When elected officials enact policies that push at the boundaries of what is considered constitutionally legitimate, it often falls upon the judicial branch to push back and uphold constitutional standards. One of the longest-standing debates in the study of judicial politics concerns when the courts are willing to involve themselves in interbranch disputes of this nature and whether and why they are successful in separation-of-powers (SOP) showdowns with the executive or legislature.
Though there is a voluminous scholarly literature on how national high courts decide SOP cases, prior work has not asked what, if any, role lower courts play in interbranch disputes. This likely reflects a sense that lower courts are more constrained than high courts and are poorly positioned to make waves in politically charged cases. Yet lower courts are often the first movers in initiating SOP conflict. Consider three particularly notable interbranch disputes from the history of the U.S. Supreme Court. In Youngstown Sheet and Tube v. Sawyer , a.k.a. the Steel Seizure case, the Court ruled Truman’s seizure of the steel mills unconstitutional; Truman backed down without challenging the decision. In United States v. Lopez , the Court struck down a bill on commerce clause grounds for the first time in decades; this decision was eventually subjected to a congressional override. In Trump v. Hawaii , the Court ultimately upheld the constitutionality of a controversial Trump administration decree on immigration after a lengthy and politically charged process during which multiple executive orders were offered and withdrawn.
What these three cases have in common is that lower courts in each dispute held the government’s actions unconstitutional prior to being reviewed by the Supreme Court. Nor are these cases cherry picked; according to the Reference Spaeth, Epstein, Martin, Segal, Ruger and Benesh2019 Supreme Court Data Base, roughly 53% of cases in which the Supreme Court overturned a federal law were affirmances of a lower court decision. This reveals a striking and surprising willingness on the part of lower court judges to insert themselves in politically consequential SOP disputes.
The other thing these three cases have in common, however, is that the final outcome ultimately reflected the Supreme Court’s preferences – or, at least, its preferences mediated by its taste for SOP conflict. Following that observation, we can see that the real question of interest must be whether lower courts are influential in SOP disputes or whether their behavior is merely epiphenomenal. Are there reasons to believe lower courts exert independent influence on interbranch conflict? Does it matter whether they rule for or against the government before the high court weighs in? What causal mechanisms might make lower courts influential?
In this paper, I advance the argument that lower courts are indeed influential and that there are several ways in which their presence can alter the course of SOP disputes. In support of this argument, I develop a formal model of an SOP dispute between the judiciary and government, but where the dispute begins in a lower court who makes an initial ruling about constitutionality that is further subject to appeal and review by a high court.
The model shows that there are conditions under which lower courts affect outcomes – where the decision made by the lower court, and indeed their presence in the system at all, affects the ultimate resolution of SOP disputes. The model supports two sets of substantive claims. The first concerns the net effect that lower courts have on SOP disputes – overall, the presence of lower courts makes the judiciary (at least weakly) more likely to intervene in SOP disputes and to rule against the government. The model reveals two mechanisms of influence, which I term institutional entanglement and information revelation. First, lower courts can draw the judiciary into SOP conflicts that the high court would choose to avoid in the absence of the lower court. This occurs because denying review of a lower court declaration of unconstitutionality amounts to a de facto anti-government decision, exposing the courts to risk of reprisal. This produces overwhelming incentives for a high court to grant review, entangling them in SOP disputes they might otherwise have preferred to avoid. This results in the high court intervening more often and even ruling against the government more often than they would have in the absence of the lower court. Second, lower court decisions can also provide information about whether the public is paying attention to a given dispute and will back the courts if the government attempts to punish their decision, which may also make the courts more likely to stand firm against a government action.
The second set of claims concerns why and when lower courts choose to challenge the government, as well as how this relates to hierarchical pressures – that is, the preferences of the high court. In the model, the presence of the high court acts as a sort of safety net that actually makes lower courts (weakly) less sensitive to the risk of government reprisal and more aggressive in striking laws. The magnitude of this effect also varies in the high court’s ideological preferences: Counterintuitively, the presence of a relatively pro-government high court actually increases lower courts’ willingness to strike. An implication is that regime-friendly high courts are particularly likely to become entangled in SOP disputes. Because this arguably resembles the arrangement of ideological preferences during the Trump presidency, this may help explain increases in lower court judicial review and interbranch conflict observed during that era (see, e.g., Barbash et al. Reference Barbash, Paul, Mayes and Rindler2019).
Related literature
The questions of how courts behave in interbranch conflicts and to what extent they can exert real constraints on other state actors are central ones for judicial politics. A large literature has established that the support of the public is an important prerequisite for judicial power (e.g. Caldeira Reference Caldeira1986; Murphy and Tanenhaus Reference Murphy and Tanenhaus1989; Gibson, Caldeira and Baird Reference Gibson, Caldeira and Baird1998). The influential work of Vanberg (Reference Vanberg2005) explores how issues may vary in their transparency or the extent to which the public aware of interbranch disputes, explaining variation in courts’ success in such disputes. Staton (Reference Staton2010) and Krehbiel (Reference Krehbiel2016) have expanded further, examining how courts can draw public attention to their cases, strengthening their hand in interbranch showdowns.
Given the contingent nature of judicial power and the difficulties courts face in this setting, many scholars have asked whether high courts, particularly the U.S. Supreme Court, behave strategically in SOP decisions. The evidence here is decidedly mixed. Some have explored whether the Court’s decisions (Segal Reference Segal1997; Hansford and Damore Reference Hansford and Damore2000; Segal and Spaeth Reference Segal and Spaeth2002; Sala and Spriggs Reference Sala and Spriggs2004; Segal, Westerland and Lindquist Reference Segal, Westerland and Lindquist2011) or case selection (Ownes Reference Owens2010) are constrained by spatial considerations, that is, the arrangement of congressional and presidential preferences. Articles in this vein generally report limited or no evidence of SOP constraint, with the notable exception of Bailey and Maltzman (Reference Bailey and Maltzman2011), who adopt an improved approach for measuring preferences comparably across institutions. Harvey and Friedman (Reference Harvey and Friedman2006) and Hall and Ura (Reference Hall and Ura2015) explore similar questions, using datasets that track congressional bills rather than Court cases and do report evidence consistent with SOP constraints. Clark (Reference Clark2011) introduces a measure of “court-curbing" activity in Congress and argues that introductions of court-curbing bills, though largely symbolic, nonetheless provide information about the Court’s standing with the public, with attendant effects on the Court’s judicial review behavior. Zilis (Reference Mark and Zilis2019) show that these effects are stronger for the Chief Justice and moderate members of the Court.
By and large, however, the work on the Court’s behavior in interbranch conflicts has ignored lower courts entirely. Only one of the above articles – Owens (Reference Owens2010) – even includes as a control variable the directionality of the lower court decision; Owens notes that a lower court declaration of unconstitutionality dramatically increases the chance of certiorari.
By the same token, the literature on the judicial hierarchy has largely focused on relationships between the Supreme Court and its lower courts (particularly the U.S. Courts of Appeals) in ordinary cases and has not explored how hierarchical relationships may be disrupted by the potential for interbranch conflict. The judicial hierarchy literature has tended to focus more on questions of the tools and informational cues the Supreme Court uses to control its subordinates (see Cameron, Segal and Songer Reference Cameron, Segal and Songer2000; Kastellec Reference Kastellec2007; Lax Reference Lax2012; Beim, Hirsch and Kastellec Reference Beim, Hirsch and Kastellec2014), and less so on how lower court decisions may influence the Court’s own decision making (though see Clark and Carrubba Reference Clark and Carrubba2012; Beim Reference Beim2017; Strayhorn Reference Strayhorn2020). The analysis below will invert this traditional emphasis, instead showing how the lower court’s decision creates different status quo points that alter the high court’s incentives in ways that influence its ultimate decision.
In what follows, I combine threads of these literatures by developing a simple model in the spirit of Vanberg (Reference Vanberg2005) and Staton (Reference Staton2010), where the courts may attempt to restrain the government in some SOP dispute but face the threat of reprisal. This dispute occurs in the shadow of a public who is not necessarily aware of disputes between the branches and only backs the courts when “activated," as described below. Unlike those models, however, the courts will operate as a hierarchical system rather than a unitary actor.
Model
Three players, a lower court
$ L $
, high court
$ H $
, and government
$ G $
, face a conflict over the constitutionality of some policy preferred by the government, where
$ x>0 $
represents the constitutional “extremeness" of the policy.Footnote
1 All their decisions are made in the shadow of a public, who, though not a strategic actor, nonetheless shapes the incentive structure, particularly for
$ G $
. The central tension of the game arises from the government’s desire to discipline the courts for adverse rulings without provoking backlash from the public.
More specifically, the model assumes that cases where courts strike down laws sometimes draw attention to the presence of a dispute, making the public aware of both the decision itself and any efforts by the government to circumvent or discipline the judiciary that follow. Unlike previous authors, I do not endogenize the courts’ decision to affirmatively seek publicity; this is assumed to occur automatically, for example, through media coverage of decisions. However, it is not guaranteed to succeed. Cases that declare laws unconstitutional are assumed to have some chance of activating the public due to their political salience, but this may sometimes not occur due to the complexity of judicial decisions or the inherent low visibility of the courts.Footnote
2 Thus, if the high court strikes a law, the public will become activated with probability
$ {\phi}_H $
.
A novel feature of this model is to extend a similar logic to lower court decisions. Motivated to some degree by events that eventually culminated in the Supreme Court decision in
Trump v. Hawaii
, where significant public attention to lower court immigration rulings accrued even before the Supreme Court’s involvement, I further assume that lower courts also possess at least some nonzero probability
$ {\phi}_L $
of activating the public. Naturally, the lower courts’ ability to drive public attention is weaker than the high court, and thus
$ {\phi}_H>{\phi}_L $
.Footnote
3 When activation occurs this fact is common knowledge.
Play begins with
$ L $
deciding whether the policy
$ x $
is constitutional or unconstitutional (denote these choices
$ c $
or
$ u $
). After a decision of
$ c $
, play proceeds to a choice node for
$ H $
where they may deny review, grant review and declare
$ x $
constitutional (affirming
$ L $
’s ruling), or grant and declare it unconstitutional (reversing). Notate these actions
$ dc $
,
$ ac $
, and
$ ru $
, respectively (for deny/constitutional, affirm/constitutional, and reverse/unconstitutional). After a lower court decision of
$ u $
, nature determines whether the public is activated, and this draw is revealed. Losing litigants automatically appeal, and
$ H $
may then choose among denial or either disposition of the case:
$ {du}_i,\hskip0.35em {au}_i $
, or
$ {rc}_i $
(deny/unconstitutional, affirm/unconstitutional, reverse/constitutional), where
$ i $
indicates whether the public is activated (denoted
$ p $
or
$ np $
, respectively). If
$ H $
hears a case and declares the policy unconstitutional, then with probability
$ {\phi}_H $
the public is activated, if it isn’t already.Footnote
4
Finally, after any branch at which the courts have declared
$ x $
unconstitutional and the judicial process is complete – whether following a high court decision or a denial of review of a lower court decision – the government may elect to discipline the judiciary or not. Disciplining the courts reinstates the policy
$ x $
that was overturned but may provoke backlash from the public.
Each actor has preferences over the final policy that take the following form: Each actor possesses a constitutionality threshold
$ {\tau}_i $
such that for actions
$ x>{\tau}_i $
they believe the policy is unconstitutional.Footnote
5 It is assumed that
$ G $
does not care about constitutionality and simply prefers its policy upheld or, equivalently, always believes its policy constitutional. Many utility functions would capture this; for symmetry with the other actors, I assume
$ G $
has a
$ {\tau}_G $
level and that
$ {\tau}_G>x $
. Then the government receives
$ {\tau}_G-x $
if the policy remains in place following play and
$ 0 $
otherwise. Finally, the government pays a backlash cost
$ b $
if it disciplines the courts when the public is activated; by assumption,
$ b>{\tau}_G-x $
, and thus the government’s disciplining decision is always determined by the state of the public.Footnote
6
While it is assumed throughout that the government
$ G $
always prefers the policy enacted, the lower and high courts may vary on this dimension. For the courts,
$ {\tau}_L $
and
$ {\tau}_H $
respectively represent thresholds in
$ x $
above which their sincere preference would be to rule the policy unconstitutional. Each court thus receives
$ {\tau}_i-x $
if the policy ultimately stands and
$ 0 $
if not, which parsimoniously generates a setting where courts that believe the policy
$ x $
is too extreme (right of their threshold) prefer to strike it and otherwise prefer not to strike. The high court, possessing discretionary review, must additionally pay a cost
$ k $
if it elects to review the lower court decision.
To motivate some results below regarding conditions under which the lower court strikes the policy and also to usefully simplify the solution space into a single statement of equilibrium, I assume that the high court’s actual
$ {\tau}_H $
is private information, known only to
$ H $
. Accordingly, let
$ {\tau}_H $
be drawn from an arbitrary log-concave distribution with mean
$ {\hat{\tau}}_H $
.
Finally, both courts pay a judicial independence cost
$ j $
if they are disciplined by the government. This cost represents the net of various consequences associated with disciplining – loss of formal powers, loss of perceived legitimacy, and so on, and I assume the courts strictly prefer to avoid disciplining, all else equal.Footnote
7 Moreover, as Keck (Reference Keck2007) has shown, in cases that implicate the powers and prerogatives of the judiciary, the U.S. Supreme Court does not always break strictly on ideological lines but may take actions to protect the integrity of the judicial branch. Taking these “institutional maintenance" preferences as a starting point, I assume that the high court pays the penalty
$ j $
even if it does not review a case – that is, if the government’s disciplining is directed at its subordinates.Footnote
8 I assume that
$ j>k $
; that is,
$ H $
is always willing to pay the cost of review to avoid discipline. The magnitude of
$ j $
is common knowledge.
The above is summarized by the extensive form given in Figure 1, with payoffs given in the order lower court, high court, government. Note that, because by assumption
$ G $
’s disciplining behavior is determined by the public’s activation,
$ G $
’s choice nodes are not shown and their behavior is taken to follow directly from the informational state.
Figure 1. Game tree and payoffs. The behavior of
$ G $
following a declaration of unconstitutionality is fully determined by the draw of
$ {\phi}_i $
, thus these branches are omitted and payoffs reflect
$ G $
’s deterministic behavior after each nature node.
Equilibrium behavior
The game’s subgame perfect Nash equilibrium solution follows very directly. I state
$ H $
’s best response profile in Lemma 1, define some notation to deal with
$ L $
’s uncertainty over
$ H $
, and then fully state equilibrium behavior in Proposition 1.
Lemma 1: If the lower court plays
$ c $
,
$ H $
plays
$ ru $
if
$ x\hskip0.35em \ge \hskip0.35em {\tau}_H+\frac{\left(1-{\phi}_H\right)j+k}{\phi_H} $
, and
$ dc $
otherwise. If the lower court plays
$ u $
and the public is not activated,
$ H $
plays
$ {au}_{np} $
if
$ x\hskip0.35em \ge \hskip0.35em {\tau}_H+\frac{\left(1-{\phi}_H\right)j}{\phi_H} $
, and
$ {rc}_{np} $
otherwise. If the lower court plays
$ u $
and the public is activated,
$ H $
plays
$ {du}_p $
if
$ x\hskip0.35em \ge \hskip0.35em {\tau}_H-k $
, and
$ {rc}_p $
otherwise.
Proof: Follows directly from
$ H $
’s payoffs.
Usefully, under all conditions
$ H $
effectively chooses between exactly two of its three potential replies because at each information set one of its strategies is dominated.Footnote
9 Given that, then, let
$ {\eta}_c $
denote the probability that
$ H $
chooses
$ dc $
after
$ L $
plays
$ c $
, given the distribution of
$ {\tau}_H $
. Similarly, let
$ {\eta}_{np} $
denote the probability that
$ H $
chooses
$ {rc}_{np} $
if
$ u $
and the public not activated and
$ {\eta}_p $
the probability that
$ H $
chooses
$ {rc}_p $
after
$ u $
and the public is activated. Thus,
$ {\eta}_i $
always represents the probability with which
$ H $
chooses the nondominated option supportive of the government.Footnote
10 Note that, given the relative locations of
$ H $
’s thresholds,
$ {\eta}_c>{\eta}_{np}>{\eta}_p $
.
Proposition 1:
$ H $
’s behavior is as in Lemma 1.
$ L $
chooses
$ u $
if
$ {\phi}_L\left[{\eta}_p\left({\tau}_L-x\right)\right]+\left(1-{\phi}_L\right)\left[{\eta}_{np}\left({\tau}_L-x\right)+\left(1-{\eta}_{np}\right)\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right)\right]\hskip0.35em \ge \hskip0.35em {\eta}_c\left({\tau}_L-x\right)+\left(1-{\eta}_c\right)\left[\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right)\right] $
or, equivalently, if
$ x\hskip0.35em \ge \hskip0.35em {\tau}_L+\frac{\left(1-{\phi}_H\right)\left[{\eta}_c-{\eta}_{np}-{\phi}_L\left(1-{\eta}_{np}\right)\right]j}{\phi_H\left({\eta}_c-{\eta}_{np}\right)+{\phi}_L\left[1-{\eta}_p-\left(1-{\eta}_{np}\right){\phi}_H\right]} $
.
Proof: Follows directly from expected utility functions of
$ G $
and
$ L $
.
How the high court’s behavior is affected by the lower court
Despite its simple foundations, several interesting behaviors arise. A natural starting point is the high court’s decision to grant review. Consider
$ H $
’s motivations to review at each of its three choice nodes. First, if the lower court held
$ x $
constitutional,
$ H $
may believe
$ x $
so extreme that it prefers to review and reverse, even despite the disciplining risk. Second, if the lower court held
$ x $
unconstitutional and activated the public,
$ H $
faces no disciplining risk but may still believe the policy is constitutional and wish to review and reverse purely on policy grounds. The high court’s motivations at these two nodes cleanly map onto theories of error correction that already exist in the literature.
Behavior if the lower court decides
$ u $
and does not activate the public, however, is much more interesting. In this circumstance,
$ H $
may sometimes review specifically to affirm a lower court declaration of unconstitutionality. When the high court chooses to review and affirm,
$ {au}_{np} $
, it does because a) it agrees with the lower court’s decision substantively and b) it is concerned that denying review may expose the judiciary to reprisal. Thus, it hears the case in the hopes that doing so will succeed in activating the public (with probability
$ {\phi}_H $
), deterring
$ G $
. In short, the high court sometimes throws its weight behind a lower court decision so as to raise the salience of that decision and potentially deter reprisal.
This review pattern constitutes one of the two novel mechanisms uncovered by the model, which I term institutional entanglement. When the public is not activated, a lower court declaration of unconstitutionality disturbs the status quo and activates the latent threat of an angry government responding to the courts. This threat, and the high court’s desire to avoid reprisal, creates overwhelming incentives to review the decision. Indeed, at the node where
$ L $
has struck the law but not activated the public, denying review is a strictly dominated strategy. Sometimes,
$ H $
reviews simply to reverse
$ L $
and reinstate the policy, backing down from
$ G $
’s latent threat. But in a mechanism analogous to one described by Staton (Reference Staton2010), the high court sometimes grants review with the intent of publicizing the case and deterring discipline. Thus, institutional entanglement provides the lower court with some de facto power to endogenously “force" a case onto
$ H $
’s discretionary docket.
Moreover, this institutional entanglement does not merely affect
$ H $
’s review decision but also the range of cases in which they will actually decide against the government. Note that if
$ L $
upholds the policy (chooses
$ c $
), the high court only chooses
$ ru $
if
$ x\hskip0.35em \ge \hskip0.35em {\tau}_H+\frac{\left(1-{\phi}_H\right)j+k}{\phi_H} $
. By contrast, if
$ L $
chooses
$ u $
(and does not activate the public),
$ H $
chooses
$ {au}_{np} $
if
$ x\hskip0.35em \ge \hskip0.35em {\tau}_H+\frac{\left(1-{\phi}_H\right)j}{\phi_H} $
. The second threshold is less than the first. That is, the high court intervenes and declares the policy unconstitutional for a wider range of
$ x $
after a lower court
$ u $
than after a lower court
$ c $
. This secondary effect means that not only can the lower court influence whether an SOP dispute is heard by the high court at all, its decision also sometimes alters the final disposition of the case, relative to a counterfactual setting without the lower court.
This effect can be seen in the visualization given in Figure 2. The figure shows the final policy outcome in each of four ranges, depending upon
$ x $
’s location relative to cut points in
$ H $
’s ideal point space. The effect of institutional entanglement on policy outcomes is seen in Region 3. In this region,
$ H $
will deny review and strategically avoid conflict after a lower court rules constitutional (or, equivalently, in an environment without the lower court). However, if the lower court declares unconstitutional (and fails to activate the public), the high court will review and affirm due to entanglement.Footnote
11
Figure 2. Judicial branch resolution of dispute, for various
$ x $
. Region boundaries are determined by the relative locations of equilibrium behavioral thresholds for the high court.
Figure 2 also illustrates the other novel causal mechanism elucidated by the model: information revelation. This mechanism reflects the impact of the lower court’s
$ {\phi}_L $
chance of activating the public and, by implication, revealing to all that the government will be unable to discipline.Footnote
12 Consider Region 2 of the figure. In this region (and those to its right), if
$ L $
successfully activates the public,
$ H $
simply denies review and lets the lower court decision stand.Footnote
13 The information revelation effect of the lower court can be seen by contrasting this with what happens if the lower court fails to activate the public or, equivalently, if they are absent from the game.
If
$ L $
’s decision fails to activate the public in Region 2, then the ultimate outcome will be that their decision is reviewed and reversed by
$ H $
and the policy upheld –
$ H $
still faces institutional entanglement incentives but backs down from conflict with
$ G $
. Thus,
$ L $
’s initial anti-government ruling produces information for
$ H $
about public attention and thus disciplining risk. Crucially,
$ L $
can provide this reconnaissance with relatively little risk. If
$ L $
declares the policy unconstitutional, then perhaps the public is activated and the courts will win out; if not, however,
$ H $
faces very strong incentives to swoop in and reverse the decision, defusing the potential conflict with the government.Footnote
14
Both mechanisms pull in the same direction, and thus there are (at least weakly) stronger constraints on the government when the lower court is present than when not. It is worth noting that these mechanisms are each driven by different assumptions, and thus no single factor, if removed from the model, zeroes out the lower court’s impact. For example, one might reasonably argue that lower court decisions are so low visibility that
$ {\phi}_L $
is effectively zero. If so, then information revelation cannot occur; however, because institutional entanglement accrues in the nonactivation state, this mechanism of lower court influence still operates. By the same token, information revelation would still occur even if review were costless for the high court.
When do lower courts challenge the government?
The model can also shed light on why and under what conditions lower courts challenge the constitutionality of government policies. As noted at the outset, lower courts are surprisingly active in challenging the government. We can ask two questions about when this is likely to occur. First, how much constraint do lower courts feel from the possibility of the courts being disciplined, and how does this interact with
$ L $
’s own policy preferences? Second, how do the high court’s preferences – that is, the hierarchical context faced by
$ L $
– affect
$ L $
’s decision?
Beginning with the first question, note from Proposition 1 that
$ L $
chooses
$ u $
when
$ x\hskip0.35em \ge \hskip0.35em {\tau}_L+\frac{\left(1-{\phi}_H\right)\left[{\eta}_c-{\eta}_{np}-{\phi}_L\left(1-{\eta}_{np}\right)\right]j}{\phi_H\left({\eta}_c-{\eta}_{np}\right)+{\phi}_L\left[1-{\eta}_p-\left(1-{\eta}_{np}\right){\phi}_H\right]} $
. Straightforwardly, then,
$ L $
declares the policy unconstitutional when it is sufficiently extreme, relative to their ideal threshold
$ {\tau}_L $
plus some additional offset. Note that this offset includes the disciplining cost
$ j $
, multiplied by various other factors. The size of this multiplier thus effectively represents the degree to which
$ L $
internalizes threats to the courts; crucially, because the multiplier depends on various parameters of the model and particularly
$ H $
’s propensity to review, it varies: There are situations where
$ L $
is keenly sensitive to the risk of disciplining but also situations
$ L $
is insensitive to disciplining risk because all that risk is effectively offloaded to the high court.
Under typical conditions,
$ L $
is sensitive to
$ j $
in the intuitive direction, meaning that the threat of disciplining constrains
$ L $
and reduces the range of
$ x $
for which
$ L $
challenges. As
$ {\phi}_L $
increases, the magnitude of the multiplier is decreasing, meaning, sensibly, that
$ L $
challenges more and more aggressively when its decision is more likely to activate the public.Footnote
15 Perhaps surprisingly, under some conditions it is possible for the multiplier to actually be negative such that
$ L $
sometimes challenges the government even when it sincerely believes the policy is constitutional and would prefer it upheld. This unusual behavior occurs when the high court is extremely likely to challenge the government itself – here, conflict with the government is a fait accompli, and the lower court benefits more from compounding
$ {\phi}_L $
into the net probability of judicial victory.
How does the lower court’s decision depend upon their hierarchical relationship with
$ H $
, and specifically
$ H $
’s ideology? Recall that
$ {\hat{\tau}}_H $
denotes the mean of the distribution of
$ {\tau}_H $
. The lower court’s decision is affected by changes in
$ {\hat{\tau}}_H $
in one of four ways, depending upon the lower court’s preferences. In the text following, I provide intuition for these behaviors; more formalized proofs of the following four claims may be found in the appendix.
First, consider the two extremes: 1) For sufficiently pro-government
$ L $
, where
$ {\tau}_L-x\hskip0.35em \ge \hskip0.35em j $
, it is a dominant strategy to declare
$ x $
constitutional. 2) For sufficiently anti-government
$ \mathrm{L}:{\tau}_L-x\hskip0.35em \le \hskip0.35em \frac{-j\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)}{\left[1-\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)\right]} $
, it is a dominant strategy for
$ L $
to declare
$ x $
unconstitutional regardless of the location of
$ H $
. Thus, lower courts with particularly extreme preferences in either direction simply choose the case disposition they prefer.
More interesting are two interior cases. 3) For
$ L $
that moderately favor the government policy, where
$ {\tau}_L-x>0 $
, but
$ {\tau}_L-x<j $
,
$ L $
’s behavior depends monotonically on its hierarchical incentives; for sufficiently anti-government
$ {\hat{\tau}}_H $
these
$ L $
choose
$ u $
, but as
$ {\hat{\tau}}_H $
increases they switch to
$ c $
.
$ L $
’s behavior here occurs not due to the threat of reversal by
$ H $
, which they do not care about, but because
$ L $
is sensitive to disciplining risk and faces a trade-off between attempting to activate the public but risking institutional entanglement that has a chance to result in discipline. As
$ H $
grows more likely to be anti-government,
$ L $
places more weight on the potential gains from activation, knowing that interbranch conflict is likely regardless. This is a fairly standard hierarchical story, albeit motivated by an interesting mechanism distinct from reversal.
4) Finally, and most interesting, is the behavior of intermediately positioned lower courts who oppose the policy but not by so much as to be insensitive to the impact of the judicial disciplining cost
$ j $
. These are
$ L $
for whom
$ {\tau}_L-x<0 $
but
$ {\tau}_L-x\hskip0.35em \ge \hskip0.35em \frac{-j\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)}{\left[1-\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)\right]} $
. For these
$ L $
, behavior is nonmonotone; they choose
$ c $
for interior values of
$ {\hat{\tau}}_H $
but choose to declare the policy unconstitutional at both extremes—that is, when
$ H $
is either sufficiently anti-government (intuitively) as well as when sufficiently pro-government. Surprisingly, the presence of a pro-government high court actually induces risk taking by ideologically divergent lower courts.
Why does this occur? Recall that
$ {\eta}_i $
represents
$ H $
’s probabilistic behavior (from
$ L $
’s perspective) at each of
$ H $
’s three possible information sets. Then
$ L $
prefers
$ u $
over
$ c $
when
$ {EU}_L(u)\hskip0.35em \ge \hskip0.35em {EU}_L(c) $
or when:
$$ {\displaystyle \begin{array}{r}{\phi}_L{\eta}_p\left({\tau}_L-x\right)+\left(1-{\phi}_L\right)\left[{\eta}_{np}\left({\tau}_L-x\right)+\left(1-{\eta}_{np}\right)\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right)\right]\hskip0.35em \ge \hskip0.35em \\ {}{\eta}_c\left({\tau}_L-x\right)+\left(1-{\eta}_c\right)\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right).\end{array}} $$
For intuition, consider a case where
$ {\eta}_c=1 $
,
$ {\eta}_{np}=1 $
, and
$ {\eta}_p<1 $
.Footnote
16 This is a case where
$ H $
will always defer to
$ G $
when the public is not activated but may sometimes let an anti-government outcome stand when the public is activated. Here, Equation 1 reduces to
$ {\phi}_L{\eta}_p\left({\tau}_L-x\right)+\left(1-{\phi}_L\right)\left({\tau}_L-x\right)\hskip0.35em \ge \hskip0.35em {\tau}_L-x $
. Choosing
$ c $
guarantees the receipt of the (negative) policy payoff
$ {\tau}_L-x $
that
$ L $
associates with an unconstitutional policy, while choosing
$ u $
gives at least some chance that the policy will ultimately be overturned.Footnote
17
More generally, the basis of this behavior is a moral hazard problem that is most obvious when
$ H $
is highly pro-government: Suppose
$ L $
knows that
$ H $
is certain to review and reverse any declaration of unconstitutionality that is accompanied by an inactive public. In such a setting,
$ L $
actually faces zero practical risk of being disciplined. Moreover,
$ L $
does not internalize
$ H $
’s cost of review but knows
$ H $
will be highly motivated to pay those costs in the relevant scenario. This frees
$ L $
to take on greater risk than it might if it fully internalized the risk of
$ j $
.
$ L $
uses this freedom to fish for activation of the public, and potential, if unlikely, overall victory.
This heightened risk taking occurs more generally, as well. A final observation that can be made about
$ L $
’s multiplier is that the lower court is always (weakly) less sensitive to the risk of disciplining than is the high court because the high court’s multiplier on
$ j $
after
$ L $
chooses
$ u $
,
$ \frac{\left(1-{\phi}_H\right)}{\phi_H} $
, is always larger than
$ L $
’s given above (see appendix). Thus, in fact all lower courts face at least some degree of moral hazard, relative to
$ H $
, and we should expect that lower courts should actually be consistently more aggressive and more willing to strike down laws than high courts.
A straightforward example of this is the string of decisions leading up to N.F.I.B. v. Sebelius. Conservative lower courts in the District of Florida and Eleventh Circuit overruled the individual mandate, leading to the eventual Supreme Court ruling, with the District Court even initially declaring the mandate unseverable and the entire law void. Consistent with this result, both these lower courts were quite aggressive in targeting the mandate – contrast that with the Supreme Court case, where of course much ink has been spilled considering the strategic dimensions of Roberts’ majority opinion and last-minute “flip” on the merits (see, e.g., Christenson and Glick Reference Christenson and Glick2015). Lower courts seemingly did not internalize the incentives for strategic avoidance nearly as strongly as the high court eventually did and acted accordingly.
Interior case 4, however, also shows the striking implication that this lower court aggression does not purely depend upon the presence of a (likely) anti-government high court. When the high court is highly pro-government, this counterintuitively also leads lower courts to strike aggressively – indeed this is actually where the moral hazard problem exerts the strongest effects on
$ L $
’s behavior. Notably, this scenario arguably bears substantial resemblance to the arrangement of preferences during the Trump administration. With a relatively pro-government Supreme Court, lower court judges who believed government policies to be unconstitutional faced strong incentives to challenge those policies because there was virtually no risk of disciplining. At worst, the conservative court might simply reverse their decisions and defuse the SOP showdown, such as in
Trump v. Hawaii
; at best, the lower court might succeed in activating the public and be lucky enough to face a Supreme Court that (perhaps barely) agrees with them on the merits and is emboldened to stand with them due to public activation. Though a long shot, the latter case is a nearly risk-free gamble. This may provide some insight into why the Trump administration accumulated such an extraordinary number of losses in the lower courts, despite the presence of a co-partisan Supreme Court.
Extensions
This simple model of interbranch politics nonetheless illustrates a variety of interesting new theoretical mechanisms regarding both how high court case selection and decision making is endogenous to lower court behavior, as well as how hierarchical incentives can sometimes induce lower courts to take highly aggressive postures with respect to declarations of unconstitutionality. This section considers to what extent these insights are affected by various reasonable extensions to the model.
The public doesn’t always support the court
One potential critique of the model is that the public may sometimes agree with the government’s policy and refuse to back the court even if activated. Thus, suppose that there is additionally a
$ \beta $
chance that the public indeed backs the judiciary, unknown at the start of play but revealed to all if the public is ever activated. This extension is extremely straightforward, as this probability compounds with the
$ \phi $
probabilities of activation. For example, the lower court has a
$ {\phi}_L\beta $
chance of activating a friendly public; if this occurs, then all downstream behavior is unchanged. Similarly, when the public is unactivated, the high court has a
$ {\phi}_H\beta $
chance of successfully protecting themselves; the trade-off between striking and upholding remains the same, but the high court will be more cautious due to the lower probability of success. One added wrinkle is that if, with probability
$ {\phi}_L\left(1-\beta \right) $
, the public is activated but revealed to be hostile to the courts, then the high court will always simply review and hold the law constitutional, backing down from the conflict.
A low
$ \beta $
setting might resemble a state with developing institutions where the public does not yet trust the judiciary (cf. Carrubba Reference Carrubba2009). In such a setting, the high court is much more constrained. Interestingly, though, lower courts remain aggressive in striking laws in this scenario because a highly constrained high court would almost certainly review and deescalate conflicts, heightening the impact of
$ L $
’s moral hazard problem. Thus, lower courts can take a flier on activating a friendly public with little or no risk, even here. Thus, in this setting the lower court’s information-revelation role is even more important, allowing the high court to gauge not just activation but also the public’s attitudes and to protect the judiciary from overreaching when the public is not an ally.
Government is sometimes undeterrable
The baseline game assumes that the government is always motivated to avoid public backlash; formally, that
$ b>{\tau}_G-x $
. Suppose instead that
$ {\tau}_G $
is a random variable, and denote the probability that the government exogenously punishes even when the public is activated,
$ b<{\tau}_G-x $
, as
$ \pi $
. This gives both courts a payoff of
$ \pi \left({\tau}_i-x-j\right) $
(minus
$ H $
’s cost
$ k $
in the relevant cases as well) at any terminal node where the public is activated. In such a setting, both the higher and lower courts are, intuitively, more constrained because all options where
$ u $
is chosen become strictly less attractive as
$ \pi $
increases. Naturally, if
$ \pi \hskip0.35em =\hskip0.35em 1 $
, the government is undeterrable and the courts will always avoid conflict.
Upholding laws can still activate the public
Suppose that any court decision can activate the public; that is, that the probability of publicity after an uphold is not
$ 0 $
, perhaps due to an active media. Let
$ {\phi}_{Lc} $
denote the activation rate after declarations of constitutionality.Footnote
18 This adds a choice node for
$ H $
after
$ c $
and activation, where it chooses sincerely modulo its cost of review. The results elsewhere are unchanged, apart from some cut-point shifts, so long as
$ {\phi}_L>{\phi}_{Lc} $
because the expected utility comparison in Proposition 1 changes only proportionally to this difference. Stated another way, all results of the model for
$ {\phi}_L $
can be interpreted as statements about the marginal increase in activation after striking a law. Thus, we can see that the information revelation results depend on the intuitive notion that conflictual decisions are more likely to generate media coverage, and so on, not the stronger claim that nonconflictual decisions cannot.
Disciplining activates the public
A final possibility is that the government engaging in disciplining may endogenously create its own backlash, even if the public was not activated during play. Thus, suppose that
$ G $
’s disciplining has some probability
$ \alpha $
of activating the public on its own. Then
$ G $
’s incentives are identical after activation, but if the public is not activated by the courts,
$ G $
only disciplines if
$ \alpha b\hskip0.35em \ge \hskip0.35em {\tau}_G-x $
. This creates a threshold effect where, if
$ \alpha $
is small enough, the game is entirely unchanged, while, if
$ \alpha $
is large enough,
$ G $
no longer has any credible threat of ever disciplining, and the behavior of both courts reduces simply to sincere voting. In other words, if
$ G $
is deterred from disciplining by factors fully independent of the behavior of the courts, then the strategic complexities of that behavior are, not surprisingly, washed out. It is worth noting that the threshold
$ \alpha b\hskip0.35em \ge \hskip0.35em {\tau}_G-x $
does depend upon
$ {\tau}_G $
, which can be interpreted as the government’s preference intensity – accordingly, on issues where the government cares intensely enough to overwhelm
$ \alpha $
and create a genuine discipline threat, the incentives characterized by the model will remain in play.
Discussion
To summarize, the model provides insights into the effects of lower courts on SOP disputes that fall along two different lines. The first concerns how lower court declarations of unconstitutionality – and the presence of the lower court more generally – alter how SOP disputes play out and ultimately the policy outcomes that the judiciary will reach. Outcomes are always at least weakly more anti-government with the lower court than without. Lower courts can be influential by entangling the judiciary in an SOP dispute that
$ H $
might otherwise prefer to avoid or providing information to other actors about the state of the public.
Second, the model shows how lower court behavior responds to changes in the preferences of the high court. Surprisingly, as the high court grows more anti-government, this has the counterintuitive effect of sometimes making the lower court more aggressive, rather than less. Both these sets of claims are new to the literature and suggest several avenues for further thinking about SOP disputes, the judiciary, and how elected officials are constrained.
Activists and forum shopping
One implication of the model is that the ideology of the lower court judges who initially hear constitutional disputes affects its ultimate resolution. Accordingly, this implies that forum shopping – the ability of litigants to choose where to file their initial challenges – actually enhances the judiciary’s ability to constrain the state. Unsurprisingly, of the various challenges to Trump administration policies, a disproportionate number were filed in various districts of the Ninth Circuit, widely considered the most liberal in the nation. While a simplistic view of the judicial hierarchy might suggest that lower court wins in such liberal fora will simply be slapped down by a conservative Supreme Court, the model instead provides reason to believe that the effects on outcomes will be nonnegligible. Because forum shopping is often possible on questions of federal law, this suggests that the lower courts’ presence in the system per se places additional constraints on the elected branches. It is particularly notable that this is true even when the typical lower court judge is pro-government, so long as there exists sufficient ideological diversity within the lower courts to incentivize forum shopping.
Ideology versus deference
The model speaks to questions about the judicial nomination process and what sorts of virtues nominating presidents might look for, particularly in lower court judges. At first blush, one simple way to resolve the “problem” – from the government’s perspective – of laws being struck down too frequently is to stack all levels of courts with judges who value deference to government action, in the traditional judicial restraint sense. However, this same goal can also be achieved by ideological loyalty – appointing judges who agree with one’s policy program will also result in them striking fewer of your own laws; moreover, these pro-government judges will quickly become anti-government judges if power flips to a different party regime. That is, under Obama, liberal judges are pro-government, but once power flips to Trump, they become anti-government judges who may constrain that regime to some degree. This downstream effect of placing checks on potential future governments further exacerbates incentives to nominate ideological judges to lower court posts. A less obvious corollary is that the ideological polarization of the lower courts will result in the high court becoming increasingly entangled in separation-of-powers conflict, with potential consequences for its public legitimacy.
Judicial institutional design
The model also implicitly demonstrates the importance of two systemic features of judicial institutional design. The first is relatively obvious: In some systems, particularly civil law systems, lower courts are not involved in constitutional review at all. This is especially true of systems that use pre-enactment advisory review to decide the constitutionality of statues. In such systems, high courts may be somewhat less likely to challenge government policies due to the absence of the mechanisms described above. Relatedly, the model also implicitly highlights the importance of access to justice in strengthening the rule of law. The model assumes a dispute in progress, brought by an appropriately situated litigant. This is by no means automatic; even in systems where litigants initiate constitutional review, not all litigants possess the resources or knowledge necessary to file the appropriate challenges. In countries with weak support structures (Epp Reference Epp1998) or with high barriers to entry litigants may be unable to gain access to the judiciary, in which case lower courts will be unable to prod their high courts into action. A weak support structure may make it easier for national high courts to duck important questions, while a robust one may obligate them to inject themselves more frequently into national controversies.
Implications for empirical work
The model also suggests some implications for how to interpret judicial behavior in interbranch conflict cases and, particularly, how to move forward in analyzing the U.S. Supreme Court’s responsiveness to SOP considerations. At the most basic level, the model suggests that hypotheses about the Court’s behavior should be conditional on the directionality of the lower court decision. Cases where the lower court strikes should be substantially more likely to be reviewed, and moreover the Court’s incentives to review in such cases are so overwhelming that features of the SOP environment (e.g., ideological placement of other actors, court-curbing activity) would be expected to have little effect on the cert decision. Put another way, strategic avoidance in cases where the lower court strikes looks like review and reversal, not the denial of cert. By contrast, the Court’s behavior cases where the lower court upholds should hew much closer to standard intuitions. More broadly, the model also calls attention to the possibility that significant selection effects may occur not just at the cert phase but even before it, suggesting that statute-centered research designs such as Harvey and Friedman (Reference Harvey and Friedman2006) and Hall and Ura (Reference Hall and Ura2015) may be preferable to case-centered approaches.
Outcome-specific costs and the judicial hierarchy
Finally, the model suggests some broader points relevant to future theoretical and empirical work on the judicial hierarchy. The main “engine” of the model is a basic asymmetry in the consequences of decisions to uphold or strike a law. Striking exposes the judiciary to potential reprisal, while upholding does not. From this asymmetry flows the lower court’s impact on case selection and thus potentially on outcomes. Such asymmetries are not necessarily limited to interbranch conflict. Consider, for example, a lower court deciding whether to create a circuit split; one outcome of the case creates a (potentially costly) split, while the other does not (cf. Strayhorn Reference Strayhorn2020). Similarly, appellate courts sometimes justify the adoption of rules that place limits on civil liability by asserting that the alternative would lead to a “flood of litigation,” creating burdens for lower courts. The implication is that this flood occurs after only one of the potential outcomes of the case but not the other, creating cost asymmetry. Future work could consider whether these or other such scenarios with asymmetric outcome-specific costs alter incentives in the judicial hierarchy in interesting ways.
Conclusion
This paper has considered the role that lower courts play in the initiation and resolution of interbranch conflicts. The formal model developed above describes nonobvious mechanisms by which lower courts’ decisions in such cases affect not merely superficial process factors but also how they can materially influence the final outcomes of interbranch disputes. The model also explores when lower courts will be most likely to overturn government policies and finds that this can occur under surprising conditions, particularly when the high court is highly pro-government. Centrally, the model identifies that lower courts’ impact is asymmetric: Lower courts that rule in favor of the constitutionality of government policies do not inhibit later action by high courts, but lower courts that challenge them disturb the status quo in ways that can ultimately result in tighter constraints on government behavior.
The analysis here has important implications for how we understand the ways in which the judicial branch – as opposed to merely national high courts – can work to constrain the state and protect constitutional guarantees. Conceptions of judicial independence, in particular, have often focused wholly on government–high court relations, yet this analysis shows that courts at all levels have an important role to play in defending the rule of law and suggests that future theorizing about interbranch conflict between the elected branches and judiciary take a more holistic view of the latter.
Appendix
This section proves the claims made around
$ L $
’s expected utilities as
$ {\hat{\tau}}_H $
varies. In particular, note that:
$ {EU}_L(u)={\phi}_L{\eta}_p\left({\tau}_L-x\right)+\left(1-{\phi}_L\right)\left[{\eta}_{np}\left({\tau}_L-x\right)+\left(1-{\eta}_{np}\right)\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right)\right] $
and
$ {EU}_L(c)\hskip0.35em =\hskip0.35em {\eta}_c\left({\tau}_L-x\right)+\left(1-{\eta}_c\right)\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right) $
. Then, taking the claims as numbered in the text:
Proof of (1): follows immediately from substitution of
$ {\tau}_L-x=j $
into
$ {EU}_L(c)-{EU}_L(u) $
, which is always true for this value of the policy but only at the knife-edge for
$ {\eta}_i\hskip0.35em =\hskip0.35em 0 $
.
Proof of (2): first, note that for any
$ L $
for whom
$ {\tau}_L-x\hskip0.35em \ge \hskip0.35em \frac{-j\left(1-{\phi}_H\right)}{\phi_H} $
, choosing
$ c $
is most tempting when
$ {\eta}_c=1 $
. Note also that the threshold
$ {\tau}_L-x\hskip0.35em \le \hskip0.35em \frac{-j\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)}{\left[1-\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)\right]} $
is strictly narrower (closer to
$ 0 $
). Then the latter threshold is derived where
$ c $
is as tempting as possible, that is,
$ {\eta}_c=1 $
, and gives the range for which it is impossible for
$ c $
to be preferred for any values of
$ {\eta}_{np} $
or
$ {\eta}_p $
.
Proof of (3): first, note that, given the two
$ EU $
in part (1) above, for these values
$ {EU}_L(u)>{EU}_L(c) $
as
$ {\hat{\tau}}_H $
approaches negative infinity (i.e., all
$ {\eta}_i $
approach 0), and both asymptote to
$ {\tau}_L-x $
as
$ {\hat{\tau}}_H $
approaches positive infinity (i.e., as all
$ {\eta}_i $
approach 1). Then, noting that all
$ {\eta}_i $
are increasing functions of
$ {\hat{\tau}}_H $
, we can see that
$ \frac{\partial }{\partial {\hat{\tau}}_H}{EU}_L(c)\hskip0.35em =\hskip0.35em {\eta}_c^{\prime}\left[\left({\tau}_L-x\right)-\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right)\right] $
and that
$ \frac{\partial }{\partial {\hat{\tau}}_H}{EU}_L(u)\hskip0.35em =\hskip0.35em {\phi}_L{\eta}_p^{\prime}\left({\tau}_L-x\right)+\left(1-{\phi}_L\right){\eta}_{np}^{\prime}\left[{\tau}_L-x-\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right)\right] $
. For the range discussed here, where
$ {\tau}_L-x>0 $
but
$ {\tau}_L-x-j<0 $
, both these derivatives are strictly positive, and it must be true that each
$ EU $
approaches
$ {\tau}_L-x $
from below. Because both functions are monotone in
$ {\hat{\tau}}_H $
, this must imply that they cross at most once.
Proof of (4): for
$ L $
of this type, for whom
$ {\tau}_L-x<0 $
, but
$ {\tau}_L-x\hskip0.35em \ge \hskip0.35em \frac{-j\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)}{\left[1-\left(1-{\phi}_H\right)\left(1-{\phi}_L\right)\right]} $
,
$ {EU}_L(c) $
remains strictly increasing in
$ {\hat{\tau}}_H $
because
$ \left({\tau}_L-x\right)-\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right)>0 $
. Thus,
$ {EU}_L(c) $
continues to approach
$ {\tau}_L-x $
from below. However, for these
$ L $
,
$ {EU}_L(u) $
is sometimes greater than
$ {\tau}_L-x $
, and moreover approaches
$ {\tau}_L-x $
from above in its positive asymptote. To see this, note that the
$ \frac{\partial }{\partial {\hat{\tau}}_H}{EU}_L(u) $
given in the previous section is negative when the contribution from
$ {\eta}_p^{\hbox{'}} $
is large enough relative to
$ {\eta}_{np}^{\hbox{'}} $
(because for these
$ L $
,
$ {\tau}_L-x $
is negative while
$ {\tau}_L-x-\left(1-{\phi}_H\right)\left({\tau}_L-x-j\right) $
is not). By the log-concavity of the distribution of
$ {\tau}_H $
,
$ \frac{\eta_p^{\prime }}{\eta_{np}^{\prime }} $
is strictly increasing, and thus this must eventually be true. By the result of section (2) above,
$ L $
in this range can also prefer
$ c $
for some values of
$ {\eta}_i $
.
Proof that lower court is less sensitive to discipline: Compare the multiplier on
$ j $
for
$ H $
after
$ u $
to that of
$ L $
; simplifying and collecting terms, this reduces to
$ \left(1-{\eta}_{np}\right)\left(1-{\phi}_H\right){\phi}_H{\phi}_L\left[{\phi}_H\left({\eta}_c-{\eta}_{np}\right)+\left(1-{\eta}_{np}\right){\phi}_L\right]\hskip0.35em \ge \hskip0.35em 0 $
. Because
$ {\eta}_c>{\eta}_{np} $
, this is always true.
Extension 1: Public does not always back court
To support the claim in the text that the lower court may actually become more aggressive when
$ \beta $
is low, consider a setting where
$ \beta =\varepsilon $
. This implies
$ {\eta}_c=1 $
and
$ {\eta}_{np}=1 $
because
$ H $
will never be willing to gamble on activating the public, but
$ {\eta}_p<1 $
because this depends only on the draw of
$ {\tau}_H $
. Then
$ L $
prefers
$ u $
over
$ c $
, by Proposition 1, when
$ {\phi}_L\beta \left[{\eta}_p\left({\tau}_L-x\right)\right]+{\phi}_L\left(1-\beta \right)\left({\tau}_L-x\right)+\left(1-{\phi}_L\right)\left({\tau}_L-x\right)\hskip0.35em \ge \hskip0.35em {\tau}_L-x $
, which is strictly true if
$ {\tau}_L<x $
.
Extension 4: Disciplining creates backlash
For the claim that judicial behavior is sincere when
$ \alpha $
is large enough, note that the setting where
$ G $
never disciplines is equivalent to
$ {\phi}_L={\phi}_H=1 $
. Substitution into the two thresholds for
$ H $
in Lemma 1 that occur after activation, and
$ L $
’s threshold in Proposition 1 will then return
$ x>{\tau}_L $
and
$ x>{\tau}_H-k $
.
$ H $
’s other threshold can no longer occur.
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