# What About the Precedent:
An Information-Theoretic Analysis of Common Law

Josef Valvoda${}^{\text{{D}}}$ Tiago Pimentel${}^{\text{{D}}}$ Niklas
Stoehr${}^{\text{{Q}}}$ Ryan Cotterell${}^{\text{{D}},\text{{Q}}}$ Simone
Teufel${}^{\text{{D}}}$

${}^{\text{{D}}}$University of Cambridge, ${}^{\text{{Q}}}$ETH Zürich
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

In common law, the outcome of a new case is determined mostly by precedent
cases, rather than by existing statutes. However, how exactly does the
precedent influence the outcome of a new case? Answering this question is
crucial for guaranteeing fair and consistent judicial decision-making. We are
the first to approach this question computationally by comparing two
longstanding jurisprudential views; Halsbury's, who believes that the
arguments of the precedent are the main determinant of the outcome, and
Goodhart's, who believes that what matters most is the precedent's facts. We
base our study on the corpus of legal cases from the European Court of Human
Rights (ECtHR), which allows us to access not only the case itself, but also
cases cited in the judges' arguments (i.e. the precedent cases). Taking an
information-theoretic view, and modelling the question as a case outcome
classification task, we find that the precedent's arguments share $0.38$ nats
of information with the case's outcome, whereas precedent's facts only share
$0.18$ nats of information (i.e., $58$% less); suggesting Halsbury's view may
be more accurate in this specific court. We found however in a qualitative
analysis that there are specific statues where Goodhart's view dominates, and
present some evidence these are the ones where the legal concept at hand is
less straightforward.

##  1 Introduction

Legal systems around the world can be divided into two major categories
Joutsen (2019): civil law systems, which rely predominantly on the rules
written down in statutes, and common law systems, which rely predominantly on
past judicial decisions, known as the precedent. Within common law systems,
jurisprudential scholars have pondered over the nature of precedent in law for
at least a century Halsbury (1907). Is it the judges' argumentation in the
precedent, or is it the claimants' specific individual circumstances that are
the deciding factor in what becomes the law? Here, we present a new
information-theoretical methodology that helps answer this question.

In common law countries, statutes establish the general idea of the law, but
the actual scope of the law is determined by the courts during a trial. To
keep case outcomes consistent and predictable in subsequent cases, judges are
forced to apply the reasoning developed in prior cases with similar facts
(precedent), to the facts of the new case under the doctrine of _stare
decisis_ (Duxbury, 2008; Lamond, 2016; Black, 2019). This is done by
identifying the _ratio decidendi_ (the reasons for the decision) as opposed to
the _obiter dicta_ (that which is said in passing). The distinction between
ratio and obiter is an important one, since ratio is binding, whereas obiter
is not. This means that courts will only strive to remain consistent in
upholding ratio, but can freely depart from the obiter.

Figure 1: The text of ECtHR cases can be divided into _facts_ , _arguments_
and _outcome_. _Arguments_ cite relevant cases, also known as the _precedent_.

But what does the ratio consist of? There is no accepted overarching theory of
precedent (Duxbury, 2008), but there are two tests of ratio. On the one hand,
Lord Halsbury (1907) claims that what is binding is the judge's reasoning and
arguments. For instance, by using a high degree of abstraction, judges can
analogise physical and psychological pain. A different view has been put
forward by Goodhart (1930), who argues it is the analogy of the facts of the
precedent and the case at hand, without the need for reasoning (e.g. comparing
the pain caused by a knife to that caused by another instrument, requiring a
far lower degree of abstraction). These give rise to the two well-known legal
tests for ratio: Halsbury's test and Goodhart's test.

In this paper, we are the first to approach this problem from a data-driven
perspective, using the European Court of Human Rights (ECtHR)111European Court
of Human Rights (ECtHR) is the court that adjudicates on cases dealing with
the European Convention of Human Rights (ECHR). case law; see Figure 1. We
build a citation network over this corpus in order to have access to many
precedents' full text. Training our model on either the facts or the arguments
of the precedent, we can put Halsbury's and Goodhart's views to the test. We
cast this problem as an information-theoretic study by measuring the mutual
information Shannon and Weaver (1962) between the case outcome and either the
precedent facts or arguments. We find that precedent arguments and case
outcome share information to the degree of $0.38$ nats, whereas facts and case
outcome only share information to the degree of $0.18$ nats (i.e., $58$%
less). We therefore observe that—at least for ECtHR—Halsbury's view of the
precedent is more accurate than that of Goodhart.

##  2 Legal Background

Despite the importance of the precedent in civil law, its operationalization
remains shrouded in philosophical debate centred around _how_ the precedent
actually forms the binding law. Jurisprudentially, we can think of this as
searching for the ratio decidendi in the judgement, i.e. separating the ratio
decidendi from the obiter dicta, or binding law from merely circumstantial
statements. It is the nature of ratio that distinguishes Halsbury's view from
Goodhart's.

###  2.1 Halsbury: Arguments as ratio

The case argument contains the judge's explanation of why the case is decided
the way it is. It incorporates knowledge of the precedent, facts of the case
and any new reasoning the judge might develop for the case itself. We consider
the intuitive position that a legal test is formulated by the argument that
the judge put forward when deciding the case.

A legal test is by its nature part of the ratio and, thus, would be binding on
all subsequent cases. This is the position endorsed by Lord Halsbury (1907).
Under this conception of the ratio, it is the arguments that matter, becoming
the law; the facts of the case are of secondary importance. If a judge acts as
Halsbury suggests they should extract the logic of the implicit legal test of
the precedent, and attempt to largely ignore the specific facts of the case.
Halsbury's view remains the conventional view of the precedent to this day
(Lamond, 2005).

###  2.2 Goodhart: Facts as ratio

In contrast, Goodhart (1930) observes that many cases do not contain extensive
reasoning, or any reasoning at all; judges seem to decide the outcome without
these. Therefore, he claims that the facts of the case together with its
outcome must form the ratio; otherwise, a hypothetical new case with the same
facts as any given precedent could lead to a different outcome. Duxbury (2008)
observes that judges, when in disagreement with the precedent, concentrate on
the facts of a previous case more than one would expect if Halsbury's
hypothesis were fully correct. Halsbury would predict that they should talk
about the facts of previous cases as little as possible, and seek the most
direct route to ratio in the form of argument, but they evidently do not. A
potential explanation is that, when disagreement arises, it is easier for
judges to claim that the facts are substantially different, than to challenge
the logic of the precedent, i.e. to overrule that case. Overruling a previous
judgement is a rare and significant legal event Dunn (2003); Spriggs and
Hansford (2001) because it threatens the stability of the legal system. By
concentrating on facts rather than running the risk of overruling, the judge
can avoid this problem, including the threat of overruling her own previous
judgement.

In support of this view, inspection of the argumentative part of the judgement
reveals judges do not usually formulate legal tests of the kind Halsbury
implies (Lamond, 2005). Neither do judges usually search the precedent for
such legal tests (Alexander and Sherwin, 2008). Goodhart's position suggests
that the precedent operates less as an enactment of rules, but more as
reasoning by analogy; hence it is the good alignment between the facts of the
two cases that leads to consistent outcomes.

##  3 An Information-theoretic Approach

##### Notation.

We denote the set of cases as $\mathcal{C}$, writing each of its element as
$c$. The set of cases that form the precedent for case $c$ are denoted
$\mathcal{P}_{c}\subset\mathcal{C}$. We will consider three main random
variables in this work. First, we consider $O$, a random variable that ranges
over a binary outcome space $\mathcal{O}=\\{0,1\\}^{K}$, where $K$ is the
number of Articles. An instance $o\in\mathcal{O}$ tells us which Articles have
been violated. Since $o$ is a vector of binary outcomes for all Articles, we
can index it as $o_{k}$ to get the outcome of a specific $k^{\text{th}}$
Article and we analogously index the random variable $O_{k}$. We will denote
$o_{c}$ the outcome of a specific case $c$.222We note here that we overload
the subscript notation in this paper. We will use subscript $c$ to denote a
specific case and subscript $k$ to denote a specific article. Next, we
consider $F$, a random variable that ranges over the space of facts. We denote
the space of all facts as $\mathcal{F}=\Sigma^{*}$, where $\Sigma$ is a set of
sub-word units and $\Sigma^{*}$ is its Kleene closure. We denote an instance
of $F$ as $f$. We will further denote the facts of a specific case $c$ as
$f_{c}$. Finally, we consider $A$, a random variable that ranges over the
space of Arguments. Analogously to facts, the space of all Arguments is
$\mathcal{A}=\Sigma^{*}$. An element of $\mathcal{A}$ is denoted as $a$, which
we again term $a_{c}$ when referring to a specific case.

##### Operationalising Halsbury and Goodhart.

In this work, we intend to measure the use of Halsbury's and Goodhart's views
in practice, which we operationalise information-theoretically following the
methodology proposed by Pimentel et al. (2019). To test the hypothesis, we
construct two collections of random variables, which we denote $H$ and $G$. We
define an instance $h_{c}$ of random variable $H$ as the union of arguments
and outcomes for all precedent cases of $c$, i.e.
$\bigcup_{c^{\prime}\in\mathcal{P}_{c}}\\{a_{c^{\prime}},o_{c^{\prime}}\\}$.
We will denote the instance $h$ when referring to it in the abstract (without
referring to a particular case). We analogously define instances of random
variable $G$ as
$g_{c}=\bigcup_{c^{\prime}\in\mathcal{P}_{c}}\\{f_{c^{\prime}},o_{c^{\prime}}\\}$.
While the set-theoretic notation may seem tedious, it encompasses the essence
of the distinction between Halsbury's and Goodhart's view: Each view
hypothesises a different group of random variables should contain more
information about the outcome $O$ of a given case. In terms of mutual
information, we are interested in comparing the following:

$\displaystyle\mathrm{MI}(O;H\mid F),\quad\mathrm{MI}(O;G\mid F)$ (1)

If ${\mathrm{MI}(O;H\mid F)>\mathrm{MI}(O;G\mid F)}$, then Halsbury's view
should be more widely used in practice. Conversely if the opposite is true,
i.e. ${\mathrm{MI}(O;G\mid F)>\mathrm{MI}(O;H\mid F)}$, then Goodhart's view
should be the one more widely used.

Figure 2: Our formulation of Halsbury's and Goodhart's tests as a
classification task. Current case facts are truncated to $512$ tokens. Outcome
of the precedent is concatenated with either the precedent's facts or
arguments, and both are jointly truncated at $512$ tokens. Finally, these are
concatenated together and embedded in $768$ dimensions before being fed into
the Longformer.

The $\mathrm{MI}$ is calculated by subtracting the outcome entropy conditioned
on the case facts and either $H$ or $G$ from the outcome entropy conditioned
on the facts alone. Therefore, to compute the $\mathrm{MI}$ we need to compute
the Halsbury's and Goodhart's conditional entropies first:

$\displaystyle\mathrm{H}(O\mid$ $\displaystyle\,H,F)$ (2)
$\displaystyle=-\sum_{o,h,f}p(o,h,f)\log p(o\mid h,f)$
$\displaystyle\mathrm{H}(O\mid$ $\displaystyle\,G,F)$ (3)
$\displaystyle=-\sum_{o,g,f}p(o,g,f)\log p(o\mid g,f)$

as well as the entropy conditioned on the facts of the current case alone:

$\displaystyle\mathrm{H}(O\mid F)$ $\displaystyle=-\sum_{o,f}p(o,f)\log
p(o\mid f)$ (4)

The conditional entropies above reflect the uncertainty (measured in
nats)333Nats are computed with $\ln$, while bits use $\log_{2}$. of an event,
given the knowledge of another random variable. For instance, if $G$
completely determines $O$, then ${\mathrm{H}(O\mid G)}$ is $0$; there is no
uncertainty left. Conversely, if the variables are independent, then
${\mathrm{H}(O)=\mathrm{H}(O\mid G)}$, where $\mathrm{H}(O)$ denotes the
unconditional entropy of the outcomes $O$. We now note a common decomposition
of mutual information that will help with the approximation:

$\displaystyle\mathrm{MI}(O;H\mid F)$ $\displaystyle=\mathrm{H}(O\mid
F)-\mathrm{H}(O\mid H,F)$ (5) $\displaystyle\mathrm{MI}(O;G\mid F)$
$\displaystyle=\mathrm{H}(O\mid F)-\mathrm{H}(O\mid G,F)$ (6)

In this work, we consider the conditional probabilities $p(o\mid\bullet)$ as
the independent product of each Article's probability, i.e.
$\prod_{k=1}^{K}p(o_{k}\mid\bullet)$. Information-theoretically, then, they
are related through the following equation:

$\mathrm{H}(O\mid\bullet)=\sum_{k=1}^{K}\mathrm{H}(O_{k}\mid\bullet)$ (7)

Following Williams et al. (2020), we further calculate the uncertainty
coefficient Theil (1970) of each of these mutual informations. These
coefficients are easier to interpret, representing the percentage of
uncertainty reduced by the knowledge of a random variable:

$\displaystyle\mathrm{U}(O\mid H;F)$ $\displaystyle=\frac{\mathrm{MI}(O;H\mid
F)}{\mathrm{H}(O\mid F)}$ (8) $\displaystyle\mathrm{U}(O\mid G;F)$
$\displaystyle=\frac{\mathrm{MI}(O;G\mid F)}{\mathrm{H}(O\mid F)}$ (9)

##  4 Experimental Setup

We choose to work with the ECtHR corpus for three reasons. First, it can be
treated as operating under precedential law, in the vein of common law
countries. This is not a given, as the ECtHR is an international court of
highest appeal without a formal doctrine of stare decisis Jacob (2014), but
there is nevertheless strong evidence that it is precedential. This evidence
comes from the court's own guidelines ECtHR (2014), but can also be found in
the writings of a former judge of the ECtHR (Zupancic, 2016) and of legal
scholars Lupu and Voeten (2010). Second, there is existing research on the
neural modelling of ECtHR case law we can build upon Aletras et al. (2016);
Chalkidis et al. (2019, 2020). Third, the documents of the ECtHR case law,
unlike those of most other courts, textually separate the _facts_ from the
_arguments_ , which is crucial for our experiments.

Case facts are descriptions of what had happened to the claimant before they
went to the court; they include domestic proceedings of their case before it
was appealed to the ECtHR as a form of a last resort. They do not contain any
reference to European Convention of Human Rights (ECHR) Articles or ECtHR case
law. Arguments on the other hand contain judges' discussion of ECHR articles
and ECtHR case law in relation to the facts. The ECtHR corpus has been scraped
from the HUDOC444HUDOC: https://hudoc.echr.coe.int/eng. database and contains
$11{,}000$ cases reported in English Chalkidis et al. (2019).555ECtHR cases
are reported either in English, French or both. Additionally, some cases are
also reported in the language of the state they take place in. Judges decide
for each Article of ECHR whether it has been violated with respect to the
claimant's circumstances. In the ECtHR corpus, each case therefore comes with
a pre-extracted decision in form of a set of violated ECHR Article numbers. We
refer to this set as the _outcome_ of a case. Out of $30$ Articles, $18$ are
from the Convention itself (Articles $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$,
$10$, $11$, $12$, $13$, $14$, $18$, $34$, $38$, $41$, $46$), while the rest
($1.1$, $1.2$, $1.3$, $4.2$, $4.4$, $6.1$, $6.3$, $7.1$, $7.2$, $7.3$, $7.4$,
$12.1$) comes from the Protocols to the Convention.

For our experiment, we need a sub-corpus where each case has at least one
outgoing citation where the full text is contained in our corpus. In practice,
there will be other outgoing citations we cannot resolve, for instance because
the document is not in English or HUDOC happens not to contain them. We also
need our citations to be de-duplicated. We create such a sub-corpus, which
contains $9{,}585$ documents (i.e., citing documents), with $94{,}167$ in-
corpus links (tokens) to $7{,}113$ cases (types) and $65{,}495$ out-of-corpus
links to $22{,}328$ types (cited documents). We start from the original ECtHR
split of $9{,}000$ training, $1{,}000$ validation and $1{,}000$ test cases,
and after citation filtering arrive at $7{,}627$ training, $976$ validation
and $982$ test cases. For every citation, we extract the text under headings
with regular expressions such as ``THE FACTS'' and ``THE LAW'', labelling it
as facts and arguments, respectively.

###  4.1 Approximations

The mutual information values that we intend to analyse need to be
approximated. We follow Pimentel et al.'s (2019; 2021) methodology for this,
approximating them as the difference between two cross-entropies:

$\displaystyle\mathrm{MI}(O;H\mid F)$
$\displaystyle\phantom{:}\approx\mathrm{H}_{\theta}(O\mid
F)-\mathrm{H}_{\theta}(O\mid H,F)$ $\displaystyle\mathrm{MI}(O;G\mid F)$
$\displaystyle\phantom{:}\approx\mathrm{H}_{\theta}(O\mid
F)-\mathrm{H}_{\theta}(O\mid G,F)$

Indeed, although several estimates for the mutual information exist,
McAllester and Stratos (2020) argues that estimating it as this difference is
the most statistically justified way. These conditional entropies are
themselves approximated through their sample estimate. For instance, we
compute:

$\displaystyle\mathrm{H}_{\theta}(O\mid G,F)$
$\displaystyle\approx-\frac{1}{|\mathcal{C}|}\sum_{c\in\mathcal{C}}\log
p_{\theta}(o_{c}\mid g_{c},f_{c})$ (10)

which is exact as $|\mathcal{C}|\rightarrow\infty$. We note that the cross-
entropy is an upper bound on the entropy, which uses a model
$p_{\theta}(o\mid\bullet)$ for its estimate. The better this model, the
tighter our estimates will be. The only thing left to do now, is to obtain
these probability estimates. We thus model Halsbury's view as a classification
task (see Figure 2) estimating the probability:

$\displaystyle p_{\theta}(o\mid h,f)$
$\displaystyle=\prod_{k=1}^{K}p_{\theta}(o_{k}\mid h,f)$ (11)

We analogously model Goodhart's view as:

$\displaystyle p_{\theta}(o\mid g,f)$
$\displaystyle=\prod_{k=1}^{K}p_{\theta}(o_{k}\mid g,f)$ (12)

Finally, we model the $p_{\theta}$ of the model conditioned only on the facts
of the case at hand as:

$\displaystyle p_{\theta}(o\mid f)$
$\displaystyle=\prod_{k=1}^{K}p_{\theta}(o_{k}\mid f)$ (13)

These models can be approximated using deep neural networks as introduced in
the next section. We train deep neural networks on our training sets, using a
cross-entropy loss function and a sub-gradient descent method. Given the
trained models, we can then answer if it is Halsbury's view or Goodhart's that
is more widely used by the ECtHR judiciary.

###  4.2 Implementation Details

All experiments are conducted using a Longformeraclassifier Beltagy et al.
(2020).666Our code is available here: https://github.com/valvoda/Precedent.
The Longformerais built on the same TransformeraVaswani et al. (2017)
architecture as BERTaDevlin et al. (2019), but allows for up to $4{,}096$
tokens, using an attention mechanism which scales linearly, instead of
quadratically. We choose this architecture in particular as it achieves state-
of-the-art performance in tasks similar to ours, e.g. on the IMDB sentiment
classification Maas et al. (2011) and Hyperpartisan news detection Kiesel et
al. (2019).

To find the probability of violation of the $K$ Articles we compute:

$\displaystyle\mathbf{h}=\textsc{Longformer}(g,f)$ (14) $\displaystyle
p_{\theta}(o\mid g,f)=\sigma(W^{(1)}\,\mathrm{ReLU}(W^{(2)}\,\mathbf{h}))$

where $\mathbf{h}\in\mathbb{R}^{d_{1}}$ is a high dimensional representation,
$W^{(1)}\in\mathbb{R}^{K\times d_{2}}$ and $W^{(2)}\in\mathbb{R}^{d_{2}\times
d_{1}}$ are learnable parameters in linear projections, and $\sigma$ is the
sigmoid function. Eq. 14 will thus output a $K$-dimensional vector with the
probabilities for all articles, by indexing this vector we retrieve the
probabilities of the individual articles applying. Due to resource limitations
we set the models' hidden size to $50$ and batch size to $16$, and also
truncate individual cases to $512$ tokens. For the models
$p_{\theta}(o_{k}\mid g,f)$ and $p_{\theta}(o_{k}\mid h,f)$, which are trained
on the combination of $f$ and either $h$ or $g$, we concatenate cases to the
maximum length of $1{,}024$ tokens (as exemplified in Figure 2). While we do
not fully utilise the $4{,}096$ word limit of the Longformer, we are able to
process twice as many tokens as standard BERTawithout pooling; memory
limitations prevent us from using the full $4{,}096$ tokens, though.

Our Longformeramodels are implemented using the Pytorch Paszke et al. (2019)
and Hugginface Wolf et al. (2020) Python libraries. We train all our models on
$4$ Nvidia P$100$ $16$GiB GPU's for a maximum of $6$ hours using Longformer-
base model. Our results are reported in terms of the models cross entropy.

Model Input |  $\mathrm{H}_{\theta}$ |  $\mathrm{MI}$ |  $\mathrm{U}$
---|---|---|---
Facts |  2.99 |  - |  -
Goodhart |  2.81 |  0.18 |  6%
Halsbury |  2.68 |  0.31 |  10%
Table 1: The cross entropy $\mathrm{H}_{\theta}$, mutual information
$\mathrm{MI}$ and uncertainty coefficient $\mathrm{U}$ results.

##  5 Results

Our experimental results are contained in Table 1. We first note that both our
mutual information estimates are statistically larger than zero, i.e.
Goodhart's and Halsbury's cross-entropies are statistically smaller than that
of the Facts.777We measure significance using the two tailed paired
permutation tests with $p<0.05$ after Benjamini and Hochberg’s (1995)
correction. The question we asked ourselves at the outset, though, concerns
whether the data supports Halsbury's or Goodhart's view. We find that our
estimate of $\mathrm{MI}(O;H\mid F)$ is significantly larger at $0.31$ nats
than our estimate of $\mathrm{MI}(O;G\mid F)$ at $0.18$ nats. These results
suggest that the information contributed by the precedent arguments give us
nearly $58$% more information about the outcome of the case than the
information contained in the facts of the precedent. In terms of the
uncertainty coefficient, the outcome entropy is reduced by 6% for facts and by
10% for arguments. We therefore observe that Halsbury's view is more widely
used in the domain of ECtHR than Goodhart's.

##  6 Discussion & Analysis

A more nuanced story can be told if we inspect the individual Articles even
though the small number of cases per Article does not allow for conclusive
significance tests. The core rights of the Convention are contained in
(Articles $2$-$18$).888The Convention Section $1$ is the first section of the
ECHR and elevates some of the Universal Declaration of Human Rights principles
into actionable rights of European citizens Schindler (1962). Figure 3 shows
that for some of the core Articles, we see the opposite effect from what we
observed for the entirety of Articles, namely that facts outperform arguments,
in particular for Articles $2$, $4$, $9$, $11$, $13$, $18$.

We hypothesise the reason for this is either that the judges have not yet
developed a functional legal method for these Articles, that the relevant
precedent has been placed late in the list of precedents (and thus was
truncated away by our methodology), or that the complexity of the arguments
requires a reasoning ability our models are simply not capable of. We consider
each hypothesis separately below.

Figure 3: Uncertainty coefficient for the Articles of the ECHR Convention.

###  6.1 Conceptual Uncertainty

For some Articles, it is more difficult to develop a legal method than for
others because the logic of the argument is elusive for some reason. This
holds, for instance, for Articles encoding a vague concept such as ``right to
life'', cf. the discussion below. If a case deals with such an Article, the
argument of a potential precedent will be less useful to determine the
outcome. We hypothesise that in such a case the judges will be more willing to
depart from the logic of past cases, which they might perceive as
unsatisfactory in search of a better legal reasoning. However, judges strive
to maintain consistency between decisions as their authority is based on this
consistency. Under these conditions, a judge might take the approach of trying
to find precedent cases that match the current case in terms of facts even if
not in terms of logic. Case law dealing with such Articles would therefore be
more likely to follow Goodhart's view.

To support or disprove this hypothesis would require an in-depth legal
analysis far beyond the scope of this paper; one would need to robustly argue
why judges find it relatively more difficult to develop legal reasoning for
certain articles. However, looking at the Articles where our data indicate
that Goodhart's view is the one more widely used, it seems to us that they
indeed concern legal concepts that are more slippery than others, which we
categorised as follows.

####  6.1.1 Corporal Articles

We can contrast Articles $2$ and $4$, where judges follow Goodhart's view, to
Article $3$, for which judges follow Halsbury's view instead, see Table 2. All
three Articles are concerned with the fundamental respect of human life, and
we therefore consider them together as the _corporal_ Articles.

Article $2$: Right to Life prohibits the _intentional deprivation of life,
save for circumstances where it is a penalty for a crime, in defence, during
an arrest, or riot suppression_. In the context of the criminal code of
Europe, this is a very restricted prohibition. Every country already encodes
these rules. On the other hand, it raises the difficult issues of beginning
and end of life. Is Article $2$ for or against abortion Cosentino (2015)? What
is its stance on euthanasia Hendriks (2019)? Developing a legal test for
Article $2$ seems very hard indeed.

Similarly, Article $4$: _Prohibition of slavery and forced labour_ , excludes
work forced in detention, compulsory military service, any service during
emergency or ``normal'' civic obligations. Due to the large number of
exceptions to the general rule it seems very hard to establish what exactly
this Article does prohibit.

Let us compare these to Article $3$: _Prohibition of torture_ , where
Halsbury's view prevails. This Article simply states that _no one shall be
subjected to torture or inhuman or degrading treatment or punishment_. No
exceptions are given. It seems much easier to develop a legal test for Article
$3$ than for Articles $2$ and $4$. The judges are free to establish what
constitutes torture; whereas when it comes to Articles $2$ and $4$, they are
facing many restrictions—both legal and political.

####  6.1.2 Faith and Family Articles

Above, we compare Articles concerned with corporal matters. In a similar way
we can also group Articles $8$, $9$, $10$, $11$ and $12$ as the Articles
broadly concerning belief, family and religion.

The two outliers here are Articles $9$ and $11$. Article $9$ provides the
_freedom of thought, conscience and religion_ , Article $11$ provides the
_freedom of assembly and association_. For both Articles, Goodhart's test
outperforms Halsbury's.

Just like above, the nature of Articles $9$ and $11$ seems more complicated
compared to Article $8$, which is similar, but narrower in scope: _Right to
respect for private and family life_ , Article $10$: _Freedom of expression_
and Article $12$: _Right to marry_.

We would argue that since Articles $8$ and $12$ provide a _right_ as opposed
to a _freedom_ , they define more narrowly the obligation on the part of the
State. Compared to the _freedom of thought_ and _association_ (Articles $9$
and $11$), the _right to marry_ and the right to _privacy_ (Article $8$ and
$12$) seem to be more concrete and testable obligations.

We can further view Article $10$: _freedom of expression_ , as dealing with an
action brought about by the exercise of Article $9$: _freedom of thought_.
While similar in concept, regulating speech seems far easier in practice than
regulating thought.

Finally, an inspection of the ECHR guidelines to Article $11$ reveals that
judges seem to be often torn between Articles $10$ and $11$.999Article $11$
guidance: https://www.echr.coe.int/Documents/Guide_Art_11_ENG.pdf. This is
because much of the cases dealing with Article $11$ concern themselves with
disentangling what constitutes an expression during an assembly and conversely
which assembly is a form of an expression. Many cases deal with the question
of religious gathering as an assembly. This is obviously not an easy position
for a judge to divine a legal test for, and perhaps a good reason for turning
to the facts of the precedent cases for consistency instead.

|  | Goodhart | Halsbury
---|---|---|---
Art | $\mathrm{H}_{\theta}(O_{k}\mid F)$ | $\mathrm{MI}$ | $\mathrm{U}$ | $\mathrm{MI}$ | $\mathrm{U}$
2 | 0.065 | 0.014 | 21.97% | 0.010 | 15.27%
3 | 0.272 | 0.028 | 10.15% | 0.047 | 17.23%
4 | 0.028 | 0.020 | 71.26% | 0.011 | 39.27%
5 | 0.275 | 0.019 | 7.05% | 0.021 | 7.53%
6 | 0.493 | 0.042 | 8.50% | 0.089 | 17.95%
7 | 0.024 | -0.003 | -12.01% | -0.000 | -1.52%
8 | 0.298 | 0.063 | 21.15% | 0.084 | 28.33%
9 | 0.022 | 0.005 | 23.14% | -0.003 | -15.74%
10 | 0.173 | 0.003 | 1.92% | 0.034 | 19.90%
11 | 0.074 | 0.018 | 24.29% | -0.004 | -5.66%
12 | 0.006 | -0.001 | -11.09% | 0.003 | 46.60%
13 | 0.235 | -0.000 | -0.10% | -0.006 | -2.38%
14 | 0.071 | -0.005 | -7.30% | -0.005 | -7.28%
18 | 0.031 | -0.003 | -10.00% | -0.007 | -24.01%

Table 2: The cross-entropy $\mathrm{H}_{\theta}$, mutual information
$\mathrm{MI}$ and uncertainty coefficient $\mathrm{U}$ results of each of the
core ECHR Articles. We note that these values are empirical estimates, so
negative $\mathrm{MI}$ results are caused by an approximation error in our
models.

###  6.2 Late Precedent

There is a group of Articles in the last quarter of Figure 3 ($13$, $14$,
$18$) for which neither Goodhart's nor Halsbury's view seem to hold. We
speculate that the reason for this is that these Articles never appear alone,
and instead always appear in conjunction with another Article, and also that
they appear late in the list of precedents, so get truncated with our
methodology.

Articles $13$: _Right to an effective remedy_ , $14$: _Prohibition of
discrimination_ and $18$: _Limitation on use of restrictions on rights_ , are
designed to ensure that states provide remedy for their wrongdoing, equal
access to the rights, and do not use the restrictions in Articles for Human
Rights abuse.

To claim any one of these Articles, the claimant will also have to claim a
violation of one of the primary Articles as their core grievance for which
they seek the remedy or equal treatment, for instance Article $3$:
_Prohibition of torture_. This means that any case dealing with Articles $13$,
$14$ and $18$ is likely to focus on the violation of that primary right.

While there might be a precedent present for the secondary Articles, the
probability is high that our models will not have the chance to train on them
because they appear late and because our method truncates text due to
computational complexity reasons. This could explain why for these Articles,
all our models trained on the precedent cases underperform when compared to
the models trained on the facts of the case alone.

###  6.3 Model Limitations

Another possible explanation for the different behaviour between Articles
could lie within the limitations of the neural architecture. There could be a
model bias for facts in precedent since they are more similar to the facts at
hand as opposed to the arguments. If this is the case our results understate
the value of arguments. While this is a concern, the overall results of our
paper would not change even if we could remove this bias since we find
arguments more important than facts despite this potential handicap.

On a more nuanced level, Articles $2$ and $4$ above might require a higher
level of reasoning than their Article $3$ counterpart. So while the judges
might have developed a satisfying legal test for them, our models simply
aren't able to learn it. For example for Article $7$: _No punishment without
law_ , our precedent models fail to learn any additional information from the
precedent facts or arguments.

This might simply be the result of an insufficient representation of Article
$7$ in training cases, or of its appearance truncated out of the input.
However it also raises the question of what a Transformeramodel can learn.

The nascent field of _BERTology_ has explored exactly this question Rogers et
al. (2020); Pimentel et al. (2020). In particular the work of Niven and Kao
(2019), examining BERTaperformance on the English Argument Reasoning
Comprehension Task Habernal et al. (2018), suggest that instead of BERTabeing
able to reason, it is merely very good at utilising the artefacts in the data
when compared to previous approaches. As Bender and Koller (2020) contend a
system can't ever learn meaning from form alone. According to their view,
description of the case facts alone will never fully capture the reality of
the world the claimant inhabits.

On the other hand, there is some evidence towards transformers being able to
reason over simple sentences Clark et al. (2020). While this is encouraging,
legal documents are far more complicated than the simple sentences considered
in the study above. Either way, the models' ability to reason in the way a
human lawyer would is certainly limited and could explain the diminished
performance for the more complicated Articles.

##  7 Related work

In this section, we contextualise our work with relation to the related
research on legal AI. Computational approaches to solving legal problems go
back at least as far as the late 1950's (Kort, 1957; Nagel, 1963). Early
research has focused on crafting rule-based systems for case outcome
prediction, achieving human-like performance by the early 2000's (Ashley,
2017). These systems however proved too brittle to keep up with the ever-
changing legal landscape and never transitioned from research into industry.

More recently, a new wave of deep learning methods has reinvigorated the
research interest in legal AI. The majority of this new work has been
conducted on statutory legal systems which do not rely on the doctrine of
precedent to nearly the same extent as their common law counterparts. For
instance, in Chinese law the use of neural models for case outcome
classification has already been investigated extensively Hu et al. (2018);
Zhong et al. (2018); Xu et al. (2020). In the precedential legal domain,
smaller corpora of annotated cases have been investigated over the years
(Grover et al., 2003; Valvoda et al., 2018). However, large-scale corpora
necessary for deep learning architectures have become available only recently.
The Caselaw Access Project101010Caselaw Access Project:, https://case.law
introduced a large dataset of American case law in 2018. Aletras et al. (2016)
have introduced the ECtHR corpus, and Chalkidis et al. (2019) have run deep
neural networks on it in order to predict outcome. Similarly, the Canadian
Supreme Court Case corpus has been used in information retrieval for the first
time by Rabelo et al. (2020). This improved access to a high quality common
law datasets has opened up a potential for new work in the field of legal AI.

Particularly similar to our work is the study done by Sim et al. (2016), who
have considered the influence of petitioners and responders (amicus) briefs on
the US Supreme Court decision and opinions.

##  8 Conclusion

In this paper, we have shifted the focus of legal AI research from practical
tasks such as precedent retrieval or outcome prediction, to a theoretical
question: which aspect of the precedent is most important in forming the law?
To this end, we trained a similar neural modelling approach as Chalkidis et
al. (2019) to predict the outcome of a case on the ECtHR dataset, and
inspected the difference in the mutual information between our
operationalisations of Halsbury's and Goodhart's view. We have used a method
inspired by Pimentel et al. (2019) to approximate the $\mathrm{MI}$. We
observe that out of the two archetypal views on precedent, that of Halsbury
and Goodhart, the former has a better empirical support in the domain of ECtHR
case law.

This study has demonstrated a novel method of approaching jurisprudential
questions using the information-theoretic toolkit. We hope that future work
can leverage our methodology towards answering other questions of legal
philosophy. However, our results are not only of an interest in the context of
legal theory, but they can also inform a development of better legal models in
practice. Since most precedential reasoning is conducted using the arguments
in the precedent, outcome prediction models should take advantage of the case
arguments, instead of relying solely on the facts.

## Ethical Considerations

While our work is not concerned with a legal application, it is important to
note that the results presented here are qualified by the limitations of
contemporary NLP models' ability to process language. It should therefore
serve as no indication that judges could (or should) be replaced by models or
techniques discussed in this paper.

## Acknowledgements

We are grateful to Prof. Ken Satoh for all the fruitful discussions leading
towards this paper. We further thank the National Institute of Informatics
(NII) Japan and Huawei research UK for their financial support enabling this
research.

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##  Appendix A Glossary:

Legal Terms |
---|---
_Facts_ |  The description of what had happened to the claimant. This includes more general description of who they are, circumstances of the perceived violation of their rights and the proceedings in domestic courts before their appeal to ECtHR.
_Arguments_ |  The judges explanation of why did they decide the case the way they did. This includes citations of previous cases, application of any relevant legal test, development of a new legal test, analysis of the facts etc.
_Precedent_ |  Cases that have been cited by the judges as part of their arguments.
_ Ratio Decidendi _ |  The reasons for the decision in a case that is binding on the subsequent cases. Also known as the __ratio__. What exactly is ratio is contested by legal scholars.
_Obiter Dicta_ |  The non-binding discussions in the case. Whatever is not ratio.
_Binding_ |  Judges are expected to adhere to the binding rules of law and decide future access accordingly.
_ Stare Decisis _ |  New cases with the same facts to the already decided case should lead to the same outcome. This is the doctrine of precedent by which judges can create law.
_Caselaw_ |  Transcripts of the court proceedings.
_ECHR_ |  European Convention of Human Rights, comprises of the Convention and the Protocols to the convention. The Protocols are the additions and amendments to the Convention introduced after the signing of the original Convention.
_ECtHR_ |  European Court of Human Rights, adjudicates ECHR cases.

Selected ECHR Articles |
---|---
Article 2: |
_Right to life_ |  Everyone’s right to life shall be protected by law. No one shall be deprived of his life intentionally save in the execution of a sentence of a court following his conviction of a crime for which this penalty is provided by law.
Article 3: |
_Prohibition of torture_ |  No one shall be subjected to torture or to inhuman or degrading treatment or punishment.
Article 4: |
_Prohibition of slavery and forced labour_ |  No one shall be held in slavery or servitude.
Article 8: |
_Right to respect for private and family life_ |  Everyone has the right to respect for his private and family life, his home and his correspondence.
Article 9: |
_Freedom of thought, conscience and religion_ |  Everyone has the right to freedom of thought, conscience and religion; this right includes freedom to change his religion or belief and freedom, either alone or in community with others and in public or private, to manifest his religion or belief, in worship, teaching, practice and observance.
Article 10: |
_Freedom of expression_ |  Everyone has the right to freedom of expression. This right shall include freedom to hold opinions and to receive and impart information and ideas without interference by public authority and regardless of frontiers. This Article shall not prevent States from requiring the licensing of broadcasting, television or cinema enterprises.
Article 11: |
_Freedom of assembly and association_ |  Everyone has the right to freedom of peaceful assembly and to freedom of association with others, including the right to form and to join trade unions for the protection of his interests.
Article 12: |
_Right to marry_ |  Men and women of marriageable age have the right to marry and to found a family, according to the national laws governing the exercise of this right.
Article 13: |
_Right to an effective remedy_ |  Everyone whose rights and freedoms as set forth in this Convention are violated shall have an effective remedy before a national authority notwithstanding that the violation has been committed by persons acting in an official capacity.
Article 14: |
_Prohibition of discrimination_ |  The enjoyment of the rights and freedoms set forth in this Convention shall be secured without discrimination on any ground such as sex, race, colour, language, religion, political or other opinion, national or social origin, association with a national minority, property, birth or other status.
Article 18: |
_Limitation on use of restrictions on rights_ |  The restrictions permitted under this Convention to the said rights and freedoms shall not be applied for any purpose other than those for which they have been prescribed.

##  Appendix B Facts & Arguments Examples

Fact |  _The applicants, D.P. and J.C., who are sister and brother, are United Kingdom nationals, born in 1964 and 1967 and living in London and Nottingham, respectively…_
---|---
Argument |  _Article 2 of the Convention provides, in its first sentence: “1. Everyone's right to life shall be protected by law. …” 46. The applicants complain that the authorities failed to protect the life of their son and were responsible for his death…_