I. INTRODUCTION
Jeremy Bentham derided the doctrine of precedent as tantamount to “acting without reason, to the declared exclusion of reason and thereby in opposition to reason.”Footnote 1 Defending the coherence of the common law method requires demonstrating, in opposition to Bentham, that precedent imposes a coherent set of constraints on our practical reasoning. What I will call the prioritized reason model, drawn from work by Grant Lamond and developed by John Horty, offers an attractive formal account of precedent in terms of constrained practical reasoning.Footnote 2 The model utilizes factor-based accounts of common law reasoning first developed in artificial intelligence and law.Footnote 3 According to the prioritized reason model, rules used to determine the outcome of past decisions reflect previous decision-makers' assessment of the underlying weight of reasons in the case.Footnote 4 Courts in subsequent decisions are constrained in the sense that they must not depart from the priority order established in past cases.
The prioritized reason model occupies an intermediate position between theories that equate precedential reasoning with the application of strict and inflexible rules, and theories that understand precedent in terms of less constrained forms of natural reasoning—for instance wholly analogical reasoning.Footnote 5 My purpose here is not to compare the merits of the model with these alternatives, though I am most sympathetic to the prioritized reason model. Rather I will critique the particular account of authoritative legal reasoning adopted on the prioritized reason model, before suggesting a revised account of precedential constraint in terms of protected reasons.
One interesting aspect of the prioritized reason model is its apparent departure from the view that authoritative common law rules constrain subsequent courts by creating protected reasons for action.Footnote 6 According to Joseph Raz's influential account, rules—at least those rules that create obligations—are understood in terms of protected reasons.Footnote 7 Obligation-imposing rules are both a reason for an action and an exclusionary reason not to act on reasons that are inconsistent with conformity to the rule. Aside from its independent philosophical contribution to the theory of practical reasoning, the thesis that obligatory rules comprise protected reasons has played an important role in contemporary legal philosophy. To provide one example: it is the basis of a powerful argument for the thesis that the validity of all law can be determined through reference to its sources, without recourse to moral argument.Footnote 8 More fundamentally, the view that legal rules purport to impose protected reasons for action provides an attractive reason-based explanation of the peremptory character of obligations issuing from legal authority. If obligations are binding, they have a characteristic “content-independent” deliberative function that is difficult to explain if we regard their force as depending on their underlying merit.Footnote 9
There are important objections to Raz's analysis that I will not address.Footnote 10 My purpose is not to revisit these debates, as significant as they are, but to consider the application of the account to the common law—in particular to precedential reasoning. It would be interesting, to say the least, if such a well-known account of legal authority were challenged by the prioritized reason model of precedential constraint. I intend to show that the protected reason model gives a coherent account of precedential constraint—at least as coherent as that offered by the prioritized reason model.
Section II of this article sets out the necessary formal preliminaries. Section III simply restates the prioritized reason model of precedent.Footnote 11 The presentation of the model will be brief, but readers already familiar with it are invited to proceed to Section IV of this article. Section IV sets out and independently motivates the protected reason model of precedential constraint. Section V compares the protected reason model with the prioritized reason model of precedent. I observe that the protected reason model and the prioritized reason model offer equivalent accounts of the outcome of precedentially constrained reasoning. I argue that the protected reason model gives an independently plausible account of precedential constraint, which coheres with an attractive account of the role of mandatory norms in practical reasoning. I then present an account of precedential constraint that reconciles the prioritized reason model with the protected reason model. In Section VI, I offer, in passing, some brief reflections on the relation between the protected reason model and strict rule-based approaches to precedent.
II. PRELIMINARIES
The prioritized reason model of precedent works on the assumption that legal problems can be described in terms of reasons, understood as sets of factors, that favor an outcome for either the plaintiff or the defendant (the reasons’ “polarity”). For simplicity's sake I rely on the same notation as Horty.Footnote 12 I will briefly introduce this notation and basic concepts for readers who are unfamiliar.
The set F is a postulated set of all possible legally salient factors. A fact scenario X is any subset of F that represents the set of factors that apply to a given case. Let
$F^\pi = \lcub {f_1^\pi \comma \;\ldots \comma \;f_n^\pi } \rcub $ represent the set of factors favoring an outcome for the plaintiff, and
$F^\delta = \lcub {f_1^\delta \comma \;\ldots \comma \;f_n^\delta } \rcub $ represent the set of factors favoring an outcome for the defendant. We stipulate that
$F = F^\pi \cup F^\delta $ (i.e., that all factors favor the plaintiff or the defendant). Where X is a fact scenario, let
$X^\pi = X \cap F^\pi $ and
$X^\delta = X \cap F^\delta $.
A reason R is any subset of factors in F favoring the same outcome. (This definition disallows a set like
$\lcub {f_1^\pi \comma \;f_2^\delta } \rcub $ from being a reason, since one of the factors in the set favors an outcome for the plaintiff while the other favors the defendant.) A reason is satisfied in a given fact scenario just in case it is some subset of the reasons that describe that scenario.
Definition 1 (Satisfaction of Reasons): For a given fact scenario X and reason R, X satisfies R, written
$\;X \,{\rm \models }R\comma \;$ just in case R ⊆ X.
In justifying outcomes for the plaintiff and the defendant, courts formulate rules that state the basis of their judgment. Formally, a rule r is a conditional of the form R → s, where R is the reason cited by a court for the outcome s. The rule, in other words, states the ratio decidendi of a case. A function Premise is used to identify the reason for an outcome for an individual rule, while the function Conclusion is used to identify the outcome of that rule. So for the rule
$r\colon \lcub {f_1^\pi \comma \;f_2^\pi } \rcub \to \pi $,
$Premise\lpar r \rpar = \lcub {f_1^\pi \comma \;f_2^\pi } \rcub $ and Conclusion(r) = π. A rule is applicable in a fact scenario just in case the reason for the outcome, identified by the Premise function, is satisfied by that fact scenario.
Definition 2 (Applicable Rule): A rule r is applicable in fact scenario X just in case
$X \, {\rm \models }Premise\lpar r \rpar $, or, equivalently, Premise(r) ⊆ X.
Precedent cases involve a fact scenario X along with an outcome s and a rule r connecting some salient set of factors in X with the outcome. A case base is any set of cases. Three functions Factors, Rule, and Outcome identify the factors, rule, and outcome of the case respectively. For any case 〈c = X, r, s〉, Factors(c) = X, Rule(c) = r and Outcome(c) = s. The notation
$\bar{s}$ will be used to indicate that the outcome of a case or the polarity of a set of reasons is the opposite of s (e.g., where s is π then
$\bar{s}$ is δ). The notation X s represents the set of all factors in X favoring outcome s.
Definition 3 (Cases and Case Bases): A case c is a triple
$c = \langle X\comma \;\;r\comma \;\;s\rangle$ where X is a set of factors that apply to the case, r is a rule, and s the outcome of the case. A case base Γ is any set of cases {c, c′, …, c″}.
The outcome of a decision, s, must be π, an outcome for the plaintiff or δ, an outcome for the defendant. In order to ensure coherence, we stipulate that for any case 〈c = X, r, s〉 belonging to a case base Γ, Premise(r) ⊆ X s. The reason cited by the court in ruling for an outcome must be a reason favoring that outcome. Moreover, it must be a reason favoring that outcome that is satisfied in the context of the fact scenario facing the court.Footnote 13 We also stipulate that Conclusion(c) = Outcome(r). The ratio of a case cannot be framed in terms of a rule supporting the opposite outcome to the case.
With these preliminaries in mind, I will now turn to offering a brief exposition of the prioritized reason model of precedent.
III. THE PRIORITIZED REASON MODEL OF PRECEDENT
The prioritized reason model exploits the idea that each decision in a factual scenario X involving a rule r allows us to derive a priority order over the reasons that apply in that factual scenario. To offer a simplistic example, consider a court's approach to determining whether a defendant is liable for injury caused to the plaintiff because of their operating a vehicle. Suppose the court reasons against the background of a case base Γ1 that contains only one case, 〈c 1 = X 1, r 1, π〉. In c 1 the court considered two salient plaintiff-favoring reasons, so that
$X_1^\pi = \lcub {f_1^\pi \comma \;\;f_2^\pi } \rcub $. First, let
$\lcub {f_1^\pi } \rcub $ represent the court's reason to rule for the plaintiff because the defendant was traveling too quickly. Second, let
$\lcub f_2^\pi $} represent the court's reason to rule for the plaintiff because the defendant knew that the plaintiff was on the road when the accident occurred and should therefore have been more careful. Furthermore, suppose that in c 1 the court considered a single defendant-favoring reason, so that
$X_1^\delta = \lcub {f_1^\delta } \rcub $, where
$\lcub {f_1^\delta } \rcub $ represents the court's reason to find for the defendant because the defendant was riding a bicycle, which is an environmentally friendly vehicle. The court then decided for the plaintiff in terms of rule
$r_1\colon \lcub {f_1^\pi } \rcub \to \pi $.
This outcome for the plaintiff can be understood in terms of the c 1 court's decision to give a reason for the plaintiff (that the defendant was traveling too quickly) priority over the reason to find for the respondent because the defendant was riding an environmentally friendly vehicle. In other words, the explicit priority order for the case is such that
$\lcub {f_1^\delta } \rcub \lt _{c_1}\lcub {f_1^\pi } \rcub $. (Read
$P \lt _{c_1}Q$ as meaning that the reason Q is of higher priority than reason P according to the priority order derived from the case c 1.) Implicitly, the plaintiff will also prefer any plaintiff-sided reason of which
$\lcub {f_1^\pi } \rcub $ is a subset over any defendant-sided reason that is a subset of
$\lcub {f_1^\delta } \rcub $. Any reason of which
$\lcub {f_1^\pi } \rcub $ is a subset would be, ipso facto, at least as strong or stronger for the plaintiff, while any reason that is a proper subset of
$\lcub {f_1^\delta } \rcub $ would be at least as weak or weaker for the defendant. For example, we can imply from a decision for the plaintiff based on rule r 1 in c 1 that
$\lcub {f_1^\delta } \rcub \;\lt _{c_1}\;\lcub {f_1^\pi \comma \;\;f_2^\pi \comma \;f_3^\pi } \rcub $, where
$f_3^\pi $ is any further factor favoring the plaintiff. For any case c a priority ordering over the reasons applicable in that case can be derived in this fashion. More formally, we define the derived priority order for a case as follows.
Definition 4 (Derived Priority Order for a Case): For any case
$c = \langle X\comma \;\;r\comma \;\;s\rangle$ a priority order between reasons, <c is derived by stipulating that for any two reasons P and Q, P < cQ just in case
$P\subseteq \;X^{\bar{s}}\;$and Premise(r)⊆ Q.
This definition of a derived priority order for a case is then extended to define a derived priority order for a case base.
Definition 5 (Derived Priority Order for a Case Base): A priority order for a case base
$\lt _\Gamma $ is derived by stipulating that for two reasons P and Q,
$P \lt _\Gamma Q\;$just in case P < cQ for some case c in Γ.
We then introduce the notion of reason inconsistency and use it to define consistency for a case base. Informally, a case base is reason consistent just in case we cannot derive an inconsistent priority order—i.e., if there are no two cases such that in the first case a reason P is of higher priority than Q in the derived priority order while in the second case Q is of higher priority than P in the derived priority order.
Definition 6 (Reason Consistency for a Case Base): A derived priority order for a case base Γ,
$\lt _\Gamma $, is reason inconsistent just in case there are reasons P and Q such that
$P\;\lt _\Gamma \;Q$ and
$Q \lt _\Gamma P$. A case base Γ is reason consistent just in case it is not reason inconsistent.
From this account of reason consistency we derive an account of precedential constraint. According to the prioritized reason model of precedential constraint, a new decision is constrained by prior decisions in the sense that the new decision must be consistent with the priority order fixed by the earlier body of precedent. In other words, a new decision must not introduce reason inconsistency into the case base.
Definition 7 (The Prioritized Reason Model of Precedential Constraint): In a new fact scenario X, a decision in X based on the rule r and leading to outcome s will satisfy the prioritized reason model of precedential constraint just in case
${\rm \Gamma } \cup \lcub {X\comma \;r\comma \;s} \rcub $ is reason consistent.
To illustrate the prioritized reason model of precedent, consider again the position of a court that reasons against the background of Γ1. In the new fact scenario before them,
$X_2 = \lcub {f_1^\pi \comma \;f_2^\pi \comma \;f_3^\pi \comma \;\;f_1^\delta } \rcub $, the same reasons apply as in X 1 except that there is a further plaintiff-favoring reason,
$\lcub {f_3^\pi } \rcub $, which is that the defendant was riding their bike without any lights after dark, and no other salient reason for the defendant. Suppose the members of the court are particularly environmentally conscious, and wish to adopt the rule
$r_2\colon \lcub {f_1^\delta } \rcub \to \delta $ and rule in favor of the defendant because they want to promote cycling, which is environmentally friendly. The court is constrained from ruling for the defendant on this basis. Adding the case 〈c 2 = X 2, r 2, δ〉 to Γ1 would introduce inconsistency into the case base because we could then derive the priority relation
$\lcub {f_1^\pi \comma \;f_2^\pi \comma \;f_3^\pi } \rcub \lt _{c_2}\lcub {f_1^\delta } \rcub $, which is inconsistent with the priority order
$\lt _{c_1}$.
The prioritized reason model offers a useful framework for exploring the relationship between individual decisions and the emergence of a settled priority order through collective adoption of precedents. It offers a particularly attractive framework with which to study the dynamics of a case base. Over time, precedential decision-making is taken to fix a sort of collective priority order over a set of relevant factors. An individual i deciding against the background of a case base Γ is required to reconcile their own priority order <i with the priority order derived from the case base
$\lt _\Gamma $.Footnote 14 The priority order that emerges from a body of precedent reflects the gradual contributions of individual decision-makers. When unconstrained, decision-makers are free to decide cases in terms of their own priorities. However, if they are to be consistent with precedent, then subsequent decisions cannot unsettle the priority order established by earlier judgments.
The prioritized reason model also offers an elegant explanation of the way in which courts entrench rules through application to future cases. Suppose a court faces a new fact scenario
$X_3 = \lcub {f_1^\pi \comma \;\;f_2^\delta } \rcub \comma \;$ against the background of Γ1, and decides to apply rule r 1. In this fact scenario, the court is not bound by precedent on the prioritized reason model, since
$\lcub {f_2^\delta } \rcub $ was available as a distinguishing reason for ruling for the defendant. The court's decision, represented in the case
$c_3 = \langle X_3\comma \;\;r_1\comma \;\;\pi \rangle$, further entrenches the rule r 1. Since
$\lcub {f_2^\delta } \rcub \lt _{c_3}\lcub {f_1^\pi } \rcub $, this prioritization of reasons is added to the derived priority order for the case base
$\lt _{\Gamma _1 \cup \lcub {c_3} \rcub }$ and the reason
$\lcub {f_2^\delta } \rcub $ is now unavailable as a distinguishing reason in future cases in which r 1 is applicable.
The prioritized reason model, like the protected reason model developed below, offers a sort of intermediate position between models that take precedent to consist in following strict rules that are incapable of modification, and models that take precedential reasoning to be nothing other than a form of unconstrained natural reasoning.Footnote 15 As Horty notes, the prioritized reason model also holds particular interest when viewed from a social choice perspective: social priorities are aggregated through a process of constrained individual reasoning that is “piecemeal, distributed, and responsive to particular circumstances.”Footnote 16 This is a particularly valuable aspect of the model—one that in my opinion deserves further attention. Nonetheless, a striking feature of the prioritized reason model is that it offers a somewhat novel account of the function of common law rules. Rather than excluding reasons from consideration in future cases in which the rules are applicable, the model treats decisions as reasons for assigning certain weight or priority to other reasons.Footnote 17 In the remainder of this article I compare the prioritized reason model with an alternative, though closely related, model of precedent, which is based on the idea that binding precedent creates protected reasons.
IV. THE PROTECTED REASON MODEL OF PRECEDENT
Protected reasons were introduced into the philosophy of practical reason by Raz, though the idea has precursors in the work of other moral and legal philosophers.Footnote 18 A protected reason is both a reason for an action and an “exclusionary” reason not to act on some set of other reasons inconsistent with that action. Raz illustrates the notion of a protected reason with a set of examples, one of which is the case of Ann, who is considering a good way to invest her money. Late one night Ann is offered an opportunity to make an investment. She is told that she must decide before midnight, when the offer is withdrawn.Footnote 19 Ann decides that she is too tired to make a rational decision about the investment on its merits, so she rejects the offer. Her decision to reject the offer without considering it on its merits can be interpreted in terms of a protected reason. She has a good reason not to make the investment, because she is too tired. But she also has a good exclusionary reason not to base her decision on those reasons relating to the merits of the investment.Footnote 20 Importantly, protected reasons do not exclude all other reasons. Ann's decision, for instance, appears only to exclude reasons relating to the merits of the investment. It may be that there are reasons for making the investment on which it would still be appropriate for Ann to base her judgment—maybe, for instance, Ann has a pressing taxation deadline that means she must make an investment as quickly as possible, in spite of her fatigue.Footnote 21 The scope of exclusion is restricted. In legal settings, the scope of exclusion usually reflects the scope of the authority issuing the directive. I discuss the implications of this for the protected reason model in Section VI.
Protected reasons explain the content-independence of legal obligations: the purported force of legal obligations is not dependent on their underlying merit.Footnote 22 In this respect, legal obligations resemble other forms of content-independent obligation, such as promissory obligations. If the protected reason account of legal content is correct, then it should be equally applicable to common law reasoning. Obligatory legal norms create protected reasons. Precedential constraint imposes obligations on judges.Footnote 23 We would therefore expect precedential constraint to be a source of protected reasons.Footnote 24
According to the protected reason model of precedential constraint, a case will constrain a subsequent court or decision-maker when the rule formulated by the court in a prior case is applicable to the new fact scenario and where there are no new distinguishing reasons, since the decisive reason for the outcome identified in the prior case is satisfied by the new scenario. The protected reason model has its origins in a reason-based account of precedent initially offered by Grant Lamond in the same article cited by Horty in his development of the prioritized reason model.Footnote 25 In his presentation of the account, Lamond suggests that precedents may provide protected reasons:
Applying this analysis to precedents, the ratio would provide the basis for the first-order part of the protected reason. The other facts of the case would provide the basis for the exclusionary reason; later courts are excluded from relying on reasons provided by features that were present in the precedent case to defeat the first-order reason for the result.Footnote 26
On the protected reason model the previous decision provides a reason to decide in the same way whenever the rule enacted in the decision is applicable to a future case. It also provides a reason to exclude reasons for the opposing outcome in the same future cases.
Lamond is careful not to endorse the protected reason model. In fact he uses it only to anticipate a possible objection to his account—that it is simply a version of the rule model of precedent.Footnote 27 (I return to this point in discussion below.) It is nonetheless an approach that I find appealing, since it coheres with an influential account of the role of legal sources in practical reasoning. In the remainder of this section I will attempt to formalize the insights behind Lamond's protected reason model of precedential constraint and then defend its merits as an account of precedential constraint. Unsurprisingly given that they both are indebted to Lamond's proposal, the protected reason model and the prioritized reason model are formally very similar.
The first step toward formalizing the protected reason account is to identify the reasons excluded as a result of a decision. In a formal setting, exclusionary reasons can be modeled as undercutting reasons connecting a set of applicable facts with the undercutting or exclusion of an otherwise applicable reason for the opposing outcome.Footnote 28 Wherever the precedent rule is applicable, it would provide reasons for excluding all such reasons in future decisions. In the context of our case-based models, however, we will not need to introduce exclusionary reasons themselves into the model. It will be sufficient to identify a set of otherwise satisfied reasons that are excluded in a given case. Recall that on the protected reason model, a previous decision in a case acts as a reason for excluding all reasons for the opposing outcome that were satisfied in that case. For instance, if the previous decision is represented with the case
$c_4 = \langle X_4\comma \;r_3\comma \;\pi \rangle$, where
$X_4^{{\vskip-3pt-}{\hskip-6pt \pi }} = \lcub {f_1^\delta \comma \;f_2^\delta } \rcub $, then reasons
$\lcub {f_1^\delta } \rcub $,
$\lcub {f_2^\delta } \rcub $, and
$\;\lcub {f_1^\delta \comma \;\;f_2^\delta } \rcub $ would all be excluded from acting as the basis for a decision for δ in a subsequent case in which the binding rule r 3 was applicable. This idea is captured in the following definition of the set of excluded reasons for a case. The definition uses the power set notation,
${\cal P}\lpar {X^{\bar{s}}} \rpar \comma \;\;$to refer to the set of all sets of factors for the opposing outcome present in scenario X. In the case c 4 = 〈X 4, r 3, π〉, for instance,
${\cal P}\lpar {X_4^{{\vskip-3pt-}{\hskip-6pt \pi }} } \rpar = \lcub {\emptyset \comma \;\lcub {f_1^\delta } \rcub \comma \;\lcub {f_2^\delta } \rcub \comma \;\lcub {f_1^\delta \comma \;f_2^\delta } \rcub } \rcub $.
Definition 8 (Excluded Reasons for a Case): For any case
$c = \langle X\comma \;\;r\comma \;\;s\rangle$, a set of excluded reasons for that case is defined by taking every subset of factors for the opposing outcome,
$\bar{s}$, that were satisfied in that case. More formally, for a case
$c = \langle X\comma \;\;r\comma \;\;s\rangle$, Excluded c
$ = {\cal P}\lpar {X^{\bar{s}}} \rpar.$
Of course, that reasons were excluded in a prior case does not prevent a court from basing a future decision on one of those reasons, unless the precedent rule established in the prior case is applicable to the present case. The protected reason mode of precedential constraint developed here exploits the idea of exclusion consistency. A case base will be exclusion inconsistent just in case there is a case that invokes a reason for its outcome that is excluded by an applicable prior rule. Recalling that a rule r established in a prior decision will be applicable in a fact scenario X whenever the rule's premise is satisfied in X, i.e., when
$X \,{\rm \models }Premise\lpar r \rpar $, we can adopt the following formal definition of exclusion consistency.
Definition 9 (Exclusion Consistency): A case base Γ is exclusion consistent just in case there is no case
$c = \langle X\comma \;r\comma \;s\rangle$ in Γ such that for another case
$\langle{c}^{\prime} = {X}^{\prime}\comma \;{r}^{\prime}\comma \;\bar{s}\rangle\;$in Γ,
${X}^{\prime} \,{\rm \models } \,Premise\lpar r \rpar $ and Premise(r′) ∈ Excluded c.
This then allows us to give a straightforward account of precedential constraint in terms of the preservation of exclusion consistency for a case base.
Definition 10 (Protected Reason Model of Precedential Constraint): Let Γ be a case base. In a new fact scenario X, a decision in X based on the rule r and leading to outcome s will satisfy the protected reason model of precedential constraint just in case
${\rm \Gamma } \cup \lcub {X\comma \;r\comma \;s} \rcub $ is exclusion consistent.
It is useful to consider an example of precedential constraint on the protected reason model. As before, we will suppose that our decision-maker must decide whether to find for the plaintiff in a dispute over injury caused while the defendant was driving their vehicle, where they have a single prior decision
$c_1 = \langle X_1\comma \;r_1\comma \;\pi \rangle$ in the case base Γ1, where
$X_1^\pi = \lcub {f_1^\pi \comma \;\;f_2^\pi } \rcub $, where
$X_1^\delta = \lcub {f_1^\delta } \rcub $, and where the rule applied in c 1 was
$r_1\colon \lcub f_1^\pi \rcub \to \pi $. Suppose that the decision-maker faces the fact scenario introduced earlier,
$X_2 = \lcub {f_1^\pi \comma \;f_2^\pi \comma \;\;f_3^\pi \comma \;\;f_1^\delta } \rcub $. Suppose again that we have an environmentally concerned judge, whose personal assessment of the case on the merits is to rule for the defendant on the basis of the rule
$r_2\colon \lcub f_1^\delta \rcub \to \delta $, because the defendant was riding a bicycle. The court is again constrained by precedent from giving such a ruling on the protected reason model. First, note that
$\lcub {f_1^\delta } \rcub \in Excluded_{c_1}$since
$\lcub {f_1^\delta } \rcub \subseteq X_1^{{\vskip-3pt-}{\hskip-6pt \pi }} $. Second, note that the rule r 1 formulated in c 1 is applicable to the new scenario X 3, because
$Premise\lpar {r_1} \rpar = \lcub {f_1^\pi } \rcub $ and
$X_2{\rm \models }\lcub {f_1^\pi } \rcub $. It follows that
$\Gamma _1 \cup \lcub {X_2\comma \;\;r_2\comma \;\;\delta } \rcub $ would be exclusion inconsistent. The judge cannot rule for the defendant on the basis of rule r 2 without introducing exclusion inconsistency into the case base. Now suppose that our judge is faced with a different scenario
$X_5 = \lcub {f_1^\pi \comma \;f_1^\delta \comma \;f_3^\delta } \rcub $, where
$\lcub {f_3^\delta } \rcub $ represents a new reason to find for the defendant, this time because the defendant is a surgeon who was desperately cycling to hospital to help out in an emergency. In this scenario, the judge is not constrained from finding for the defendant on the basis of
$r_4\colon \lcub {f_3^\delta } \rcub \to \delta $, since
$\lcub f_3^\delta \rcub \notin Excluded_{c_1}\;$and this new reason is therefore available as a distinguishing factor. Supposing that the decision for defendant in this case is represented by the case
$\langle c_5 = X_5\comma \;r_4\comma \;\delta\rangle \comma \;\;\Gamma _1 \cup \lcub {c_5} \rcub $ will not be exclusion inconsistent.
Unsurprisingly given their common origins, there are obvious similarities between the prioritized reason model and the protected reason model. In fact, it can be demonstrated that a new decision will satisfy the protected reason model of precedent on just the same cases as it will satisfy the prioritized reason model. The equivalence, in this sense, between the two models of precedential constraint follows from the correspondence of reason consistency and exclusion consistency.
Fact 1: A case base Γ is reason consistent just in case Γ is exclusion consistent.
Since a case base is reason consistent just in case it is exclusion consistent, it follows that a decision in some new fact scenario will satisfy the protected reason model of precedential constraint just in case it will satisfy the prioritized reason model.
Fact 2: Let Γ be a case base and X be a new fact scenario; then a decision in the situation X satisfies the protected reason model of precedential constraint if and only if that same decision satisfies the prioritized reason model.
These facts are verified in an Appendix to this article. To illustrate the equivalence between the two approaches we can return to the same example of a case base Γ1 involving the previous decision c 1 = {X 1, r 1, π}, where the decision-maker is as before faced with the new fact scenario
$X_2 = \lcub {f_1^\pi \comma \;f_1^\delta } \rcub $. On the prioritized reason model, because
$Premise^\pi \lpar {r_1} \rpar \subseteq \lcub f_1^\pi \rcub $ and
$\lcub f_1^\delta \rcub \subseteq X_1^{{\vskip-3pt-}{\hskip-6pt \pi }} $, then according to the derived priority order, {
$f_1^\pi \rcub \lt _{c_1}\lcub {f_1^\delta } \rcub $. The judge is precedentially constrained from giving a decision for the defendant on the reason account. Any case c 2 allowing an outcome for the defendant would introduce reason inconsistency into the case base, since it would follow that
$\lcub {f_1^\delta } \rcub \lt _{c_2}\lcub {f_1^\pi } \rcub $. On the protected reason model, since
$Premise\lpar {r_1} \rpar = \lcub {f_1^\pi } \rcub $ and
$\lcub f_1^\pi \rcub \subseteq X_2$, r 1 will be applicable in fact scenario X 2. Since
$\lcub f_1^\delta \rcub \subseteq X_1^{{\vskip-3pt-}{\hskip-6pt \pi }} $, it follows that
$\lcub f_1^\delta \rcub \in Excluded_{c_1}.\;$This constrains the judge from adopting any rule r 2 such that Outcome(r 2) = δ and
$Premise\lpar {r_2} \rpar = \lcub {f_1^\delta } \rcub.$
Lamond's initial version of the protected reason account of precedential constraint utilized a simple list of excluded factors. A list of factors that is excluded is extracted from past decisions by identifying all factors that were applicable in previous decisions with an opposing outcome.Footnote 29 Any combination of these factors cannot then be relied on in a further judgment in which a past decision was applicable. As Horty notes, Lamond's use of a simple list of excluded factors precludes the possibility that two factors that formed part of past cases but were never considered together may nonetheless comprise a new reason that should not be excluded.Footnote 30 To illustrate this, consider a case base Γ2 involving the two cases introduced above, c 1 = {X 1, r 1, π} and
$c_3 = \langle X_3\comma \;\;r_1\comma \;\;\pi \rangle$, recalling that
$X_1^{{\vskip-3pt-}{\hskip-6pt \pi }} = \lcub {f_1^\delta } \rcub $ and
$X_3^{{\vskip-3pt-}{\hskip-6pt \pi }} = \lcub {f_2^\delta } \rcub $. Using Lamond's original approach, the list of excluded factors would include
$\;f_1^\delta \;$and
$\;f_2^\delta $. Against the background of Γ2, a judge faced with fact scenario
$X_6 = \lcub {f_1^\pi \comma \;\;f_1^\delta \comma \;\;f_2^\delta } \rcub \;$would therefore be bound to rule for the plaintiff on the basis of rule r 1, since the rule is applicable and both of the factors present belong to the list of excluded factors. On the protected reason model developed here, however, though the rule r 1 is applicable in scenario X 6, the reason
$\lcub {f_1^\delta \comma \;\;f_2^\delta } \rcub $ was not excluded in any of the applicable cases in Γ2, so a ruling for the defendant would not introduce exclusion inconsistency into the case base.
Like the prioritized reason model, the protected reason model modifies Lamond's approach by treating reasons as sets of factors, rather than individual factors. On both models, cases reveal a relation between the reason for the outcome, as expressed in the premise of the rule applied in a given case, and any applicable reasons for the opposing outcome. The difference is that where the prioritized reason model interprets the relation between two sets of reasons in terms of priority or weight, the protected reason model interprets the relation in terms of exclusion. The close similarities between the prioritized reason model and the protected reason model are therefore unsurprising. The remainder of this article is devoted to discussing the philosophical significance of this result. I first argue that the protected reason model is better able to account for the phenomenology of precedential constraint. I then suggest that the prioritized reason model and the protected reason model can be incorporated into a unified account of precedential reasoning. I conclude by reflecting on some important points of distinction between the protected reason model and an account of precedent in terms of strong rules.
V. THE PRIORITIZED REASON MODEL AND THE PROTECTED REASON MODEL
On the protected reason model developed in the previous section, a past decision binds a subsequent decision-maker when the rule relied on in the previous decision is applicable to the factual scenario that applies in the subsequent case. The decision-maker must take the ratio of the previous decision as a reason for deciding in the same way and a reason for excluding otherwise applicable reasons present in these past cases from acting as the basis for an inconsistent judgment. By way of comparison, on the prioritized reason model of precedential constraint the ratio of a previous decision can be construed as providing both a reason for the outcome and a second “intensifying” reason for assigning greater priority to the decisive reason over any applicable reason for the opposing outcome.Footnote 31
From one perspective, the difference between the prioritized reason model and the protected reason model is relatively small. In both approaches, a decision in a case is interpreted in terms of a reason for an outcome and another modifying reason that strengthens that reason through a process of either intensification or exclusion.Footnote 32 Moreover, as we have seen, in simple factor-based accounts of precedent both generate the same result. However, I wish to argue that the protected reason model offers a superior account of the phenomenology of precedential constraint: when a decision-maker takes themselves to be bound by precedent, they exclude what might otherwise be good reasons for their decision from providing a basis for their judgment.Footnote 33
Raz suggests a test with which we can distinguish cases where a reasoner is constrained by a protected reason from cases in which one reason is simply regarded as weightier or more stringent than another. He suggests that there is “a peculiar feeling of unease, which will show itself when we wish to censure a person who acted on the balance of reasons for disregarding the exclusionary reason and when we have to justify someone's acting on an exclusionary reason against claims that the person should have acted on the balance of reasons.”Footnote 34 The judge who refuses to be constrained by precedent from following their own assessment of the balance of reasons puts us in exactly the situation of unease that Raz identifies. On the one hand, they are acting in a way that we regard as rationally intelligible, and even praiseworthy, since they are following what, on their own lights, they regard as the best course of action. On the other hand, they are neglecting the duties of their office, which give them reason not to act on their own assessment of reasons.
It is useful to compare the situation of the common law judge with the situation faced by an individual who reevaluates one of her own prior decisions.Footnote 35 Suppose that Mary receives two attractive offers for a Friday lunch date—one from her sister and another from her friend—and decides that she will have lunch with her friend and send apologies to her sister. Mary soon realizes that she made the wrong decision—she had better reasons to meet her sister for lunch. Once she has made her decision, however, Mary takes herself to have a good reason not to revise it, even given her previous assessment on the merits. It seems just as wrong in Mary's case to suggest that she must reconcile herself with the earlier priority she assigned to the two lunch offers. For why then should she feel any unease or regret about changing her mind? Rather Mary takes her previous decision as a reason not to act on any revision she makes to her priorities in this case. She may still wish to bear in mind, for the sake of future decision-making, that she regards meeting her sister as having priority over lunch with a friend. But, thanks to her decision, Mary is constrained in this case from acting on her own assessment of the balance of reasons.
It is open to proponents of the prioritized reason model to say that their own account of the nature of precedential reasoning is consistent with the “peculiar feeling of unease” that Raz identifies in these cases. On one interpretation, however, the prioritized reason model treats previous decisions as reasons for a court to alter its assessment of the underlying strength of reasons. If this were the case, then in the absence of reasons not to alter their assessment, there would be no rational tension for courts to resolve. The proper effect of the precedent would be to alter the weight the court assigns to its underlying reasons. By way of contrast, protected reasons seem to offer a plausible account of the source of this discomfort. The court does not alter its own assessment of underlying reasons, it simply takes itself to have good reason not to rely on that assessment.
More plausibly, proponents of the prioritized reason model argue that our unease or discomfort with following precedent contrary to our own assessment of the balance of reasons is a result of the requirement that the court reason as if certain reasons have greater strength than the court believes they possess. According to Horty, precedential constraint provides courts with “further, higher-level reasons for favoring reasons derived from earlier cases over those deriving from their own values.”Footnote 36 Stephen Perry similarly claims that precedent gives past decisions a certain “presumptive weight” when compared with the court's own assessment of the underlying merits of the case.Footnote 37 These are intriguing suggestions. However, both still rely on an account of precedential constraint in terms of courts’ having a reason to favor, or prioritize, reasons derived from past cases over their own assessment, rather than a reason to exclude reasons to act on their own assessment altogether.
On the prioritized reason model, the court's assessment of the underlying reasons is compared with the priorities revealed by past cases, and the priorities revealed by past cases are favored. On this model, a strong enough reason for following their own assessment could defeat a court's reason to follow the priorities revealed by a past case. This may be the correct account of precedential constraint in courts that are given a power to depart from their own precedents in cases where they regard themselves as having a sufficiently strong reason to do so.Footnote 38 But courts bound by precedent do not merely seem to favor reasons from past cases over their own assessment of the reasons. Where they accept the authority of a binding precedent, courts take themselves to have a reason not to base their judgment on their own assessment of reasons, however strong their reasons for departing from precedent might be.
As I noted in my presentation of the prioritized reason model, one of the many valuable contributions made by the model is that it draws attention to the relationship between institutional priorities and the priorities of individual decision-makers. Fortunately, it is possible to present a unified account of the reason and protected reason models that combines the strengths of both models of precedential constraint. In fact, my conjecture is that both the prioritized reason model and the protected prioritized reason model are accurate, but that they describe different aspects of the complex process of reasoning that allows for a collective preference order to emerge from different decision-makers following precedent. The models differ in their account of the reasons imposed by precedential constraint, but not in their account of unconstrained reasoning, nor in their view of underlying structure of the priority relations revealed by precedential judgments. According to the protected reason model, when a decision-maker takes themselves to be bound by precedent, they take opposing reasons that were applicable in that prior decision to be excluded from being relied on as grounds for their decision. When a decision-maker is not constrained by precedent, then they engage in the usual process of comparison familiar from natural reasoning. They act as a kind of restricted legislator—adopting the rule they think best resolves the dispute before them.Footnote 39 The reasons excluded from consideration in subsequent cases are excluded because, in a former case, they were deemed by an unconstrained court to be of lesser priority than the same reasons applicable in the subsequent case. Over time a series of decisions by courts bound by precedent will reveal a sort of collective priority order, one that is determined through a series of piecemeal acts of judicial discretion.
Consider, yet again, the position of our environmentally concerned judge, who is reasoning against the background of a case base Γ1 = {c 1} and who would like to rule for the defendant in fact scenario
$X_2 = \lcub {f_1^\pi \comma \;f_1^\delta } \rcub $ on the basis of the rule
$r_2\colon \lcub {f_1^\delta } \rcub \to \delta $. Instead the judge rules for the plaintiff, with the ruling represented by case 〈c 6 = X 2, r 1, π〉 because they take
$\lcub {f_1^\delta } \rcub $ to be excluded from being a reason for ruling for the defendant. Now suppose that in the decision in
$c_5 = \langle X_5\comma \;r_4\comma \;\delta \rangle$ where fact scenario
$X_5 = \lcub {f_1^\pi \comma \;\;f_1^\delta \comma \;f_3^\delta } \rcub $, a different court is unconstrained and so rules for the defendant on the basis of
$r_4\colon \;\lcub {f_3^\delta } \rcub \to \delta $, where
$\lcub {f_3^\delta } \rcub $ is a reason to find for the defendant because they were rushing to the hospital to perform emergency surgery. Let all three decisions now be represented by the updated case base
$\Gamma _3 = \Gamma _1 \cup \lcub {c_5\comma \;c_6} \rcub $. These decisions can be interpreted in terms of a priority order such that
$\lcub f_1^\delta \rcub \lt _{\Gamma _3}\lcub {f_1^\pi } \rcub $ and
$\lcub {f_1^\pi } \rcub \lt _{\Gamma _3}\lcub f_3^\delta \rcub $. Though they are not identical to any individual decision-maker's priority order over a set of reasons, the decisions in question can still be taken to reveal a collective priority order.Footnote 40 This revealed priority order will be consistent so long as subsequent courts take themselves to be constrained from basing their judgments on excluded reasons. In this way we can unify the protected reason and reason models of precedent. The protected reason model is adapted as an account of precedential constraint, while the prioritized reason model is retained as an account of the collective priority order over reasons that is revealed through a process of precedential reasoning.
Having suggested this unified account of the protected and prioritized reason models, I should acknowledge one way in which the models may diverge. Horty notes that the prioritized reason model can be extended by an assumption of transitivity, so that for any given case base Γ, where P, Q, and R are reasons, if
$P \lt _\Gamma Q$ and
$\;Q\;\lt _\Gamma \;$R then
$P \lt _\Gamma R$.Footnote 41 Horty then shows that an account of precedential constraint can be adopted that requires new decisions to be consistent with a priority order extended by the addition of the transitivity assumption.Footnote 42 While it might be formally possible to modify the protected reason model to capture a similar relationship of transitivity, I do not think it is plausible. It does not seem safe to infer from the fact that reason P excludes reason Q in one scenario, while reason Q excludes reason R in another, that reason P will exclude R in a third scenario.Footnote 43 It is therefore not plausible to represent this stronger form of precedential constraint within the protected reason model. If we adopt an assumption of transitivity on the priority order that exists over a case base, then the account of precedential constraint offered by the prioritized reason model will be stronger than that offered by the protected reason model.
The issues surrounding transitivity merit lengthier discussion than I am able to give them here. Nonetheless, I will note that there are good reasons to be wary of strengthening our account of precedent with an assumption of transitivity. Against the background of a case base Γ,
$\lt _\Gamma $ is best interpreted as a collective priority order, rather than reflecting the priorities of any individual court or judge. From a formal perspective, as Horty notes, strengthening the prioritized reason model to accommodate transitivity raises important concerns about the aggregation of the judgments of different judges and courts into a collective priority order.Footnote 44 In fact, the question of transitivity draws attention to an important difference in perspective between the two different models of precedent I have been considering. At least on one interpretation of the prioritized reason model, consistency in the collective priority order is the primary rationale of case-based reasoning. From this perspective, it is more plausible to think that courts are bound to respect the transitivity of priorities revealed by past cases. On the protected reason model, however, courts are constrained because they take certain reasons to be excluded from providing the basis for their decision, not because they have reason to ensure consistency with a collective priority order. The consistency of the collective priority order emerges only as a result of this reasoning process. Precedential reasoning, like all forms of legal reasoning, takes place against a background struggle between conflicting interests and divergent political forces. In this respect, the protected reason model of precedent provides an explanation for the reasoning process through which courts are constrained from developing the law according to their view of its merits, even where they do not share the commitments or priorities of past courts.
It is true that a court that reaches an outcome that preserves transitivity in the collective priority order is promoting a certain kind of coherence. Courts sometimes have reason to promote the coherence of bodies of law. They can do this in any number of ways. For instance, in addition to preserving the transitivity of the collective priority order, courts may be persuaded that the underlying social values or principles that are promoted by previous decisions favor a certain outcome in a new case.Footnote 45 Even in common law systems, however, courts are not duty-bound to promote coherence.Footnote 46 Later courts can come to disagree with earlier courts about the social values that justify a body of law, even where they agree with the outcomes reached in past cases.Footnote 47 This may lead courts to develop the law in a different direction from that envisaged by earlier courts.
VI. PROTECTED REASONS AND LEGAL RULES
An important further feature of the protected reason model is that, like the prioritized reason model, it incorporates a role for legal rules.Footnote 48 On the protected reason model, the ratio decidendi of a case, which is formulated as a rule stating the court's justification for the outcome, provides the basis for determining when reasons for the opposing outcome should be excluded in future cases. A reason excluded in a prior case is not excluded in a new fact scenario unless the rule determined in the prior case is applicable to the new case. In this sense the protected reason model is compatible with a rule-based approach to precedential reasoning.
There is, however, an important point of distinction between the protected reason model of precedent and the model of precedent in terms of what Larry Alexander and Emily Sherwin call “serious rules.”Footnote 49 This distinction was noted by Lamond in his discussion of the precedential reason model.Footnote 50 (For this reason, in fact, Lamond resisted an analysis of precedent in terms of rules.) The rules that introduce the ratio of a case are far narrower and more easily distinguished than statutory rules. Except in extraordinarily rare circumstances, courts are not allowed to appeal to distinguishing factors in the application of a statute. If precedent does consist in following rules, then on the protected reason model considered here the rules in question are quite narrow—they do not apply to cases in which any single distinguishing factor is present. (Indeed, for proponents of strong rule-based models of precedential reasoning this is seen as a weakness of the prioritized reason model.Footnote 51)
Like the prioritized reason model, the protected reason model offers a moderate rule-based account of precedential reasoning. The ratio of a case provides only a pro tanto reason for later courts to reach the same judgment as in previous cases. On the protected reason model, the rules created by a past case only bind a subsequent court where there is no relevant distinguishing factor. By way of contrast, proponents of the serious rule model of precedent regard common law rules as preempting a decision based on the merits of the case in all cases where the antecedent conditions of the rule are satisfied.Footnote 52 Departure from these serious rules requires courts to explicitly overrule past decisions, or at least identify a clear mistake or exception that was unforeseen by the previous court.Footnote 53 Avoidance of a binding precedent only requires courts to identify a distinguishing reason that was not applicable in any of the past cases that established the precedent. Later courts must treat previous courts’ decisions as correct on their own facts, but are otherwise free to decide new cases on their merits. As Lamond observes, the protected reason model preserves the sense in which the common law involves case-by-case decision-making.Footnote 54 Courts are afforded a high degree of freedom to decide new cases on their merits.
Both serious rules and precedential reasoning can be understood in terms of protected reasons. Unlike serious rules, which purport to exclude all or most inconsistent reasons for action, precedential reasoning only excludes inconsistent reasons that were present in preceding cases.Footnote 55 It is reasonable to expect proponents of the protected reason model to account for the fact that the scope of reasons excluded by binding precedential rules is so narrow. I suspect that the answer lies in the relatively narrow scope of the authority of common law courts. Raz explains that the “difference in the binding force of statutory and common law rules is reasonable given the difference in the circumstances in which the two kinds of rules are made.”Footnote 56 The authority of the common law judge is limited to the resolution of dispute before them. Their judgments cannot exclude from consideration in future cases matters that did not arise. Common law rules only exclude reasons that were applicable in the precedent case because the authority of the court was limited to the resolution of that case. Legislators, on the other hand, are endowed with broader legal authority. The rules they create can be directed at diverse matters and their authority may come from a range of different sources, including their putative democratic legitimacy. Legislative rules are therefore capable of excluding a far more diverse array of reasons from providing the basis for an exception.
VII. CONCLUSION
There are some important limitations to the models of precedential constraint considered here, which lend to both of them a certain degree of artificiality. I have not considered whether the protected reason model could be expanded to deal with dimensions and magnitudes.Footnote 57 Nor have I considered the role played by “intermediate factors” in legal reasoning, where the determination of those factors might also be the result of precedentially constrained reasoning.Footnote 58 In my opinion, neither of these challenges is likely to reveal any theoretically significant point of distinction between the prioritized reason model and the protected reason model. But it remains possible that once the models are adapted to account for these challenges an otherwise hidden point of distinction between the two models will be revealed.
My discussion has also avoided what, for want a better phrase, we might call interpretive issues in precedential reasoning. The ratio of a case can be indeterminate in two ways. First the identification of the justification adopted by a court for a given outcome is often indeterminate—courts are not always explicit about what they take the decisive reasons for the outcome of the case before them to be. Judgments often require interpretation in order for the rule to be determined. Second, even when courts formulate their decisions in terms of explicit rules supporting the outcome of the case, the application of those rules to future cases can be indeterminate. Courts certainly exploit both kinds of interpretive freedom in their judgments, but this aspect of common law reasoning has not been a focus of my discussion.
In his initial formulation of the prioritized reason model, Horty noted the difference between his model and Lamond's, which invoked protected reasons.Footnote 59 He acknowledged finding Lamond's view attractive, but stated that he did not find it necessary to use protected reasons in developing his account. If nothing else, I hope that this article has drawn out an important point of connection between the prioritized reason model as it has developed and its philosophical origins. It is not necessary to appeal to protected reasons in order to develop a formal reason-based model of precedential constraint. But an appeal to protected reasons is not precluded by such an approach.
VERIFICATION OF FACTS
Fact 1: A case base Γ is reason consistent just in case Γ is exclusion consistent.
Verification: We begin by proving that if a Γ is reason consistent then it is exclusion consistent.
Suppose that Γ is reason consistent but not exclusion consistent, meaning that there is some case
$c = \langle X\comma \;r\comma \;s\rangle$ in Γ such that for another case
$c^{\prime} = \langle X^{\prime}\comma \;\;r^{\prime}\comma \;\;\bar{s}\;\rangle$ in Γ, (1)
$X^{\prime} \, {\rm \models } \,Premise\lpar r \rpar $ and (2) Premise(r′) ∈ Excluded c. It follows from (2) and Definition 8 that (3)
$Premise\lpar {r^{\prime}} \rpar \subseteq X^{\bar{s}}$. It follows from (3) and Definition 4 that Premise(r′) <c Premise(r). From (1) it also follows, according to our coherence constraints, that (4)
$Premise\lpar r \rpar \subseteq X^{\prime \bar{\hskip-1pt s}}$. From (4) and Definition 4, it follows that
$Premise\lpar r \rpar \lt _{{c}^{\prime}}Premise\lpar {{r}^{\prime}} \rpar $. But then Γ is not reason consistent, as we had supposed (see Definition 6). We therefore conclude that if Γ is exclusion consistent it is reason consistent.
We then prove that if Γ is exclusion consistent then it is reason consistent.
Suppose Γ is exclusion consistent but reason inconsistent, meaning that there are two cases c and c′ in Γ such that for some reasons P and Q, (5) P <c Q and
$\lpar 6 \rpar \;Q \lt _{c^{\prime}}P$. It follows from (5) and Definition 4 that where 〈c = X, r, s〉, (7)
$P\subseteq X^{\bar{s}}$ and (8) Premise(r)⊆ Q. It follows from (6) and Definition 4 that where
${c}^{\prime} = \langle X^{\prime}\comma \;{r}^{\prime}\comma \;\bar{s}\rangle$, (9) Q ⊆ X ′s and (10) Premise(r′⊆ P. It follows from (7) and (10) that (11)
$Premise\lpar {r^{\prime}} \rpar \subseteq X^{\bar{s}}$. It follows from (11) and Definition 8 that (12) Premise(r′) ∈ Excluded c. It follows from (8) and (9) that Premise(r)⊆ X ′ and therefore that (13)
$X^{\prime} \, {\rm \models } \,Premise\lpar r \rpar $. So it follows from (12) and (13) that Γ is not exclusion consistent as we had assumed (see Definition 9). We therefore conclude that if Γ is exclusion consistent then it is reason consistent.
Fact 2: Let Γ be a case base and X be a new fact scenario, then a decision in the situation X satisfies the protected reason model of precedential constraint if and only if that same decision satisfies the prioritized reason model.
Verification: Verification follows immediately from Fact 1. Let
$c = \langle X\comma \;r\comma \;s\rangle$ be the new decision arising from new fact scenario X. If c satisfies the prioritized reason model of precedential constraint, it follows that
${\rm \Gamma } \cup \lcub c \rcub $ is reason consistent. If
${\rm \Gamma } \cup \lcub c \rcub $ is reason consistent, then it follows from Fact 1 that
${\rm \Gamma } \cup \lcub c \rcub $ is exclusion consistent. If
${\rm \Gamma } \cup \lcub c \rcub $ is exclusion consistent, then c satisfies the protected reason model of precedential constraint. If c satisfies the protected reason model of precedential constraint, it follows that
${\rm \Gamma } \cup \lcub c \rcub $ is exclusion consistent. It therefore follows from Fact 1 that
${\rm \Gamma } \cup \lcub c \rcub $ is reason consistent. If
${\rm \Gamma } \cup \lcub c \rcub $ is reason consistent, it follows that c satisfies the prioritized reason model of precedential constraint.