## 1. Conceptions of Evidence: What does Evidence Refer to in Law?



Stephen (1872: 3-4, 6-7) long ago noted that legal usage
of the term "evidence" is ambiguous. It sometimes refers
to that which is adduced by a party at the trial as a means of
establishing factual claims. ("Adducing evidence" is the
legal term for presenting or producing evidence in court for the
purpose of establishing proof.) This meaning of evidence is reflected
in the definitional section of the Indian Evidence Act (Stephen 1872:
 149).[3]
 When lawyers use the term "evidence" in this way, they
have in mind what epistemologists would think of as "objects of
sensory evidence" (Haack 2004: 48). Evidence, in this sense, is
divided conventionally into three main
 categories:[4]
 oral evidence (the testimony given in court by witnesses),
documentary evidence (documents produced for inspection by the court),
and "real evidence"; the first two are self-explanatory
and the third captures things other than documents such as a knife
allegedly used in committing a crime.



The term "evidence" can, secondly, refer to a proposition
of fact that is established by evidence in the first
 sense.[5]
 This is sometimes called an "evidential fact". That the
accused was at or about the scene of the crime at the relevant time is
evidence in the second sense of his possible involvement in the crime.
But the accused's presence must be proved by producing evidence
in the first sense. For instance, the prosecution may call a witness
to appear before the court and get him to testify that he saw the
accused in the vicinity of the crime at the relevant time. Success in
proving the presence of the accused (the evidential fact) will depend
on the fact-finder's assessment of the veracity of the witness
and the reliability of his testimony. (The fact-finder is the person
or body responsible for ascertaining where the truth lies on disputed
questions of fact and in whom the power to decide on the verdict
vests. The fact-finder is also called "trier of fact" or
"judge of fact". Fact-finding is the task of the jury or,
for certain types of cases and in countries without a jury system, the
judge.) Sometimes the evidential fact is directly accessible to the
fact-finder. If the alleged knife used in committing the crime in
question (a form of "real evidence") is produced in court,
the fact-finder can see for himself the shape of the knife; he does
not need to learn of it through the testimony of an intermediary.



A third conception of evidence is an elaboration or extension of the
second. On this conception, evidence is relational. A factual
proposition (in Latin, *factum probans*) is evidence in the
third sense only if it can serve as a premise for drawing an inference
(directly or indirectly) to a matter that is material to the case
(*factum probandum*) (see
 section 2.2
 below for the concept of materiality). The fact that the
accused's fingerprints were found in a room where something was
stolen is evidence in the present sense because one can infer from
this that he was in the room, and his presence in the room is evidence
of his possible involvement in the theft. On the other hand, the fact
that the accused's favorite color is blue would, in the absence
of highly unusual circumstances, be rejected as evidence of his guilt:
ordinarily, what a person's favorite color happens to be cannot
serve as a premise for any reasonable inference towards his commission
of a crime and, as such, it is irrelevant (see discussion of relevance
in
 section 2.1
 below). In the third sense of "evidence", which conceives
of evidence as a premise for a material inference, "irrelevant
evidence" is an oxymoron: it is simply not evidence. Hence, this
statement of Bentham (1825:
 230):[6]



> 
> 
> To say that testimony is not pertinent, is to say that it is foreign
> to the case, has no connection with it, and does not serve to prove
> the fact in question; in a word, it is to say, that it is not
> evidence.
> 
> 
> 



There can be evidence in the first sense without evidence in the
second or third sense. To pursue our illustration, suppose it emerges
during cross-examination of the expert that his testimony of having
found a finger-print match was a lie. Lawyers would describe this
situation as one where the "evidence" (the testimony of
the expert) fails to prove the fact that it was originally produced to
prove and not that no "evidence" was adduced on the
matter. Here "evidence" is used in the first
sense--evidence as testimony--and the testimony remains in
the court's record whether it is believed or not. But lawyers
would also say that, in the circumstances, there is no
"evidence" that the accused was in the room, assuming that
there was nothing apart from the discredited expert testimony of a
fingerprint match to establish his presence there. Here, the
expert's testimony is shown to be false and fails to establish
that the accused's fingerprints were found in the room, and
there is no (other) factual basis for believing that he was in the
room. The factual premise from which an inference is sought to be
drawn towards the accused's guilt is not established.



Fourthly, the conditions for something to be received (or, in
technical term "admitted") as evidence at the trial are
sometimes included in the legal concept of evidence. (These conditions
are discussed in
 section 2
 below.) On this conception, legal evidence is that which counts as
evidence in law. Something may ordinarily be treated as evidence and
yet be rejected by the court. Hearsay is often cited as an example. It
is pointed out that reliance on hearsay is a commonplace in ordinary
life. We frequently rely on hearsay in forming our factual beliefs. In
contrast, "hearsay is not evidence" in legal proceedings
(Stephen 1872: 4-5). As a general rule, the court will not rely
on hearsay as a premise for an inference towards the truth of what is
asserted. It will not allow a witness to testify in court that another
person *X* (who is not brought before the court) said that
*p* on a certain occasion (an out-of-court statement) for the
purpose of proving that *p*.



In summary, at least four possible conceptions of legal evidence are
in currency: as an object of sensory evidence, as a proposition of
fact, as an inferential premise and as that which counts as evidence
in law. The sense in which the term "evidence" is being
used is seldom made explicit in legal discourse although the intended
meaning will often be clear from the context.


## 2. Conditions for Receiving Evidence: What Counts as Evidence in Law?



This section picks up on the fourth conception of evidence. To recall,
something will be accepted by the court as evidence--it is, to
use Montrose's term, *receivable* as evidence in legal
proceedings--only if three basic conditions are satisfied:
*relevance*, *materiality,* and *admissibility*
(Montrose 1954). These three conditions of receivability are discussed
in turn below.


### 2.1 Relevance


#### 2.1.1 Legal Significance of Relevance



The concept of relevance plays a pivotal role in legal fact-finding.
Thayer (1898: 266, 530) articulates its significance in terms of two
foundational principles of the law of evidence: first, without
exception, nothing which is not relevant may be received as evidence
by the court and secondly, subject to many exceptions and
qualifications, whatever is relevant is receivable as evidence by the
court. Thayer's view has been influential and finds expression
in sources of law, for example, in Rule 402 of the Federal Rules of
Evidence in the United
 States.[7]
 Thayer claims, and it is now widely accepted, that relevance is a
"logical" and not a legal concept; in
 section 2.1.3,
 we will examine this claim and the dissent expressed by Wigmore.
Leaving aside the dissenting view for the moment, we will turn first
to consider possible conceptions of relevance in the conventional
sense of logical relevance.


#### 2.1.2 Conceptions of Logical Relevance



Evidence may be adduced in legal proceedings to prove a fact only if
the fact is relevant. Relevance is a relational concept. No fact is
relevant in itself; it is relevant only in relation to another fact.
The term "probable" is often used to describe this
relation. We see two instances of this in the following well-known
definitions. According to Stephen (1886: 2, emphasis added):



> 
> 
> The word "relevant" means that any two facts to which it
> is applied are so related to each other that according to the common
> course of events one either taken by itself or in connection with
> other facts proves or renders *probable* the past, present, or
> future existence or non-existence of the other.
> 
> 
> 



The second definition is contained in the United States' Federal
Rule of Evidence 401 which (in its restyled version) states that
evidence is relevant if "it has a tendency to make a fact more
or less *probable* than it would be without the evidence"
(emphasis added). The word "probable" in these and other
standard definitions is sometimes construed as carrying the
mathematical meaning of
 probability.[8]
 In a leading article, Lempert gave this example to show how relevance
turns on the likelihood ratio. The prosecution produces evidence that
the perpetrator's blood found at the scene of the crime is type
A. The accused has the same blood type. Suppose fifty percent of the
suspect population has type A blood. If the accused is in fact guilty,
the probability that the blood found at the scene will be type A is
1.0. But if he is in fact innocent, the probability of finding type A
blood at the scene is 0.5--that is, it matches the background
probability of type A blood from the suspect population. The
likelihood ratio is the ratio of the first probability to the
second--1.0:0.5 or, more simply, 2:1. Evidence is considered
relevant so long as the likelihood ratio is other than 1:1 (Lempert
1977). If the ratio is 1:1, that means that the probability of the
evidence is the same whether the accused is guilty or innocent.



The conventional view is that relevance in law is a binary concept:
evidence is either relevant or it is not. So long as the likelihood
ratio is other than 1:1, the evidence is considered
 relevant.[9]
 However, the greater the likelihood ratio deviates from 1:1, the
higher the so-called probative value of the evidence (that is, on one
interpretation of probative value). We will take a closer look at
probative value in
 section 3.1
 below.



While the likelihood ratio may be useful as a heuristic device in
analysing evidential reasoning, it is controversial as to whether it
captures correctly the concept of relevance. In the first place, it is
unclear that the term "probable" in the standard
definitions of relevance was ever intended as a reference to
mathematical probability. Some have argued that relevance should be
understood broadly such that any evidence would count as relevant so
long as it provides some reason in support of the conclusion that a
proposition of fact material to the case is true or false (Pardo 2013:
576-577).



The mathematical conception of relevance has been disputed. At a
trial, it is very common for the opposing sides to present competing
accounts of events that share certain features. To use Allen's
example, the fact that the accused drove to a particular town on a
particular day and time is consistent with the prosecution's
case that he was driving there to commit a murder and also with the
defence's case that he was driving there to visit his mother.
This fact, being a common feature of both sides' explanations of
the material events, is as consistent with the hypothesis of guilt as
with the hypothesis of innocence. On the likelihood ratio conception
of relevance, this fact should be irrelevant and hence evidence of it
should not be allowed to be adduced. But in such cases, the court will
let the evidence in (Park et al. 2010: 10). The mathematical theory of
relevance cannot account for this. (For critical discussion of this
claim, see section 4.2 of the entry on 
 legal probabilism.) It is
argued that an alternative theory of relevance better fits legal
practice and is thus to be preferred. On an explanatory conception of
relevance, evidence is relevant if it is explained by or provides a
reason for believing the particular explanation of the material events
offered by the side adducing the evidence, and it remains relevant
even where, as in our example, the evidence also supports or forms
part of the explanation offered by the opponent (Pardo and Allen 2008:
241-2; Pardo 2013: 600).



One possible response to the above challenge to the likelihood ratio
theory of relevance is to deny that it was ever meant to be the
*exclusive* test of relevance. Evidence is relevant if the
likelihood ratio is other than 1:1. But evidence may also be relevant
on other grounds, such as when it provides for a richer narrative or
helps the court in understanding other evidence. It is for these
reasons that witnesses are routinely allowed to give their names and
parties may present diagrams, charts and floor plans (so-called
"demonstrative evidence") at the trial (McCormick 2013:
995). The admission of evidence in the scenario painted by Allen above
has been explained along a similar line (Park et al. 2010: 16).


#### 2.1.3 Logical Relevance versus Legal Relevance



The concept of relevance examined in the preceding section is commonly
known as "logical relevance". This is somewhat of a
misnomer: "Relevance is not a matter of logic, but depends on
matters of fact" (Haack 2004: 46). In our earlier example, the
relevance of the fact that the accused has type A blood depends
obviously on the state of the world. On the understanding that
relevance is a probabilistic relation, it is tempting to think that in
describing relevance as "logical", one is subscribing to a
logical theory of probability (cf. Franklin 2011). However, the term
"logical relevance" was not originally coined with this
connotation in mind. In the forensic context, "logic" is
used loosely and refers to the stock of background beliefs or
generalisations and the type of reasoning that judges and lawyers are
fond of labelling as "commonsense" (MacCrimmon
2001-2002; Twining 2006: 334-335).



A key purpose of using the adjective "logical" is to flag
the non-legal character of relevance. As Thayer (1898: 269) famously
claimed, relevance "is an affair of logic and not of law."
This is not to say that relevance has no legal dimension. The law
distinguishes between questions of law and questions of fact. An issue
of relevance poses a question of law that is for the judge to decide
and not the jury, and so far as relevance is defined in legal sources
(for example, in Federal Rule of Evidence 401 mentioned above), the
judge must pay heed to the legal definition. But legal definitions of
relevance are invariably very broad. Relevance is said to be a
logical, and non-legal, concept in the sense that in answering a
question of relevance and in applying the definition of relevance, the
judge has necessarily to rely on extra-legal resources and is not
bound by legal precedents. Returning to Federal Rule of Evidence 401,
it states generally that evidence is relevant if "it has a
tendency to make a fact more or less probable than it would be without
the evidence". In deciding whether the evidence sought to be
adduced does have this tendency, the judge has to look outside the
law. Thayer was most insistent on this. As he put it, "[t]he law
furnishes no test of relevancy. For this, it tacitly refers to logic
and general experience" (Thayer 1898: 265). That the
accused's favorite color is blue is, barring extraordinary
circumstances, irrelevant to the question of his intention to commit
theft. It is not the law that tells us so but "logic and general
experience". On Thayer's view, the law does not control or
regulate the assessment of relevance; it assumes that judges are
already in possession of the (commonsense) resources to undertake this
assessment.



Wigmore adopts a different position. He argues, against Thayer, that
relevance is a legal concept. There are two strands to his contention.
The first is that for evidence to be relevant in law, "a
generally higher degree of probative value" is required
"than would be asked in ordinary reasoning":



> 
> 
> legal relevance denotes...something more than a minimum of
> probative value. Each single piece of evidence must have a plus value.
> (cf. Pattenden 1996-7: 373)
> 
> 
> 



As Wigmore sees it, the requirement of "plus value" guards
against the jury "being satisfied by matters of slight value,
capable to being exaggerated by prejudice and hasty reasoning"
(Wigmore 1983b: 969, cf. 1030-1031). Opponents of Wigmore
acknowledge that there may be sound policy reasons for excluding
evidence of low probative value. Receiving the evidence at the trial
might raise a multiplicity of issues, incur too much time and expense,
confuse the jurors or produce undue prejudice in their mind. When the
judge excludes evidence for any of these reasons, and the judge has
the discretion to do so in many countries, the evidence is excluded
*despite* it being relevant (e.g., United States' Federal
Rule of Evidence 403). Relevance is a relation between facts and the
aforesaid reasons for exclusion are extrinsic to that relation; they
are grounded in considerations such as limitation of judicial
resources and jury psychology. The notion of "plus value"
confuses relevance with extraneous considerations (James 1941;
Trautman 1952).



There is a second strand to Wigmore's contention that relevance
is a legal concept. Relevance is legal in the sense that the judge is
bound by previously decided cases ("judicial precedents")
when he has to make a ruling on the relevance of a proposed item of
evidence.



> 
> 
> So long as Courts continue to declare...what their notions of
> logic are, just so long will there be rules of law which must be
> observed. (Wigmore 1983a: 691)
> 
> 
> 



Wigmore cites in support the judgment of Cushing C.J. in *State v
LaPage* where it was remarked:



> 
> 
> [T]here are many instances in which the evidence of particular facts
> as bearing on particular issues has been so often the subject of
> discussion in courts of law, and so often ruled upon, that the united
> logic of a great many judges and lawyers may be said to
> furnish...the best evidence of what may be properly called
> *common*-sense, and thus to acquire the authority of law. (1876
> 57 N.H. 245 at 288 [Supreme Court, New Hampshire])
> 
> 
> 



Wigmore's position on relevance is strangely at odds with his
strong stand against the judge being bound by judicial precedents in
assessing the weight or credibility of evidence (Wigmore 1913). More
importantly, the second strand of his argument also does not sit well
with the first strand. If, as Wigmore contends, evidence must have a
plus value to make it legally relevant, the court has to consider the
probative value of the evidence and to weigh it against the amount of
time and expense likely to be incurred in receiving the evidence, the
availability of other evidence, the risk of the evidence misleading or
confusing the trier of fact and so forth. Given that the assessment of
plus value and, hence, legal relevance is so heavily contextual, it is
difficult to see how a judicial precedent can be of much value in
another case in determining a point of legal relevance (James 1941:
702).


### 2.2 Materiality and Facts-in-issue



We have just considered the first condition of receivability, namely,
relevance. That fact *A* is relevant to fact *B* is not
sufficient to make evidence of fact *A* receivable in court. In
addition, *B* must be a "material" fact. The
materiality of facts in a particular case is determined by the law
applicable to that case. In a criminal prosecution, it depends on the
law which defines the offence with which the accused is charged and at
a civil trial, the law which sets out the elements of the legal claim
that is being brought against the defendant (Wigmore 1983a,
15-19; Montrose 1954: 536-537).



Imagine that the accused is prosecuted for the crime of rape and the
alleged victim's behaviour (fact *A*) increases the
probability that she had consented to have sexual intercourse with the
accused (fact *B*). On the probabilistic theory of relevance
that we have considered, *A* is relevant to *B*. Now
suppose that the alleged victim is a minor. Under criminal law, it
does not matter whether she had consented to the sexual intercourse.
If *B* is of no legal consequence, the court will not allow
evidence of *A* to be adduced for the purpose of proving
*B*: the most obvious reason is that it is a waste of time to
receive the evidence.



Not all material facts are necessarily in dispute. Suppose the
plaintiff sues the defendant for breach of contract. Under the law of
contract, to succeed in this action, the plaintiff must prove the
following three elements: that there was a contract between the
parties, that the defendant was in breach of the contract, and that
the plaintiff had suffered loss as a result of that breach. The
defendant may concede that there was a contract and that he was in
breach of it but deny that the plaintiff had suffered any loss as a
result of that breach. In such a situation, only the last of the
material facts is disputed. Following Stephen's terminology, a
disputed material fact is called a "fact in issue"
(Stephen 1872: 9).



The law does not allow evidence to be adduced to prove facts that are
immaterial. Whether evidence may be adduced to prove a material fact
may depend on whether the material fact is disputed; for
instance, the requirement that it must be disputed
exists under Rule 210 of the Evidence Code of California but not
Rule 401 of the Federal Rules of Evidence in the United States.
"Relevance" is often used in the broader sense that
encompasses the concepts under discussion. Evidence is sometimes
described as "irrelevant" not for the reason that no
logical inference can be drawn to the proposition that is sought to be
proved (in our example, *A* is strictly speaking relevant to
*B*) but because that proposition is not material or not
disputed (in our example, *B* is not
 material).[10]
 This broader usage of the term "relevance", though
otherwise quite harmless, does not promote conceptual clarity because
it runs together different concepts (see James 1941: 690-691;
Trautman 1952: 386; Montrose 1954: 537).


### 2.3 Admissibility


#### 2.3.1 Admissibility and Relevance



A further condition must be satisfied for evidence to be received in
legal proceedings. There are legal rules that prohibit evidence from
being presented at a trial even though it is relevant to a factual
proposition that is material and in issue. These rules render the
evidence to which they apply "inadmissible" and require
the judge to "exclude" it. Two prominent examples of such
rules of admissibility or rules of exclusion are the rule against
hearsay evidence and the rule against character evidence. This section
considers the relation between the concept of relevance and the
concept of admissibility. The next section
 (section 2.3.2)
 discusses general arguments for and against exclusionary or
admissibility rules.



Here, again, the terminology is imprecise. Admissibility and
receivability are not clearly distinguished. It is common for
*irrelevant* evidence, or evidence of an *immaterial*
fact to be described as "inadmissible". What this means is
that the court will refuse to receive evidence if it is irrelevant or
immaterial. But, importantly, the court also excludes evidence for
reasons other than irrelevance and immateriality. For Montrose, there
is merit in restricting the concept of "inadmissibility"
to the exclusion of evidence based on those other reasons (Montrose
1954: 541-543). If evidence is rejected on the ground of
irrelevance, it is, as Thayer (1898: 515) puts it, "the rule of
reason that rejects it"; if evidence is rejected under an
admissibility or exclusionary rule, the rejection is by force of law.
The concepts of admissibility and materiality should also be kept
apart. This is because admissibility or exclusionary rules serve
purposes and rationales that are distinct from the law defining the
crime or civil claim that is before the court and it is this law that
determines the materiality of facts in the dispute.



Thayer (1898: 266, 530) was influential in his view that the law of
evidence has no say on logical relevance and that its main business is
in dealing with admissibility. If the evidence is logically
irrelevant, it must for that reason be excluded. If the evidence is
logically relevant, it will be received by the court unless the
law--in the form of an exclusionary or admissibility
rule--requires its exclusion. In this scheme, the concept of
relevance and the concept of admissibility are distinct: indeed,
admissibility rules presuppose the relevance of the evidence to which
they apply.



Stephen appears to hold a different view, one in which the concept of
admissibility is apparently absorbed by the concept of relevance.
Take, for example, Stephen's analysis of the rule that in
general no evidence may be adduced to prove "statements as to
facts made by persons not called as witnesses", in short,
hearsay (Stephen 1872: 122). As a general rule, no evidence may be
given of hearsay because the law prohibits it. The question then
arises as to the rationale for this prohibition. Stephen's
answer to this question is often taken to be that hearsay is not
"relevant" and he is criticised for failing to see the
difference between relevance and admissibility (Whitworth 1881: 3;
Thayer 1898: 266-268; Pollock 1876, 1899; Wigmore 1983a:
SS12). His critics point out that hearsay has or can have
probative value and evidence of hearsay is excluded despite or
regardless of its relevance. On the generalisation that there is no
smoke without fire, the fact that a person claimed that *p* in
a statement made out-of-court does or can have a bearing on the
probability that *p*, and *p* may be (logically relevant
to) a material fact in the dispute.



Interestingly, Stephen seemed to have conceded as much. He
acknowledged that a policeman or a lawyer engaged in preparing a case
would be negligent if he were to shut his ears to hearsay. Hearsay is
one of those facts that are "apparently relevant but not really
so" (Stephen 1872: 122; see also Stephen 1886: xi). In claiming
that hearsay is irrelevant, Stephen appears to be merely stating the
effect of the law: the law requires that hearsay be treated as
irrelevant. He offered a variety of justifications for excluding
hearsay evidence: its admissibility would "present a great
temptation to indolent judges to be satisfied with second-hand
reports" and "open a wide door to fraud", with the
result that "[e]veryone would be at the mercy of people who
might tell a lie, and whose evidence could neither be tested nor
contradicted" (Stephen 1872: 124-125). For his detractors,
these are reasons of policy and fairness and it disserves clarity to
sneak such considerations into the concept of relevance.



Although there is force to the criticism that Stephen had unhelpfully
conflated admissibility and relevance (understood as logical
relevance), something can perhaps be said in his defence. Exclusionary
rules or rules of admissibility--at any rate, many of
them--are more accurately seen as excluding forms of reasoning
rather than prohibiting proof of certain types of facts (McNamara
1986). This is certainly true of the hearsay rule. On one
authoritative definition of the rule (decision of the Privy Council in
*Subramaniam v PP*, (1956) 1 *Weekly Law Reports* 965),
what it prohibits is the use of a hearsay statement to prove the truth
of the facts asserted
 therein.[11]
 The objection is to the drawing of the inference that *p* from
*X*'s out-of-court statement that *p* where
*X* is not available to be examined in court. But the court
will allow the evidence of *X*'s hearsay statement to be
admitted--it will allow proof of the statement-- where the
purpose of adducing the evidence is to persuade the court that
*X* did make the statement and this fact is relevant for some
other purpose. For instance, it may be relevant as to the state of
mind of the person hearing the statement, and his state of mind may be
material to his defence of having acted under duress. Hence, two
writers have commented that "there is no such thing as hearsay
*evidence*, only hearsay *uses*" (Roberts and
Zuckerman 2010: 385).



Other admissibility rules are also more accurately seen as targeted at
forms of reasoning and not types of facts. In the United States,
Federal Rule of Evidence 404(a)(1) bars the use of evidence of a
person's character "to prove that on a particular occasion
the person acted in accordance with the character" and Federal
Rule of Evidence 404(b)(1) provides that evidence of a crime or
wrong



> 
> 
> is not admissible to prove a person's character in order to show
> that on a particular occasion the person acted in accordance with the
> character.
> 
> 
> 



It is doubtful that evidence of a person's character and past
behaviour can have no probabilistic bearing on his behaviour on a
particular occasion; on a probabilistic conception of relevance, it is
difficult to see why the evidence is not relevant. Even so, there may
be policy, moral or other reasons for the law to prohibit certain uses
of character evidence. In declaring a fact as irrelevant for a
particular purpose, we are not necessarily saying or implying anything
about probability. We may be expressing a normative judgment. For
policy, moral or other reasons, the law takes the position that
hearsay or the accused's character or previous misconduct must
not be used as the premise for a particular line of reasoning. The
line of reasoning might be morally objectionable ("give a dog a
bad name and hang him for it") or it might be unfair to permit
the drawing of the inference when the opponent was not given a fair
opportunity to challenge it (as in the hearsay situation) (Ho 2008:
chs. 5, 6). If we take a normative conception of relevance instead of
a logical or probabilistic one, it is not an abuse of language to
describe inadmissible evidence as irrelevant if what is meant is that
the evidence ought not to be taken into account in a certain way.


#### 2.3.2 Admissibility or Exclusionary Rules



On one historical account, admissibility or exclusionary rules are the
product of the jury system where citizens untrained in assessing
evidence sit as judges of fact. These rules came about because it was
thought necessary to keep away from inexperienced jurors certain types
of evidence that may mislead or be mishandled by them--for
instance, evidence to which they are likely to give too much weight or
that carries the risk of creating unfair prejudice in their minds
(Thayer 1898; Wigmore 1935: 4-5). Epistemic paternalism is
supposedly at play (Leiter 1997: 814-5; Allen and Leiter 2001:
1502). Subscription to this theory has generated pressure for the
abolition of exclusionary rules with the decline of the jury system
and the replacement of lay persons with professional judges as triers
of fact. There is doubt as to the historical accuracy of this account;
at any rate, it does not appear capable of explaining the growth of
all exclusionary rules (Morgan 1936-37; Nance 1988:
278-294).



Even if the theory is right, it does not necessarily follow that
exclusionary rules should be abolished once the jury system is
removed. Judges may be as susceptible to the same cognitive and other
failings as the jury and there may be the additional risk that judges
may over-estimate their own cognitive and intellectual abilities in
their professional domain. Hence, there remains a need for the
constraints of legal rules (Schauer 2006: 185-193). But the
efficacy of these rules in a non-jury system is questionable. The
procedural reality is that judges will have to be exposed to the
evidence in order to decide on its admissibility. Since a judge cannot
realistically be expected to erase the evidence from his mind once he
has decided to exclude it, there seems little point in excluding the
evidence; we might as well let the evidence in and allow judge to give
the evidence the probative value that it deserves (Mnookin 2006;
Damaska 2006; cf. Ho 2008: 44-46).



Bentham was a strong critic of exclusionary rules. He was much in
favour of "freedom of proof" understood as free access to
information and the absence of formal rules that restrict such access
(Twining 2006: 232, n 65). The direct object of legal procedure is the
"rectitude of decision", by which he means the correct
application of substantive law to true findings of facts. The
exclusion of relevant evidence--evidence capable of casting light
on the truth--is detrimental to this end. Hence, no relevant
evidence should be excluded; the only exceptions he would allow are
where the evidence is superfluous or its production would involve
preponderant delay, expense or vexation (Bentham 1827: Book IX;
Bentham 1825: Book VII; Twining 1985: ch. 2). Bentham's argument
has been challenged on various fronts. It is said that he overvalued
the pursuit of truth, undervalued procedural fairness and procedural
rights, and placed too much faith in officials, underestimating the
risk of abuse when they are given discretion unfettered by rules
(Twining 1985: 70-71).



Even if we agree with Bentham that rectitude of decision is the aim of
legal procedure and that achieving accuracy in fact-finding is
necessary to attain this aim, it is not obvious that a rule-based
approach to admissibility will undermine this aim in the long run.
Schauer has defended exclusionary rules of evidence along a
rule-consequentialist line. Having the triers of fact follow rules on
certain matters instead of allowing them the discretion to exercise
judgment on a case-by-case basis may produce the greatest number of
favourable outcomes in the aggregate. It is in the nature of a formal
rule that it has to be followed even when doing so might not serve the
background reason for the rule. If hearsay evidence is thought to be
generally unreliable, the interest of accuracy may be better served
overall to require such evidence to be excluded without regard to its
reliability in individual cases. Given the imperfection of human
reason and our suspicion about the reasoning ability of the
fact-finder, allowing decisions to be taken individually on the
reliability and admissibility of hearsay evidence might over time
produce a larger proportion of misjudgements than on the rule-based
approach (Schauer 2006: 180-185; Schauer 2008). However, this
argument is based on a large assumption about the likely effects of
having exclusionary rules and not having them, and there is no strong
empirical basis for thinking that the consequences are or will be as
alleged (Goldman 1999: 292-295; Laudan 2006: 121-122).



Other supporters of exclusionary rules build their arguments on a wide
range of different considerations. The literature is too vast to enter
into details. Here is a brief mention of some arguments. On one
theory, some exclusionary rules are devices that serve as incentives
for lawyers to produce the epistemically best evidence that is
reasonably available (Nance 1988, 2016: 195-201). For example,
if lawyers are not allowed to rely on second-hand (hearsay) evidence,
they will be forced to seek out better (first-hand) evidence. On
another theory, exclusionary rules allocate the risks of error. Again,
consider hearsay. The problem with allowing a party to rely on hearsay
evidence is that the opponent has no opportunity to cross-examine the
original maker of the statement and is thus deprived of an important
means of attacking the reliability of the evidence. Exclusionary rules
in general insulate the party against whom the evidence is sought to
be adduced from the risks of error that the evidence, if admitted,
would have introduced. The distribution of such risks is said to be a
political decision that should not be left to the discretion of
individual fact-finders (Stein 2005; cf. Redmayne 2006 and Nance
2007a: 154-164). It has also been argued that the hearsay rule
and the accompanying right to confront witnesses promote the public
acceptance and stability of legal verdicts. If the court relies on
direct evidence, it can claim superior access to the facts (having
heard from the horse's mouth, so to speak) and this also reduces
the risk of new information emerging after the trial to discredit the
inference that was drawn from the hearsay evidence (the original maker
of the statement might turn up after the trial to deny the truth of
the statement that was attributed to him) (Nesson 1985:
1372-1375; cf. Park 1986; Goldman 1999: 282; Goldman 2005:
166-167).


## 3. Strength of Evidence



The decision whether to allow a party to adduce a particular item of
evidence is one that the judge has to make and arises in the course of
a trial.
 Section 2
 above dealt with the conditions that must be satisfied for a
witness's testimony, a document or an object to be received as
evidence. At the end of the trial, the fact-finder must consider all
the evidence that has been presented and reach a verdict. Although
verdict deliberation is sometimes subjected to various forms of
control through legal devices such as presumptions and corroboration
rules, such control is limited and the fact-finder is expected to
exercise personal judgment in the evaluation of evidence
(Damaska 2019). Having heard or seen the evidence, the
fact-finder now has to evaluate or 'weigh' it in reaching
the verdict. Weight can refer to any of the following three properties
of evidence: (a) the probative value of individual items of evidence,
(b) the sufficiency of the whole body of evidence adduced at the trial
in meeting the standard of proof, or (c) the relative completeness of
this body of evidence. The first two aspects of weight are familiar to
legal practitioners but the third has been confined to academic
discussions. These three ideas are discussed in the same order
below.


### 3.1 Probative Value of Specific Items of Evidence



In reaching the verdict, the trier of fact has to assess the probative
value of the individual items of evidence which have been received at
the trial. The concept of probative value can also play a role at the
prior stage (which was the focus in
 section 2)
 where the judge has to make a ruling on whether to receive the
evidence in the first place. In many legal systems, if the judge finds
the probative value of a proposed item of evidence to be low and
substantially outweighed by countervailing considerations, such as the
risk of causing unfair prejudice or confusion, the judge can refuse to
let the jury hear or see the evidence (see, e.g., Rule 403 of the
United States' Federal Rules of Evidence).



The concept of probative value (or, as it is also called, probative
force) is related to the concept of relevance.
 Section 2.1.2
 above introduced and examined the claim that the likelihood ratio is
the measure of relevance. To recapitulate, the likelihood of an item
of evidence, *E* (in our previous example, the likelihood of a
blood type match) given a hypothesis *H* (that the accused is
in fact guilty) is compared with the likelihood of *E* given
the negation of *H* (that the accused is in fact innocent).
Prior to the introduction of *E*, one may have formed some
belief about *H* based on other evidence that one already has.
This prior belief does not affect the likelihood ratio since its
computation is based on the alternative assumptions that *H* is
true and that *H* is false (Kaye 1986a; Kaye and Koehler 2003;
cf. Davis and Follette 2002 and 2003). Rulings on relevance are
made by the judge when objections of irrelevance
are raised in the course of the trial. The relevance of
an item of evidence is supposedly assessed on its own, without
consideration of other evidence, and, indeed, much of the other
evidence may have yet to presented at the point when the judge
rules on the relevance of a particular item of
evidence (Mnookin 2013:
 1544-5).[12]



Probative value, as with relevance, has been explained in terms of the
likelihood ratio (for detailed examples, see Nance and Morris 2002;
Finkelstein and Levin 2003). It was noted earlier that evidence is
either relevant or not, and, on the prevailing understanding, it is
relevant so long as the likelihood ratio deviates from 1:1. But
evidence can be more or less probative depending on the value of the
likelihood ratio. In our earlier example, the probative value of a
blood type match was 1.0:0.5 (or 2:1) as 50% of the suspect population
had the same blood type as the accused. But suppose the blood type is
less common and only 25% of the suspect population has it. The
probative value of the evidence is now 1.0:0.25 (or 4:1). In both
cases, the evidence is relevant; but the probative value is greater in
the latter than in the former scenario. It is tempting to describe
probative value as the degree of relevance but this would be
misleading as relevance in law is a binary concept.



There is a second way of thinking about probative value. On the second
view, but not on the first, the probative value of an item of evidence
is assessed contextually. The probative value of *E* may be low
given one state of the other evidence and substantial given a
different body of other evidence (Friedman 1986; Friedman and Park
2003; cf. Davis and Follette 2002, 2003). Where the other evidence
shows that a woman had died from falling down an escalator at a mall
while she was out shopping, her husband's history of spousal
battery is unlikely to have any probative value in proving that he was
responsible for her death. But where the other evidence shows that the
wife had died of injuries in the matrimonial home, and the question is
whether the injuries were sustained from an accidental fall from the
stairs or inflicted by the husband, the same evidence of spousal
battery will now have significant probative value.



On the second view, the probative value of an item of evidence
(*E*) is not measured simply by the likelihood ratio as it is
on the first view. Probative value is understood as the degree to
which *E* increases (or decreases) the probability of the
proposition or hypothesis (*H*) in support of (or against)
which *E* is led. The probative value of *E* is measured
by the difference between the probability of *H* given
*E* (the posterior probability) and the probability of
*H* absent *E* (the prior probability) (Friedman 1986;
James 1941: 699).



Probative value of \(E = P(H | E) - P(H)\)



\(P(H | E)\) (the posterior probability) is derived by applying
Bayes' theorem--that is, by multiplying the prior
probability by the likelihood ratio (see discussion in
 section 3.2.2
 below). On the present view, while the likelihood ratio does not
itself measure the probative value of *E*, it is nevertheless a
crucial component in the assessment.



A major difficulty with both of the mathematical conceptions of
probative value that we have just examined is that for most evidence,
obtaining the figures necessary for computing the likelihood ratio is
problematic (Allen 1991: 380). Exceptionally, quantitative base rates
data exist, as in our blood type example. Where objective data is
unavailable, the fact-finder has to draw on background experience and
knowledge to come up with subjective values. In our blood type
example, a critical factor in computing the likelihood ratio was the
percentage of the "suspect population" who had the same
blood type as the accused. "Reference class" is the
general statistical term for the role that the suspect population
plays in this analysis. How should the reference class of
"suspect population" be defined? Should we look at the
population of the country as a whole or of the town or the street
where the alleged murder occurred? What if it occurred at an
international airport where most the people around are foreign
visitors? Or what if it is shown that both the accused and the victim
were at the time of the alleged murder inmates of the same prison?
Should we then take the prison population as the reference class? The
distribution of blood types may differ according to which reference
class is selected. Sceptics of mathematical modelling of probative
value emphasize that data from different reference classes will have
different explanatory power and the choice of the reference class is
open to--and should be subjected to--contextual argument and
requires the exercise of judgment; there is no a priori way of
determining the correct reference class. (On the reference class
problem in legal factfinding, see, in addition to references cited in
the rest of this section, Colyvan, Regan, and Ferson 2001; Tillers
2005; Allen and Roberts 2007.)



Some writers have proposed quantifiable ways of selecting, or
assisting in the selection, of the appropriate reference class. On one
suggestion, the court does not have to search for the optimal
reference class. A general characteristic of an adversarial system of
trial is that the judge plays a passive role; it is up to the parties
to come up with the arguments on which they want to rely and to
produce evidence in support of their respective arguments. This
adversarial setting makes the reference class problem more manageable
as the court need only to decide which of the reference classes relied
upon by the parties is to be preferred. And this can be done by
applying one of a variety of technical criteria that statisticians
have developed for comparing and selecting statistical models (Cheng
2009). Another suggestion is to use the statistical method of
"feature selection" instead. The ideal reference class is
defined by the intersection of all relevant features of the case, and
a feature is relevant if it is correlated to the matter under enquiry
(Franklin 2010, 2011: 559-561). For instance, if the amount of
drug likely to be smuggled is reasonably believed to co-vary with the
airport through which it is smuggled, the country of origin and the
time period, and there is no evidence that any other feature is
relevant on which data is available, the ideal reference class is the
class of drug smugglers passing through that airport originating from
that country and during that time period. Both suggestions have
self-acknowledged limitations: not least, they depend on the
availability of suitable data. Also, as Franklin stresses, while
statistical methods "have advice to offer on how courts should
judge quantitative evidence", they do so "in a way that
supplements normal intuitive legal argument rather than replacing it
by a formula" (Franklin 2010: 22).



The reference class problem is not confined to the probabilistic
assessment of the probative value of individual items of evidence. It
is a general difficulty with a mathematical approach to legal proof.
In particular, the same problem arises on a probabilistic
interpretation of the standard of proof when the court has to
determine whether the standard is met based on all the evidence
adduced in the case. This topic is explored in
 section 3.2
 below but it is convenient at this juncture to illustrate how the
reference class problem can also arise in this connection. Let it be
that the plaintiff sues Blue Bus Company to recover compensation for
injuries sustained in an accident. The plaintiff testifies, and the
court believes on the basis of his testimony, that he was run down by
a recklessly driven bus. Unfortunately, it was dark at the time and he
cannot tell whether the bus belonged to Blue Bus Company. Assume
further that there is also evidence which establishes that Blue Bus
Company owns 75% of the buses in the town where the accident occurred
and the remaining 25% is owned by Red Bus Company. No other evidence
is presented. To use the data as the basis for inferring that there is
0.75 probability that the bus involved in the accident was owned by
Blue Bus Company would seem to privilege the reference class of
"buses operating in the town" over other possible
reference classes such as "buses plying the street where the
accident occurred" or "buses operating at the time in
question" (Allen and Pardo 2007a: 109). Different reference
classes may produce very different likelihood ratios. It is crucial
how the reference class is chosen and this is ultimately a matter of
argument and judgment. Any choice of reference class (other than the
class that shares *every* feature of the particular incident,
which is, in effect, the unique incident itself) is in principle
contestable.



Critics of the mathematization of legal proof raise this point as an
example of inherent limitations to the mathematical modelling of
probative value (Allen and Pardo
 2007a).[13]
 Allen and Pardo propose an alternative, the explanatory theory of
legal proof. They claim that this theory has the advantage of avoiding
the reference class problem because it does not attempt to quantify
probative value (Pardo 2005: 374-383; Pardo and Allen 2008: 261,
263; Pardo 2013: 600-601). Suppose a man is accused of killing
his wife. Evidence is produced of his extra-marital affair. The unique
probative value of the accused's infidelity cannot be
mathematically computed from statistical base rates of infidelity and
uxoricides (husbands murdering wives). In assessing its probative
value, the court should look instead at how strongly the evidence of
infidelity supports the explanation of the material events put forward
by the side adducing the evidence and how strongly it challenges the
explanation offered by the opponent. For instance, the prosecution may
be producing the evidence to buttress its case that the accused wanted
to get rid of his wife so that he could marry his mistress, and the
defence may be advancing the alternative theory that the couple was
unusual in that they condoned extra-marital affairs and had never let
it affect their loving relationship. How much probative value the
evidence of infidelity has depends on the strength of the explanatory
connections between it and the competing hypotheses, and this is not
something that can be quantified.



But the disagreement in this debate is not as wide as it might appear.
The critics concede that formal models for evaluating evidence in law
may be useful. What they object to is



> 
> 
> scholarship arguing ... that such models establish the correct or
> accurate probative value of evidence, and thus implying that any
> deviations from such models lead to inaccurate or irrational outcomes.
> (Allen and Pardo 2007b: 308)
> 
> 
> 



On the other side, it is acknowledged that there are limits to
mathematical formalisation of evidential reasoning in law (Franklin
2012: 238-9) and that context, argument and judgment do play a
role in identifying the reference class (Nance 2007b).


### 3.2 Sufficiency of Evidence and the Standards of Proof


#### 3.2.1 Mathematical Probability and the Standards of Proof



In the
 section 3.1
 above, we concentrated on the weight of evidence in the sense of
probative value of individual items of evidence. The concept of weight
can also apply to the total body of evidence presented at the trial;
here "weight" is commonly referred to as the
"sufficiency of 
 evidence".[14]
 The law assigns the legal
burden of proof between parties to a dispute. For instance, at a
criminal trial, the accused is presumed innocent and the burden is on
the prosecution to prove that he is guilty as charged. To secure a
conviction, the body of evidence presented at the trial must be
sufficient to meet the standard of proof. Putting this generally, a
verdict will be given in favour of the side bearing the legal burden
of proof only if, having considered all of the evidence, the
fact-finder is satisfied that the applicable standard of proof is met.
The standard of proof has been given different interpretations.



On one interpretation, the standard of proof is a probabilistic
threshold. In civil cases, the standard is the "balance of
probabilities" or, as it is more popularly called in the United
States, the "preponderance of evidence". The plaintiff
will satisfy this standard and succeed in his claim only if there is,
on all the evidence adduced in the case, more than 0.5 probability of
his claim being true. At criminal trials, the standard for a guilty
verdict is "proof beyond a reasonable doubt". Here the
probabilistic threshold is thought to be much higher than 0.5 but
courts have eschewed any attempt at authoritative quantification.
Typically, a notional value, such as 0.9 or 0.95, is assumed by
writers for the sake of discussion. For the prosecution to secure a
guilty verdict, the evidence adduced at the trial must establish the
criminal charge to a degree of probability that crosses this
threshold. Where, as in the United States, there is an intermediate
standard of "clear and convincing evidence" which is
reserved for special cases, the probabilistic threshold is said to lie
somewhere between 0.5 and the threshold for proof beyond reasonable
doubt.



Kaplan was among the first to employ decision theory to develop a
framework for setting the probabilistic threshold that represents the
standard of proof. Since the attention in this area of the law tends
to be on the avoidance of errors and their undesirable consequences,
he finds it convenient to focus on disutility rather than utility. The
expected disutility of an outcome is the product of the disutility
(broadly, the social costs) of that outcome and the probability of
that outcome. Only two options are generally available to the court:
in criminal cases, it must either convict or acquit the accused and in
civil cases, it has to give judgment either for the plaintiff or for
the defendant. At a criminal trial, the decision should be made to
convict where the expected disutility of a decision to acquit is
greater than the expected disutility of a decision to convict. This is
so as to minimize the expected disutilities. To put this in the form
of an equation:

 

\[ P\cdot\textit{Dag} > (1-P)\textit{Dci} \]


*P* is the probability that the accused is guilty on the basis
of all the evidence adduced in the case, *Dag* is the
disutility of acquitting a guilty person and *Dci* is the
disutility of convicting an innocent person. A similar analysis
applies to civil cases: the defendant should be found liable where the
expected disutility of finding him not liable when he is in fact
liable exceeds the expected disutility of finding him liable when he
is in fact not liable.



On this approach, a person should be convicted of a crime only where
*P* is greater than:

 

\[ \frac{1}{1+\frac{\textit{Dag}}{\textit{Dci}}} \]


The same formula applies in civil cases except that the two
disutilities (*Dag* and *Dci*) will have to be replaced
by their civil equivalents (framed in terms of the disutility of
awarding the judgment to a plaintiff who in fact does not deserve it
and disutility of awarding the judgment to a defendant who in fact
does not deserve it). On this formula, the crucial determinant of the
standard of proof is the ratio of the two disutilities. In the civil
context, the disutility of an error in one direction is deemed equal
to the disutility of an error in the other direction. Hence, a
probability of liability of greater than 0.5 would suffice for a
decision to enter judgment against the defendant (see Redmayne 1996:
171). The situation is different at a criminal trial. *Dci*,
the disutility of convicting an innocent person is considered far
greater than *Dag*, the disutility of acquitting a guilty
 person.[15]
 Hence, the probability threshold for a conviction should be much
higher than 0.5 (Kaplan 1968: 1071-1073; see also Cullison
1969).



An objection to this analysis is that it is incomplete. It is not
enough to compare the costs of erroneous verdicts. The utility of an
accurate conviction and the utility of an accurate acquittal should
also be considered and factored into the equation (Lillquist 2002:
 108).[16]
 This results in the following modification of the formula for setting
the standard of proof:

 

\[ \frac{1}{1+\frac{\textit{Ucg}-\textit{Uag}}{\textit{Uai}-\textit{Uci}}} \]


*Ucg* is the utility of convicting the guilty, *Uag* is
the utility of acquitting the guilty, *Uai* is the utility of
acquitting the innocent and *Uci* the utility of convicting the
innocent.



Since the relevant utilities depend on the individual circumstances,
such as the seriousness of the crime and the severity of the
punishment, the decision-theoretic account of the standard of proof
would seem, on both the simple and the modified version, to lead to
the conclusion that the probabilistic threshold should vary from case
to case (Lillquist 2002; Bartels 1981; Laudan and Saunders 2009;
Ribeiro 2019). In other words, the standard of proof should be a
flexible or floating one. This view is perceived to be
problematic.



First, it falls short descriptively. The law requires the court to
apply a fixed standard of proof for all cases within the relevant
category. In theory, all criminal cases are governed by the same high
standard and all civil cases are governed by the same lower standard.
That said, it is unclear whether factfinders in reality adhere
strictly to a fixed standard of proof (see Kaplow 2012:
805-809).



The argument is better interpreted as a normative argument--as
advancing the claim about what the law ought to be and not what it is.
The standard of proof ought to vary from case to case. But this
proposal faces a second objection. For convenience, the objection will
be elaborated in the criminal setting; in principle, civil litigants
have the same two rights that we shall identify. According to Dworkin
(1981), moral harm arises as an objective moral fact when a person is
erroneously convicted of a crime. Moral harm is distinguished from the
bare harm (in the form of pain, frustration, deprivation of liberty
and so forth) that is suffered by a wrongfully convicted and punished
person. While accused persons have the right not to be convicted if
innocent, they do not have the right to the most accurate procedure
possible for ascertaining their guilt or innocence. However, they do
have the right that a certain weight or importance be attached to the
risk of moral harm in the design of procedural and evidential rules
that affect the level of accuracy. Accused persons have the further
right to a consistent weighting of the importance of moral harm and
this further right stems from their right to equal concern and
respect. Dworkin's theory carries an implication bearing on the
present debate. It is arguable that to adopt a floating standard of
proof would offend the second right insofar as it means treating
accused persons differently with respect to the evaluation of the
importance of avoiding moral harm. This difference in treatment is
reflected in the different level of the risk of moral harm to which
they are exposed.



There is a third objection to a floating standard of proof. Picinali
(2013) sees fact-finding as a theoretical exercise that engages the
question of what to believe about the disputed facts. What counts as
"reasonable" for the purposes of applying the standard of
proof beyond reasonable doubt is accordingly a matter for theoretical
as opposed to practical reasoning. Briefly, theoretical reasoning is
concerned with what to believe whereas practical reasoning is about
what to do. Only reasons for belief are germane in theoretical
reasoning. While considerations that bear on the assessment of utility
and disutility provide reasons for action, they are not reasons for
believing in the accused's guilt. Decision theory cannot
therefore be used to support a variable application of the standard of
proof beyond reasonable doubt.



The third criticism of a flexible standard of proof does not directly
challenge the decision-theoretic analysis of the standard of proof. On
that analysis, it would seem that the maximisation of expected utility
is the criterion for selecting the appropriate probabilistic threshold
to apply and it plays no further role in deciding whether that
threshold, once selected, is met on the evidence adduced in the
particular case. It is not incompatible with the decision-theoretic
analysis to insist that the question of whether the selected threshold
is met should be governed wholly by epistemic considerations. However,
it is arguable that what counts as good or strong enough theoretical
reason for judging, and hence believing, that something is true is
dependent on the context, such as what is at stake in believing that
it is true. More is at stake at a trial involving the death penalty
than in a case of petty shop-lifting; accordingly, there should be
stronger epistemic justification for a finding of guilt in the first
than in the second case. Philosophical literature on epistemic
contextualism and on interest-relative accounts of knowledge and
justified belief has been drawn upon to support a variant standard of
proof (Ho 2008: ch. 4; see also Amaya 2015:
 525-531).[17]



The premise of the third criticism is that the trier of fact has to
make a finding on a disputed factual proposition based on his belief
in the proposition. This is contentious. Beliefs are involuntary; we
cannot believe something by simply deciding to believe it. The
dominant view is that beliefs are context-independent; at any given
moment, we cannot believe something in one context and not believe it
in another. On the other hand, legal fact-finding involves choice and
decision making and it is dependent on the context; for example,
evidence that is strong enough to justify a finding of fact in a civil
case may not be strong enough to justify the same finding in a
criminal case where the standard of proof is higher. It has been
argued that the fact-finder has to base his findings not on what he
believes but what he accepts (Cohen 1991, 1992: 117-125,
Beltran 2006; cf. Picinali 2013: 868-869). Belief and
acceptance are propositional attitudes: they are different attitudes
that one can have in relation to a proposition. As Cohen (1992: 4)
explains:



> 
> 
> to accept that *p* is to have or adopt a policy of deeming,
> positing or postulating that *p*--i.e. of including that
> proposition or rule among one's premises for deciding what to do
> or think in a particular context.
> 
> 
> 


#### 3.2.2 Objections to Using Mathematical Probability to Interpret Standards of Proof



Understanding standards of proof in terms of mathematical
probabilities is controversial. It is said to raise a number of
paradoxes (Cohen 1977; Allen 1986, 1991; Allen and Leiter 2001;
Redmayne 2008). Let us return to our previous example. The defendant,
Blue Bus Company, owns 75% of the buses in the town where the
plaintiff was injured by a recklessly driven bus and the remaining 25%
is owned by Red Bus Company. No other evidence is presented. Leaving
aside the reference class problem discussed above, there is a 0.75
probability that the accident was caused by a bus owned by the
defendant. On the probabilistic interpretation of the applicable
standard of proof (that is, the balance of probabilities), the
evidence should be sufficient to justify a verdict in the
plaintiff's favour. But most lawyers would agree that the
evidence is insufficient. Another familiar hypothetical scenario is
set in the criminal context (Nesson 1979: 1192-1193). Twenty
five prisoners are exercising in a prison yard. Twenty four of them
suddenly set upon a guard and kill him. The remaining prisoner refuses
to participate. We cannot in the ensuing confusion identify the
prisoner who refrained from the attack. Subsequently, one prisoner is
selected randomly and prosecuted for the murder of the guard. Those
are the only facts presented at the trial. The applicable standard is
proof beyond a reasonable doubt. Assume that the probabilistic
threshold of this standard is 0.95. On the statistical evidence, there
is a probability of 0.96 that the defendant is criminally
 liable.[18]
 Despite the statistical probability of liability exceeding the
threshold, it is widely agreed that the defendant must be acquitted.
In both of the examples just described, why is the evidence
insufficient and what does this say about legal standards of
proof?



Various attempts have been made to find the answers (for surveys of
these attempts, see Enoch and Fisher 2015: 565-571; Redmayne
2008, Ho 2008: 135-143, 168-170; Gardiner 2019b; section 6
of the entry on 
 legal probabilism). 
 It has been argued that meeting a
legal standard of proof is not merely or fundamentally a matter of
adducing evidence to establish a mathematical probability of liability
beyond a certain level. Standards of proof should be interpreted in
epistemic rather than probabilistic terms. According to one
interpretation, the evidence is sufficient to satisfy a standard of
proof only if it is capable of justifying full or outright belief in
the material facts that constitute legal liability and bare
statistical evidence, as in our examples, cannot justify such a
belief. (Nelkin 2021; Smith 2018; Buchak 2014; Ho 2008: 89-99.)
On Smith's account, the statistical evidence in our two examples
fails to justify belief in the proposition that the defendant is
liable because the evidence does not normically support that
proposition. Evidence normically supports a proposition just in case
the situation in which the evidence is true and the proposition is
false is less normal, in the sense of requiring more explanation, than
the situation in which the evidence and the proposition are both true.
Where all that we have is statistical evidence, it could just so
happen that the material proposition is false (it could just so happen
that the accident-causing bus was red or that the accused was the one
who refused to join in the murder), so no further explanation is
needed where the proposition is false than where it is true (Smith
2018).



On a different epistemic interpretation, the evidence is sufficient to
meet a legal standard of proof, and a finding of legal liability is
permissible, only if the factfinder can gain knowledge of the
defendant's liability--to be precise, of the material facts
establishing such liability--from the evidence (Duff et al. 2007:
87-91; Pardo 2010; for a critical overview of knowledge-centered
accounts, see Gardiner forthcoming). High probability of liability
alone will not suffice. On more subtle knowledge-centered theories,
the standards of proof are met only if, on the available evidence,
there is a sufficiently high probability that the fact finder knows
that the defendant is liable (Littlejohn 2020 and 2021; Blome-Tillmann
2017), or only if the fact finder's credence in the
defendant's liability exceeds the relevant legal threshold and
the credence constitutes knowledge (Moss 2018). It is further claimed
that the relevant knowledge necessary for a finding of liability
cannot be obtained from statistical evidence alone (Littlejohn 2020
and 2021; Blome-Tillmann 2017; Moss 2018 and forthcoming). According
to Thomson, this is because the statistical evidence (to take our
first example, the 75% ownership of blue buses) is not causally
connected with the fact sought to be proved and cannot guarantee the
truth of the relevant belief (that the bus which caused the accident
was blue) (Thomson 1986). An alternative argument is that knowledge
requires the ruling out of all relevant alternatives and, to take our
prison scenario, there is no evidence that addresses the possibility
that the defendant was the one who refrained from joining in the
attack or the possibility that the defendant is less likely to be
guilty than an arbitrary prisoner in the yard. (See Moss forthcoming;
Moss 2018: 213. Gardiner 2019a adapts the relevant alternatives
framework to model legal standards of proof in a non-mathematical way
while eschewing a knowledge account of those standards.) Another
possible explanation for the failure to know relies on the notion of
sensitivity. The belief that the defendant is liable is not sensitive
to the truth where it is based on bare statistical evidence; in the
bus example, evidence of the market share of buses remain the same
whether it is true or not that a blue bus caused the accident (cf.
Enoch, Spectre, and Fisher 2012; Enoch and Fisher 2015; Enoch and
Spectre 2019 - while suggesting that the lack of knowledge has
generally to do with the insensitivity of the belief, the authors deny
that knowledge should matter to the imposition of legal liability).
Yet another explanation is that it is unsafe to find a person liable
on bare statistical evidence. Though safety is sometimes treated as a
condition of knowledge (in that knowledge requires a true belief that
is safe), one can treat safety as a condition for finding the
defendant liable without also taking the position that the finding
must be based on knowledge of liability. Safety is commonly understood
in terms of whether a belief formed on the same basis would be true in
close possible worlds. Roughly, a finding of liability is unsafe where
it can easily be wrong in the sense that little in the actual world
needs to change for it to be wrong. Whether the requirement of safety
can explain why judgment should not entered against the defendant in
our two hypothetical cases would depend on whether it can easily
happen that the accident-causing bus was red or that the accused is
innocent. (See Pritchard 2015 and 2018; Pardo 2018; cf. Gardiner
2020.) While theorizing of standards of proof in epistemic terms has
gathered pace in recent years, it is criticised for relying on
unrealistic hypotheticals that fail to attend to the actual operation
of legal systems and for making impossible epistemological demands
(Allen 2020).



There is another paradox in the mathematical interpretation of the
standard of proof. This is the "conjunction paradox". To
succeed in a civil claim (or a criminal prosecution), the plaintiff
(or the prosecution) will have to prove the material facts--or
"elements"--that constitute the civil claim (or
criminal charge) that is before the court (see discussion of
"materiality" in
 section 2.2
 above). Imagine a claim under the law of negligence that rests on two
elements: a breach of duty of care by the defendant (element
*A*) and causation of harm to the plaintiff (element
*B*). To win the case, the plaintiff is legally required to
prove *A* and *B*. For the sake of simplicity, let
*A* and *B* be mutually independent events. Suppose the
evidence establishes *A* to a probability of 0.6 and *B*
to a probability of 0.7. On the mathematical interpretation of the
civil standard of proof, the plaintiff should succeed in his claim
since the probability with respect to each of the elements exceeds
0.5. However, according to the multiplication rule of conventional
probability calculus, the probability that *A* and *B*
are both true is the product of their respective probabilities; in
this example, it is only 0.42 (obtained by multiplying 0.6 with 0.7).
Thus, the overall probability is greater that the defendant deserves
to win than that the plaintiff deserves to win, and yet the verdict is
awarded in favour of the plaintiff.



One way of avoiding the conjunction paradox is to take the position
that it should not be enough for each element to cross the
probabilistic threshold; the plaintiff (or the prosecution) should win
only if the probability of the plaintiff's (or
prosecution's) case as a whole exceeds the applicable
probabilistic threshold. So, in our example, the plaintiff should lose
since the overall probability is below 0.5. But this suggested
solution is unsatisfactory. The required level of overall probability
would then turn on how many elements the civil claim or criminal
charge happens to have. The greater the number of elements, the higher
the level of probability to which, on average, each of them must be
proved. This is thought to be arbitrary and hence objectionable. As
two commentators noted, the legal definition of theft contains more
elements than that for murder. Criminal law is not the same in all
countries. We may take the following as a convenient approximation of
what the law is in some countries: murder is (1) an act that caused
the death of a person (2) that was done with the intention of causing
the death, and to constitute theft, there must be (1) an intention to
take property, (2) dishonesty in taking the property, (3) removal of
the property from the possession of another person, and (4) lack of
consent by that person. Since the offence of theft contains twice the
number of elements as compared to murder, the individual elements for
theft would have to be proved to a much higher level of probability
(in order for the probability of their conjunction to cross the
overall threshold) than the individual elements for the much more
serious crime of murder (Allen and Leiter 2001: 1504-5). This is
intuitively unacceptable.



Another proposal for resolving the conjunction paradox is move away
from thinking of the standard of proof as a quantified threshold of
absolute probability and to construe it, instead, as a probability
ratio. The fact-finder has to compare the probability of the evidence
adduced at the trial under the plaintiff's theory of the case
with the probability of the evidence under the defendant's
theory of the case (the two need not add to 1), and award the verdict
to the side with a higher probability (Cheng 2013). One criticism of
this interpretation of the standard of proof is that it ignores, and
does not provide a basis for ignoring, the margin by which one
probability exceeds the other, and the difference in probability may
vary significantly for different elements of the case (Allen and Stein
2013: 598).



There is a deeper problem with the probabilistic conception of the
standard of proof. There does not seem to be a satisfactory
interpretation of probability that suits the forensic context. The
only plausible candidate is the subjective meaning of probability
according to which probability is construed as the strength of belief.
The evidence is sufficient to satisfy the legal standard of proof on a
disputed question of fact--for example, it is sufficient to
justify the positive finding of fact that the accused killed the
victim--only if the fact-finder, having considered the evidence,
forms a sufficiently strong belief that the accused killed the victim.
Guidance on how to process evidence and form beliefs can be found in a
mathematical theorem known as Bayes' theorem; it is the method
by which an ideal rational fact-finder would revise or update his
beliefs in the light of new
 evidence.[19]
 To return to our earlier hypothetical scenario, suppose the
fact-finder initially believes the odds of the accused being guilty is
1:1 ("prior odds") or, putting this differently, that
there is a 0.5 probability of guilt. The fact-finder then receives
evidence that blood of type A was found at the scene of the crime and
that the accused has type A blood. Fifty percent of the population has
this blood type. On the Bayesian approach, the posterior odds are
calculated by multiplying the prior odds (1:1) by the likelihood ratio
(which, as we saw in
 section 2.1.2
 above, is 2:1). The fact-finder's belief in the odds of guilt
should now be revised to 2:1; the probability of guilt is now
increased to 0.67 (Lempert 1977).



The subjectivist Bayesian theory of legal fact-finding has come under
attack (see generally Amaya 2015: 82-93; Pardo 2013: 591).
First, as we already saw in
 section 3.1,
 ascertainment of the likelihood ratios is highly problematic.
Secondly, the Bayesian theory is not sensitive to the weight of
evidence which, roughly put, is the amount of evidence that is
available. This criticism and the concept of weight are further
explored in
 section 3.3.



Thirdly, while the Bayesian theorem offers a method for updating
probabilities in the light of new evidence, it is silent on what the
initial probability should be. In a trial setting, the initial
probability cannot be set at zero since this means certainty in the
innocence of the accused. No new evidence can then make any
difference; whatever the likelihood ratio of the evidence, multiplying
it by zero (the prior probability) will still end up with a posterior
probability of zero. On the other hand, starting with an initial
probability is also problematic. This is especially so in a criminal
case. To start a trial with some probability of guilt is to have the
fact-finder harbouring some initial belief that the accused is guilty
and this is not easy to reconcile with the presumption of innocence.
(Tribe 1971: 1368-1372; cf. Posner 1999: 1514, suggesting
starting the trial with prior odds of 50:50, criticized by Friedman
2000. The problem of fixing the prior probability is said to disappear
if we base fact-finding simply on likelihood ratios: Sullivan, 2019:
45-59.)



Fourthly, we have thus far relied for ease of illustration on highly
simplified--and therefore unrealistic--examples. In real
cases, there are normally multiple and dependent items of evidence and
the probabilities of all possible conjunctions of these items, which
are numerous, will have to be computed. These computations are far too
complex to be undertaken by human beings (Callen 1982: 10-15).
The impossibility of complying with the Bayesian model undermines its
prescriptive value.



Fifthly, according to Haack, the Bayesian theory has it the wrong way
round. What matters is not the strength of the fact-finder's
belief itself. The standard of proof should be understood instead in
terms of what it is reasonable for the fact-finder to believe in the
light of the evidence presented, and this is a matter of the degree to
which the belief is warranted by the evidence. Evidence is legally
sufficient where it warrants the contested factual claim to the degree
required by law. Whether a factual claim is warranted by the evidence
turns on how strongly the evidence supports the claim, on how
independently secure the evidence is, and on how much of the relevant
evidence is available to the fact-finder (that is, the
comprehensiveness of the evidence--see further discussion in
 section 3.3
 below). Haack is against identifying degrees of warrant with
mathematical probabilities. Degrees of warrant do not conform to the
axioms of the standard probability calculus. For instance, where the
evidence is weak, neither *p* nor not-*p* may be
warranted; in contrast, the probability of *p* and the
probability of not-*p* must add up to 1. Further, where the
probability of *p* and the probability of *q* are both
less than 1, the probability of *p* and *q*, being the
product of the probability of *p* and the probability of
*q*, is less than the probability of either. On the other hand,
the degree of warrant for the conjunction of *p* and *q*
may be higher than the warrant for
 either.[20]
 (See Haack 2004, 2008a,b, 2012, 2014 for the legal application of her
general theory of epistemology. For her general theory of
epistemology, see Haack 1993: ch. 4; Haack 2009: ch. 4; Haack 2003:
ch. 3.)



Sixthly, research in experimental psychology suggests that
fact-finders do not evaluate pieces of evidence one-by-one and in the
unidirectional manner required under the mathematical model (Amaya
2015: 114-5). A holistic approach is taken instead where the
discrete items of evidence are integrated into large cognitive
structures (variously labelled as "mental models",
"stories", "narratives" and "theories of
the case"), and they are assessed globally against the legal
definition of the crime or civil claim that is in dispute (Pennington
and Hastie 1991, 1993; Pardo 2000). The reasoning does not progress
linearly from evidence to a conclusion; it is bi-directional, going
forward and backward: as the fact-finder's consideration of the
evidence inclines him towards a particular verdict, his leaning
towards that conclusion will often produce a revision of his original
perception and his assessment of the evidence (Simon 2004, 2011).



The holistic nature of evidential reasoning as revealed by these
studies has inspired alternative theories that are of a
non-mathematical nature. One alternative, already mentioned, is the
"explanatory" or "relative plausibility"
theory advanced by Allen together with Pardo and other collaborators
(Allen 1986, 1991, 1994; Pardo 2000; Allen and Leiter 2001; Allen and
Jehl 2003; Pardo and Allen 2008; Allen and Pardo 2019; cf. Nance 2001,
Friedman
 2001).[21]
 They contend that fact-finders do not reason in the fashion portrayed
by the Bayesian model. Instead, they engage in generating explanations
or hypotheses on the available evidence by a process of abductive
reasoning or drawing "inferences to the best explanation",
and these competing explanations or hypotheses are compared in the
light of the
 evidence.[22]
 The comparison is not of a hypothesis with the negation of that
hypothesis, where the probability of a hypothesis is compared with the
probability of its negation. Instead, the comparison is of one
hypothesis with one or more particular alternative hypotheses as
advocated by a party or as constructed by the fact-finder himself. On
this approach, the plausibility of X, the factual account of the case
that establishes the accused's guilt or defendant's
liability, is compared with the plausibility of a hypothesis Y, a
specific alternative account that points to the accused's
innocence or the defendant's non-liability, and there may be
more than one such specific alternative account.



On this theory, the evidence is sufficient to satisfy the
preponderance of proof standard when the best-available hypothesis
that explains the evidence and the underlying events include all of
the elements of the claim. Thus, in a negligence case, the
best-available hypothesis would have to include a breach of duty of
care by the plaintiff and causation of harm to the defendant as these
are the elements that must be proved to succeed in the legal claim.
For the intermediate "clear-and-convincing" standard of
proof, the best-available explanation must be substantially better
than the alternatives. To establish the standard of proof beyond
reasonable doubt, there must be a plausible explanation of the
evidence that includes all of the elements of the crime and, in
addition, there must be no plausible explanation that is consistent
with innocence (Pardo and Allen 2008: 238-240; Pardo 2013:
603-604).



The relative plausibility theory itself is perceived to have a number
of
 shortcomings.[23]
 First, the theory portrays the assessment of plausibility as an
exercise of judgment that involves employment of various criteria such
as coherence, consistency, simplicity, consilience, and more. However,
the theory is sketchy on the meaning of plausibility and the criteria
for evaluating plausibility are left largely
 unanalyzed.[24]



A second criticism of the relative plausibility theory is that,
despite the purported utilisation of "inference to the best
explanation" reasoning, the verdict is not controlled by the
best explanation. For instance, even if the prosecution's
hypothesis is better than the defence's hypothesis, neither may
be very good. In these circumstances, the court must reject the
prosecution's hypothesis even though it is the best of
alternatives (Laudan 2007). One suggested mitigation of this criticism
is to place some demand on the epistemic effort that the trier of fact
must take (for example, by being sufficiently diligent and thorough)
in constructing the set of hypotheses from which the best is to be
chosen (Amaya 2009: 155).



The third criticism is targeted at holistic theories of evidential
reasoning in general and not specifically at the relative plausibility
theory. While it may be descriptively true that fact-finders decide
verdicts by holistic evaluation of the plausibility of competing
explanations, hypotheses, narratives or factual theories that are
generated from the evidence, such forms of reasoning may conceal bias
and prejudice that stand greater chances of exposure under a
systematic approach such as Bayesian analysis (Twining 2006: 319;
Simon 2004, 2011; Griffin 2013). A hypothesis constructed by the
fact-finder may be shaped subconsciously by a prejudicial
generalisation or background belief about the accused based on a
certain feature, say, his race or sexual history. Individuating this
feature and subjecting it to Bayesian scrutiny has the desirable
effect of putting the generalisation or background belief under the
spotlight and forcing the fact-finder to confront the problem of
prejudice.


### 3.3 The Weight of Evidence as the Degree of Evidential Completeness



A third idea of evidential weight is prompted by this insight from
Keynes (1921: 71):



> 
> 
> As the relevant evidence at our disposal increases, the magnitude of
> the probability of the argument may either decrease or increase,
> according as the new knowledge strengthens the unfavourable or the
> favourable evidence; but *something* seems to have increased in
> either case,--we have a more substantial basis upon which to rest
> our conclusion. I express this by saying that an accession of new
> evidence increases the *weight* of an argument. New evidence
> will sometimes decrease the probability of an argument, but it will
> always increase its "weight".
> 
> 
> 



This idea of evidential weight has been applied by some legal scholars
in assessing the sufficiency of evidence in satisfying legal standards
of
 proof.[25]
 At its simplest, we may think of weight in the context of legal
fact-finding as the amount of evidence before the court. Weight is
distinguishable from probability. The weight of evidence may be high
and the mathematical probability low, as in the situation where the
prosecution adduces a great deal of evidence tending to incriminate
the accused but the defence has an unshakeable alibi (Cohen 1986:
641). Conversely, the state of evidence adduced in a case might
establish a sufficient degree of probability--high enough to
cross the supposed threshold of proof on the mathematical conception
of the standard of proof--and yet lack adequate weight. In the
much-discussed gate-crasher's paradox, the only available
evidence shows that the defendant was one of a thousand spectators at
a rodeo show and that only four hundred and ninety nine tickets were
issued. The defendant is sued by the show organiser for gate-crashing.
The mathematical probability that the defendant was a gate-crasher is
0.501 and this meets the probabilistic threshold for civil liability.
But, according to the negation principle of mathematical probability,
there is probability of 0.499 that the defendant did pay for his
entrance. In these circumstances, it is intuitively unjust to find him
liable (Cohen 1977: 75). A possible explanation for not finding him
liable is that the evidence is too flimsy or of insufficient
weight.



Proponents of the mathematical conception of the standard of proof
have stood their ground even while acknowledging that weight has a
role to play in the Bayesian analysis of probative value and the
sufficiency of evidence. If a party does not produce relevant evidence
that is in his possession, resulting in the court facing an evidential
deficiency, it may draw an adverse inference against him when
computing the posterior probability (Kaye 1986b: 667; Friedman 1997).
One criticism of this approach is that, in the absence of information
about the missing evidence, the drawing of the adverse inference is
open to the objection of arbitrariness (Nance 2008: 274). A further
objection is that the management of parties' conduct relating to
evidence preservation and presentation should be left to judges and
not to the jury. What a judge may do to optimize evidential weight is
to impose a burden of producing evidence on a party and to make the
party suffer an adverse finding of fact if he fails to produce the
evidence. This will serve as an incentive for the party to act in a
manner that promotes the interest in evidential completeness (Nance
2008, 2010, 2016).



Cohen suggests that the standard of proof should be conceived entirely
as a matter of evidential weight which, on his theory, is a matter of
the number of tests or challenges to which a factual hypothesis is
subjected to in court. He offers an account of legal fact-finding in
terms of an account of inductive probability that was inspired by the
work of writers such as Francis Bacon and J.S. Mill. Inductive
probability operates differently from the classical calculus of
probability. It is based on inductive support for the common-sense
generalisation that licences the drawing of the relevant inference.
Inductive support for a generalisation is graded according to the
number of tests that it has passed, or, putting this in another way,
by the degree of its resistance to falsification by relevant
variables. The inductive probability of an argument is equal to the
reliability grade of the inductive support for the generalisation
which covers the argument.



Proof beyond reasonable doubt represents the maximum level of
inductive probability. The prosecution may try to persuade the court
to infer that the accused was guilty of burglary by producing evidence
to establish that he was found in the vicinity of the victim's
house late at night with the stolen object on him. This inference is
licensed by the generalisation that normally if a stranger is found
immediately after a burglary in possession of the stolen object, he
intentionally removed it himself. The defence may try to defeat the
inference by showing that the generalization does not apply in the
particular case, for example, by presenting evidence to show that the
accused had found the object on the street. The prosecution's
hypothesis is now challenged or put to the test. As a counter-move, it
may produce evidence to establish that the object could not have been
lying in the street as alleged. If the generalisations on which the
prosecution's case rest survive challenges by the defence at
every possible point, then guilt is proved beyond reasonable
 doubt.[26]
 The same reasoning structure applies in the civil context except that
in a civil case, the plaintiff succeeds in proof on the preponderance
of evidence so long as the conclusion to be proved by him is more
inductively probable than its negation. (Cohen 1977, 1986; cf. Schum
 1979.)[27]



Cohen's theory seems to require that each test to which a
hypothesis is put can be unequivocally and objectively resolved. But
usually this is not the case. In our example, we may not be entirely
convinced that the accused found or did not find the object on the
street, and our evaluation would involve the exercise of judgment that
is no less subjective as the sort of judgments required when applying
the standard probabilistic conception of proof (Nance 2008:
275-6; Schum 1994: 261).