criminal law (see Sunstein et al. Reference Sunstein, Schkade, Ellman and Sawicki2006; Fischman Reference Fischman2015).Footnote 16 Third, search and seizure cases represent a sizable portion of federal courts of appeals’ dockets (Klein Reference Klein2002, 68), providing more statistical power than many other issue areas. Fourth, insights regarding search and seizure cases have been found to generalize well in many circumstances to other issue areas (see Segal Reference Segal1984; Wahlbeck Reference Wahlbeck1997; Segal and Spaeth Reference Segal and Spaeth2002; Bartels Reference Bartels2009). Finally, Friedman and Martin (Reference Friedman, Martin and Gardner Geyh2011) theorize that precedent is more likely to be stable in criminal matters than in some other areas of law, owing to the need for notice to criminal defendants. Thus, search and seizure provides an issue area that tends to represent everyday decisions by court of appeals judges in numbers that are more likely to allow us to test various mechanisms that may explain general panel effect phenomena. We look forward to future studies probing the generalizability or differential application of these mechanisms across issue areas, and we discuss in the conclusion some ways in which counterjudge success might vary by issue area.
We identify relevant cases by using Lexis to locate all published circuit opinions that cite the Fourth Amendment of the US Constitution.Footnote 17 We exclude all opinions that do not address the merits or were resolved by only two judges. In 16% of the cases, the circuit reversed in part and affirmed in part, producing a split outcome. Since these cases cannot be definitively coded as reaching a conservative or liberal outcome, we exclude them from our analysis.Footnote 18 The resulting data set contains 12,649 opinions in panel cases.
In the larger data set of search and seizure cases, the panel effects often observed in other work emerge here as well. Simple summary statistics illustrate this point (although the same patterns emerge in more sophisticated regression models as well). Unified panels issue a ruling contrary to their ideology in only 32% of cases, but split panels do so in 43% of cases. Examining all types of panels, panel majorities ruled against their own preference in 11% more cases when there was a counterjudge compared to when the panel was unified.Footnote 19 Within our data set, we estimate that 979 cases would have been decided differently if split panels issued counterideological rulings at the same rate as unified panels.
While it is reassuring to find evidence of panel effects in our larger data set in keeping with overall trends found in the existing literature, our focus is on exploring the source of this well-established pattern. To do so, we turn our attention exclusively to the cases in which those panel effects emerge: split panel cases. This allows us to consider specific mechanisms that drive panel majorities to bend to the preferences of counterjudges. Just under 30% of the cases in this data set were resolved by unified panels. We exclude those data to examine the role of the counterjudge in split panel cases. The unit of analysis is the case. Our outcome variable is whether the case is resolved consistently with the ideology of the counterjudge.Footnote 20 The outcome variable equals 1 if a Democratic panel with a Republican counterjudge reaches a conservative outcome or if a Republican panel with a Democratic counterjudge reaches a liberal outcome and 0 otherwise. Since this is a binary variable and we are focused on characteristics of the judges, we use a probit model (see Fischman Reference Fischman2015).
Using information from the text of opinions in our data set as well as information on judges from the Federal Judicial Center Biographical Database, we generate each of the variables discussed in the previous section. Table 2 lists all of these variables and describes the particulars of how each is calculated as well as its minimum and maximum values.Footnote 21
Variable Descriptions

Note.—CJ = counterjudge; SCOTUS = Supreme Court of the United States.
Although this analysis examines only cases that raise search and seizure issues, there is still important variation across cases that might be associated with acquiescence, deliberation, or strategy and must therefore be included in the model to combat omitted-variable bias. We control for the filing of amicus briefs in the case as an indicator of particularly important cases. We also include whether a particular case is a civil case (rather than a criminal case or a habeas petition). In addition, cases with more clear-cut legal issues may lead to panel majorities ruling against their own ideological preferences simply because the law requires it. In order to account for this, we control for whether an opinion is issued per curiam since such opinions are typically used in more straightforward cases. Owing to the lengthy time frame of our data, we also include a control for key variation in Supreme Court jurisprudence over time. We include an indicator variable to distinguish cases that occurred after the key shift in the Supreme Court’s search and seizure jurisprudence documented by Kritzer and Richards (Reference Kritzer and Richards2005). This change in jurisprudence was the result of six key cases that were decided between 1983 and 1984. Thus, we also include a variable for whether the case was decided after 1984.Footnote 22 Finally, we include circuit fixed effects in our model.Footnote 23
Results
Individual Predictors of Counterjudge Success
Table 3 presents the results of our model.Footnote 24 Because we are testing multiple hypotheses using several explanatory variables each, we report Bonferroni-adjusted p-values.Footnote 25 When looking at the many predictors individually, only three—one for each theory—emerge as statistically significant.Footnote 26 Age is the only indicator of acquiescence that is statistically significant. Moving age from its 25% value to its 75% value is associated with a 2.8% decrease in the probability of counterjudge success. Furthermore, the significance of Cotenure suggests the operation of deliberation. Counterjudges with greater past experience with the majority judges tend to be more successful. A change in Cotenure from the 25% value to its 75% value corresponds to a 2.4% increase in the probability a counterjudge will be successful. Finally, the significance of the ideological distance between the panel majority and the Supreme Court indicates that strategy plays a role as well. A change in Ideological Distance: Panel to SCOTUS from the 25% value to its 75% value corresponds to a 3.7% increase in the probability a counterjudge will be successful.
Probit Regression Estimates

Note.—Probit regression estimates of the effect of counterjudge (CJ), circuit, and case characteristics on whether a panel resolves the case in a manner consistent with the CJ’s ideologically preferred outcome. SCOTUS = Supreme Court of the United States. The model includes circuit fixed effects that are not shown. N = 8,902; proportional reduction in error = 39.82%; Akaike information criterion = 9,955.13; Bayesian information criterion = 10,182.14.
a Included with the strategic variables because it is a constituent term in the interaction.
* Bonferroni-adjusted p-value less than .05.
Although only three indicators are statistically significant, they jointly have a sizable effect on the probability that a counterjudge is successful. Together, an interquartile shift in these variables increases a counterjudge’s chance of success by nearly 9%. That these three variables alone would affect the outcomes of nearly 1 in 10 cases decided by a split panel is a substantively important effect.Footnote 27
Furthermore, the marginal effects of the interaction terms reveal more evidence of strategic behavior. Figure 2 shows the marginal effect of ideological distance to the reviewing court both when the counterjudge is aligned with the lower court ruling and when she is not aligned with the lower court. The difference between the marginal effects under these two situations provides evidence of the panel majority strategically accounting for the counterjudge’s alignment with the ruling below. Therefore, the figure also provides both the differences between the relevant marginal effects and the p-values of those differences. Both differences are in the expected direction and statistically significant. For both measures of ideological distance to a potential reviewing court, the marginal effect of that distance is significantly larger when the counterjudge is aligned with the lower court ruling. And the size of these effects is notable. The marginal effect of ideological distance is 0.14 higher for the distance to the full circuit and 0.16 higher for the distance to the Supreme Court when the panel majority knows that defying the counterjudge would require reversing the lower court opinion and, thus, opening itself up to an even higher probability of review.Footnote 28
Marginal effect of ideological distance (and corresponding 95% confidence interval) between the panel and a reviewing court on the case outcome reflecting the counterjudge’s ideology, by alignment with the lower court ruling. Also provided are the differences in marginal effects for each ideology measure by alignment and the p-values of those differences.

Joint Predictors of Counterjudge Success: Evaluating the Mechanisms
Having examined the individual effects of our indicators, we now assess the joint effect of each bundle of indicators to examine the substantive effects of each of the three theories. Because some of our variables could be theoretically consistent with either the acquiescence or deliberation mechanisms, we assess the groups of variables that are associated with each of the three theories uniquely. Assessing the effect of strategy is complicated by the reality that CJ Aligned with Ruling Below has an impact both as a result of strategy and as a result of other factors (such as deferential standards of review). To address this, we evaluate the effects of strategy both including and excluding alignment with the lower court ruling within the group of variables being assessed. This approach provides the upper and lower bounds for the effect size of strategy.
For each set of variables, we conduct an F-test for their joint significance. We further assess the substantive significance of each group of variables by calculating the predicted probability of counterjudge success when setting each variable in the group to their 25th/75th percentile values or 0/1 as applicable to calculate estimates for “weak” and “strong” counterjudges. For example, for a “weak” counterjudge Senior Status equals 1 and Age is set at its 75% value. Finally, we calculate the proportional reduction in error achieved by a model containing only the relevant set of variables. Table 4 provides these results as well as p-values that indicate whether the difference between the predicted probabilities for a weak and strong counterjudge is statistically significant.
Overall Evaluation of Theories

Note.—The p-value from F-test of joint significance for various subsets of variables as well as predicted probability of counterjudge (CJ) success when the applicable group of variables are set to values for a weak, and then strong, CJ in turn as well as the difference between those predicted probabilities and the p-value of that difference. Proportional reduction in error (PRE) is calculated using a model consisting only of those variables associated with the theory. See table 1 for the list of variables associated with each theory.
The F-tests for joint significance reveal that each subset of variables provides some explanation for counterjudge success. For those groups of variables we can reject the null hypotheses that all of the relevant variables have no effect on counterjudge success. A look at the substantive effect size of each group of variables suggests the need for a bit of caution in interpreting these results. For acquiescence and deliberation, changing all the variables from the value for a weak counterjudge to those for a strong counterjudge changes the overall predicted probability by 0.02 and 0.05 respectively.Footnote 29 However, for neither group is the predicted probability for a weak counterjudge statistically significantly different from the predicted probability for a strong counterjudge, nor does either set of variables measurably improve the model’s ability to reduce error.
Finally, there is strong evidence that the strategic theory explains counterjudge success. The bottom two rows of table 4 suggest that the variables associated with the strategic theory are associated with a measurable reduction in error over a baseline model. Moreover, the combined effect of the ideological distance to both reviewing courts is statistically and substantively significant both on its own and when alignment with the lower court ruling is included in the group of variables being assessed. In the former analysis, when alignment is held at its median value of 0 for the analysis, a strong counterjudge has a predicted probability of success that is 0.05 higher than a weak counterjudge in a similar position. The estimated effect size is much more dramatic when alignment with the lower court ruling is shifted as well. When a strong counterjudge is also aligned with the lower court, the probability of counterjudge success increases by a whopping 51% over the probability of success for a weak counterjudge. Although we cannot claim that this effect is due entirely to strategy, when it is taken together with the interaction effects illustrated in figure 2, we can conclude that the effect size of strategy is greater than the lower bound of 0.05 and could range as high as 0.51. Thus, it is clear that strategy plays a vital role in the operation of panel effects.
Discussion and Conclusion
The results provide a complex picture of appellate decision making. Befitting the complicated nature of judicial choice (Baum Reference Baum1997; Edwards Reference Edwards2003), there is some evidence that panel effects in these bread-and-butter cases result from the interplay of interpersonal and interinstitutional considerations. Indeed, when considering the significance of individual variables, our empirical analysis provides some evidence that the desires to defer, deliberate, and dodge review all affect the likelihood of counterjudge success in the US courts of appeals. Taken together, their effects are considerable. When a counterjudge is not aligned with the lower court and is in a weak position in terms of all three theories, the counterjudge will be successful in an estimated 11% of cases, while such a counterjudge in a strong position in terms of all three theories is successful 25% of the time. For a counterjudge who is aligned with the lower court ruling, this difference ranges from 46% for a weak counterjudge to 72% for a strong counterjudge.
However, further analysis reveals that the lion’s share of the explanatory power in these models results from hierarchical considerations outside of the counterjudge’s direct control, namely, the interplay between counterjudge alignment with the lower court and the distance of panels to potential reviewing bodies. Our conclusions underscore the important role that appellate courts play in legal developments in the United States. That the ideological location of the panel relative to the rest of the judicial hierarchy is one of the most consistent and largest predictors of counterjudge success suggests that many of the panel effects that we observe—at least on the basis of partisanship—might stem more from factors outside of the counterjudge’s control than any actions that the counterjudge takes while the panel is resolving the dispute. These results therefore stand in stark contrast to discussions of panel effects based on the panel’s demographic characteristics, which have provided strong suggestive evidence that some types of panel effects emerge owing to informational benefits that the counterjudge brings to the table (Boyd et al. Reference Boyd, Epstein and Martin2010).
This is not to dismiss deliberative and acquiescent accounts of panel effects; our results present some, admittedly modest, evidence that these considerations play a role. We acknowledge that the evidence on this front is more limited; the substantive effects of our bundle of indicators for each of these theories are more limited than those of the indicators for strategic theory; moreover, neither grouping substantially increases the model’s predictive power. Still, the individual results for age and cotenure suggest that peer effects have some role to play in the resolution of cases on the US courts of appeals. These results provide further evidence for Baum’s (Reference Baum1997) contention that judges have multiple, overlapping goals. Obtaining and promoting “good” legal policy is one of those goals, but maintaining good collegial relationships with their peers is another important goal held by US courts of appeals judges that also explains panel effects.
Our analysis provides more questions for future research than definitive conclusions. An important question for future scholarship concerns the varying explanatory power of these three theories; scholars should continue to move beyond the well-trodden question of whether panel effects exist toward asking why these effects occur and, having developed competing explanations for the occurrence of panel effects, when those theories are applicable. Future lines of inquiry could address the role of the opinion author and the composition of the panel as a whole in the complex process of how and when panel effects emerge.
Additionally, future research needs to examine how the mechanisms behind panel effects vary by issue area and partisanship. Previous work on panel effects has found that different types of factors influence panel decisions based on the legal context; specifically, prior studies regarding the influence of characteristics such as race, gender, and party indicate that the effects are not consistent across issue areas and that some features are particularly salient in certain types of cases (e.g., Sunstein et al. Reference Sunstein, Schkade, Ellman and Sawicki2006; Cox and Miles Reference Cox and Miles2008; Boyd et al. Reference Boyd, Epstein and Martin2010). Additionally, areas of law differ in the extent to which they are litigated and demand technical knowledge or skill to decide. Search and seizure cases require little technical skill and are frequently litigated (see Klein Reference Klein2002, 68). As a result, judges are unlikely to have unique expertise on the issue of search and seizure that enhances their deliberative position. One fruitful area for cross-issue comparison would be to examine whether deliberative explanations rise to the forefront in issues such as taxation or regulatory cases, in which technical expertise is particularly desirable.
Likewise, we were able to study a very common type of case at the court of appeals, but the mixture of effects may vary with less typical examples. For example, it seems likely that deliberative and acquiescent theories are most powerful in close cases, in which ideological disagreements are less profound. When two judges have profound disagreements about a case outcome, face-to-face deliberation is probably not enough, on average, to sway a judge’s interpretation of the law. In cases in which judges are less sure about the correct resolution for a case, there is room for deliberation and personal relationships to sway decision making. Thus, the “hardness” of a case might also provide important variation in the explanatory power of these three theories.
Finally, while we do not have sufficient data to provide the power necessary to test our model by party (see app. table 6), prior research and our limited data analysis indicate that the explanatory power of the three theories may vary by the partisanship of the judges in the majority. Were this the case, it would suggest additional strategic concerns beyond those in our model. However, interparty differences in the explanatory power of these theories might also implicate differences in judicial philosophies or role orientation that correlate with party. Such issues are important and deserve further research into their nature.
The use of panels to resolve cases is not limited to the US courts of appeals. Many state high courts decide cases in panels rather than en banc, many election law cases are originally heard by three-judge panels, and panels are used to resolve cases in a variety of courts outside of the United States. We build and test our theory using data from the US courts of appeals, but these theories are not unique to them. Future studies should examine the occurrence and persistence of panel effects in other judicial bodies, leveraging institutional variation—in opinion assignment procedures, in judicial retention mechanisms, and in panel assignment institutions—to determine how institutional variation affects both the presence of panel effects and the mechanism(s) through which the existence of these effects can be explained.






