Grice v Grice

Speranza

What is the best conceptual analysis of 'onus probandi'?

To what extent is the conceptual analysis of the ordinary language and 
legalese 'proof' rooted on what the Romans had behind the 'probandi'? How 
'diachronic' should 'conceptual analysis' of "legal proof" be?

In a recent post, re: Grice v Grice, McEvoy was considering 'proof', 
'provable', and 'provability', which may be a good occasion to see if we can 
analyse this, since he is assuming a problem-solving approach that may leave, 
for a Griceian, certain items 'unclarified'.

McEvoy was approaching legal proof from a problem-solving perspective; but 
surely this perspective 'presupposes' a constellation of a conceptual
analysis  (to echo Collingwood). Consider the proof for murder and the proof for
theft  (I'm simplifying legalese). It may be argued that since the
conceptual analysis  of theft includes more elements (or necessary and sufficient
conditions) than  that of murder, the standard of proof would vary. Some legal
philosophers see  this as a paradox but not one that rejects conceptual
analysis.

There are different conceptual analysis of proof'. The more philosophically
sound (qua legal philosophy) is the one more akin to the conceptual
analysis of  proof in general. But we shall see.

Problem-solving does not feature much in what analytic legal philosophers 
have considered about legal proof; instead, alternative conceptual analysis,
and  rejection of alleged counter-examples have. So one has to proceed 
carefully.

First we should start with a bit of an axiom.
i. Senses should not  be multiplied beyond necessity.
ii. "Proof" has only one sense.
The idea  that there is 'legal proof' and other types of proof would then
be judged  spurious or tendentious.
LEGALESE has a  further item of cognate vocabulary -- since we should start
with 'linguistic  botanising': "probative". Thus, In reaching the verdict,
the trier of fact has  to assess the so-called "probative value" (or
"probative force") of each  individual item of evidence which has been received at
the trial. 
An analysis of the concept of "probative value" may  play a role at a prior
stage when the judge has to make a ruling on whether to  receive the

evidence
In many legal systems, if the  judge finds this "probative value"
(concerning 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 consider the evidence.
The concept of  "probative value" is sometimes confusingly referred to in
legalese (there is  legalese and there is legalese) "probative force" -- M.
A. E. Dummett would be  delighted: he loved force! The concept of "probative
value" has been analysed in  terms of a likelihood ratio. Evidence
(including hearsay evidence) can be more  or less PROBATIVE depending on the value of
the likelihood ratio. The probative  value of a blood type match may be
1.0:0.5 (or 2:1) as 50% of the suspect  population may have the same blood type
as the accused. But if 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).  The probative value is greater  in the latter than in the
former scenario.

There may be an alternative  conceptual analysis for "probative value". 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. If some evidence shows that
a woman has 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 if
the other evidence shows that the wife had  died of injuries in the
matrimonial home, 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 this
alternative conceptual analysis, the "probative value"  of an item of evidence E
is NOT measured simply by the objective context-free  likelihood ratio. The
concept of "probative value" is, now, rather, analysed 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
defined, conceptually, as any difference between the  probability of H given
E (the posterior probability) and the probability of H  absent E (the prior
probability). The 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.

On this second  conceptual analysis, the likelihood ratio does not itself
constitute the  probative value of E, even it is nevertheless a crucial
component -- a necessary  condition -- in the analysis of the concept. A major
difficulty with both  analysis of probative value is that for most evidence,
obtaining the figures  necessary for computing the likelihood ratio is
problematic (Grice's example,  "When did you last see your father?"). 
Exceptionally, quantitative base  rates data exist, as in human blood types.  Where
objective data is  unavailable, the fact-finder has to draw on background
experience and knowledge  to come up with subjective values. With blood types, a
critical factor in  computing the likelihood ratio is the percentage of the “
suspect population” who  has the same blood type as the accused. "Reference
class" is the general  statistical term (as "most grices are extinct,
statistically") for the role that  the suspect population plays in this
conceptual analysis. But how should the  reference class of “suspect population” be
defined? Should we look at the  population of the country -- say, of
Ruritania -- as a whole? Or of the town or  the street where the palace is situated
and the the alleged murder of the King  of Ruritania 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  emphasise 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 would
be, contra H. L. A. Hart, no a-priori, purely analytic, way of  determining
the correct reference class.  Some legal philosophers 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. The 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.

Another suggestion is to use the statistical method  of "feature selection"
instead. The ideal reference class is thus conceptually  analysed as the
intersection of all relevant features of the case, and a feature  is relevant
if it is correlated to the matter under enquiry. E.g. 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. Now, 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.

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, and  that's why it
is of particular interest to the analytic legal philosopher. The  same
problem arises on a probabilistic interpretation of the standard of legal  proof
when a court has to determine whether the standard is met based on all the 
evidence adduced in the case. How does the "reference-class" problem can
arises  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 the plaintiff's
testimony, that  the plaintiff was run down by a recklessly-driven bus. It was,
alas, dark and  the plaintiff can NOT really tell whether the bus belonged to
The Blue Bus  Company. Assume that there is evidence which establishes that
The Blue Bus  Company owns 75% of the buses in the capital of Ruritania, where
the accident  occurred, and the remaining 25% is owned by The Red Bus
Company. To use the data  as the basis for inferring that there is p = 0.75 that
the bus involved in the  accident was owned by The Blue Bus Company would
seem to privilege the  "reference class" of "buses operating in the capital of
Ruritania" over other  possible reference classes such as "buses plying the
street in the capital of  Ruritania where the accident occurred" or "buses
operating at the time in  question". I.e. A different "reference class" may
produce a very different  likelihood ratio. It is crucial how the "reference
class" is CHOSEN and this is  ultimately a matter of argument and judgment.
Any choice of a "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 mathematisation of legal "proof" raise this  point of the
arbitrariness of the 'reference class' as an example of inherent  limitations
to the axiomatic modelling of probative value. But there is an  alternative:
an explanatory analysis of legal "proof". This explanatory analysis  of
'legal proof' has the advantage of avoiding the "reference class" problem 
because it does not attempt to quantify probative value. Suppose a man is 
accused of killing his wife. Evidence is produced of the man's extra-marital 
affair. The unique "probative value" of the accused’s infidelity can NOT be 
mathematically computed from statistical base rates of infidelity and 
uxoricides. In assessing its "probative value", the court looks instead at how 
strongly the evidence of infidelity supports the explanation of the events put 
forward by the side adducing the evidence and how strongly it challenges
the  explanation offered by the opponent. 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. The defence may be advancing the
hypothesis  that the couple was unusual in that they condoned extra-marital
affairs and had  never let it affect their marriage. 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 axiomatic 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. On the other side, it is acknowledged that there are limits to 
mathematical formalisation of evidential reasoning in law and that context, 
argument and judgment do play a role in identifying the "reference class". 

We have thus far concentrated on "probative value" of an individual item 
of evidence. But the conceptual analysis should extend to the TOTAL body of 
evidence presented at the trial. The law assigns the legal "onus probandi" 
between parties to a dispute. E.g. at a criminal trial, the accused is
presumed  innocent; "onus probandi" is on the prosecution to prove that the
accused 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". A
verdict will be  given in favour of the side bearing the "onus probandi" iff,
having considered  all of the evidence, the fact-finder is satisfied that the
applicable standard  of "proof" is met.

Now, the standard of "proof" may receive different  conceptual analyses. On
one such analysis, the standard of "proof" is a  probabilistic threshold.
In civil cases, the standard is the "balance of  probabilities" or, the
"preponderance of evidence". The plaintiff may 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  a criminal trial, the
standard for a guilty verdict is -- to use a very  'dogmatic' or rather
anti-sceptical turn of phrase which is SO LEGALESE it  hurts: "legal 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
the legal philosopher for the sake of his analysis. 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 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".

Some conceptual-analytic legal philosophers employ  decision-theory to
develop a framework for setting the probabilistic threshold  that represents the
standard of legal proof. Since the attention in this area of  the law tends
to be on the avoidance of errors and their undesirable  consequences, it is
convenient to focus on disutility. The expected DISutility  of an outcome
is the product of the DISutility -- 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; 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. If we formulate the conceptual analysis axiomatically,
we  have:

pDag>(1−P)Dci -- where "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 DISsutility of  convicting
an innocent person. A similar conceptual 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 conceptual 
analysis, a person should be convicted of a crime only where p is greater than: 
11+DagDci. A similar conceptual analysis applies in civil cases, except
that the  two DISutilities (Dag and Dci) are 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 the DISutility of awarding the
judgment to a defendant  who in fact does not deserve it. On this conceptual
analysis, the crucial  determinant of the standard of "legal proof" becomes 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. The
situation is somewhat 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.  Hence, the probability threshold for a
conviction should be much higher than  0.5.

An objection to this conceptual analysis may be that it is  incomplete, and
that it allows for alleged counter-examples, as Grice would put  it. Thus,
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. This results in the 
following modification of the conceptual analysis for setting the standard of 
legal "proof":

11+Ucg−UagUai−Uci -- where "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, this 
decision-theoretic conceptual analysis of the standard of legal "proof" leads to 
the conclusion that the probabilistic threshold should vary from case to case
--  which should not please all legal philosophers (it pleased H. L. A.
Hart). In  other words, the standard of "legal proof" is flexible or as Hart
has it,  "floating". This conceptual analysis is perceived by some to be
problematic.  First, the conceptual analysis falls short descriptively. The law
is alleged to  require the court to apply a FIXED standard of "legal proof"
for ALL cases  within the relevant category. All criminal cases are governed
by the same high  standard; all civil cases are governed by the same lower
standard. That said, it  is unclear whether fact-finders in reality adhere
strictly to a FIXED standard  of "legal proof" (but this does not mean that
'proof' now has two  senses!).

The conceptual analysis includes a valuational component: it  advances a
claim about what the law OUGHT to be, is DEEMED to be, and not what  it
perhaps alas is. The standard of "legal proof" ought to vary from case to  case.
But this conceptual analysisl faces a second objection. In principle,  civil
litigants have the same two rights that we shall identify. Moral harm 
arises as an objective moral FACT when a person is erroneously convicted of a 
crime. Moral harm is distinguished from, to use McEvoy's favourite adjective, 
"mere" harm (in the form of pain, frustration, deprivation of liberty and
so  forth) that is suffered by a wrongfully convicted and punished person.
While an  accused person does have a right not to be convicted if innocent, an
accused  person does NOT have the right to the most accurate procedure
possible for  ascertaining their guilt or innocence. However, an accused person
does 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. An accused person has, further, the right to a
consistent weighting of  the importance of moral harm and this further right
stems from their right to  equal concern and respect. Such a conceptual
analysis carries an implication. It  is arguable that to adopt a "floating"
standard of "legal proof" offends the  second right insofar as it means
treating an accused person 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 an accused person is
exposed.

There is a still another  objection to the "floating" standard of legal
"proof". Fact-finding is a  theoretical exercise that engages the question of
what to believe about the  disputed facts. What counts as "reasonable" for
the purpose of applying the  standard of legal "proof beyond reasonable doubt"
is, accordingly a matter for  theoretical (or as Grice prefers, 'alethic'),
not practical, reasoning. Only  reasons for BELIEF are germane in "alethic"
reasoning. While considerations that  bear on the assessment of utility and
disutility provide rather "practical"  reasons for action, and thus,
analytically, not a reason TO BELIEVE in the  accused’s guilt. Thus, it is
alleged, a decision-theoretical conceptual analysis  cannot therefore be used to
support a variable application of the standard of  legal "proof beyond

reasonable doubt".

Another criticism of a conceptual  analysis of a flexible standard of
"legal proof" is that it would seem that the  maximisation of expected utility is
a criterion for selecting the appropriate  probabilistic threshold to apply
but that it should play 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 "alethic" reasons. However, it is arguable that  what counts as good or
strong enough theoretical reason for judging, and hence  alethically
BELIEVING, that something is true is dependent on the context, such  as what is at
stake in believing that it is true. Intuitively, as far as  ordinary
language goes (to stick with Grice's methodology), more is at stake at  a trial
involving the death penalty than in a case of petty shop-lifting. 
Accordingly, there should be stronger "alethic" justification for a finding of  guilt
in a trial involving the death penalty (Grice is killed) than in a case of 
petty shop-lifting (a grice, an extinct Scottish pig, is stolen). The 
conceptual-analytic literature on alethic contextualism and on interest-relative 
accounts of knowledge sd justified true belief can thus be drawn upon to
support  a variant standard of legal "proof".

Behind this criticism to this type  of conceptual analysis is that the
trier of fact has to make a finding on a  disputed factual proposition based on
his alethic BELIEF in the proposition.  This is contentious. It may be
argued that, as far as ordinary language goes,  some beliefs are involuntary. It
would seem that 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. E.g.  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 "legal
proof" is higher. The fact-finder has to base his findings,  allegedly, not
on what he believes but what he accepts. Belief and acceptance  are what
Grice calls 'psychological attitudes". They are different psychological 
attitudes that one can have in relation to a proposition. 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.

So perhaps we should go back to an  axiomatic conceptual analysis of 'legal
proof'. Alas, understanding standards of  "legal proof" in terms of
mathematical probabilities has been found to be  controversial. It is said to raise
a number of paradoxes. E.g. The defendant,  Blue Bus Company, owns 75% of
the buses in the capital of Ruritania where the  plaintiff was injured by a
recklessly driven bus and the remaining 25% is owned  by The Red Bus Company.
No other evidence is presented. Leaving aside the  reference class problem
there is a p = 0.75 that the accident was caused by a  bus owned by the
defendant. On the probabilistic interpretation of the  applicable standard of
"legal proof", i.e. the balance of probabilities, the  evidence should be
sufficient to justify a verdict in the plaintiff’s favour.  But lawyers seem to
think that the evidence is insufficient. The puzzle is why  this is so.
Various attempts have been made to solve this puzzle. On one  solution, the
statistical evidence -- the 75% ownership of buses -- is not  CAUSALLY CONNECTED
with the fact sought to be proved (the accident) and as such  cannot
justify belief in or knowledge of the fact (vide Grice "The Causal Theory  of
Perception"). But it is questionable that the court should aim at knowledge  of
the disputed fact and not simply at accuracy in its finding. Another paradox
in the mathematical interpretation of the standard of "legal proof" is the
"conjunction paradox". To succeed in a civil claim or a criminal
prosecution,  the plaintiff or the prosecution will have to PROVE the facts -- or
"elements,"  as legalese goes (legalese can be corpuscularianistic) -- that
constitute the  civil claim or criminal charge that is before the court.
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". Let "A and  B" be mutually independent events. Suppose the
evidence establishes "A" to a p =  0.6 and "B" to a p = 0.7. On the
mathematical interpretation of the standard of  "legal 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, p s only
0.42 (= 0.6 x 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 this
"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 iff the probability of the plaintiff’s or  prosecution’
s case as a whole exceeds the applicable probabilistic threshold.  So, the
plaintiff should lose since the overall p < 0.5. But this suggested  solution
may not satisfy all. 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 commentators have noted, the legal
conceptual  anaysis of "theft" contains more "elements" than the legal
conceptual analysis  of "murder". Criminal law is not the same in all countries --
never mind  Ruritania. We may take the following as a convenient
approximation of what the  law is in some countries, including Ruritania.

"X has murdered Y" iff  (i) X's act caused the death of Y & (ii) that was
done with the intention of  causing the death.

"X has robbed Y" iff (i) X intends to take Y's  property & (ii) X is
dishones in taking the Y's property & (iii) X  removes Y's property from Y's
possession & (iv) Y lacks consent 

Since the conceptual analysis of the offence of theft contains twice the 
number of "elements" (or necessary and sufficient conditions, or 'throngs',
to  use Grice's jargon) as compared to the conceptual analysis of the offence
of  murder, the individual elements for theft would have to be PROVED to a
much  higher level of probability, in order for the probability of the
"conjunction"  of (i) & (ii) & (iii) & (iv) to cross the overall threshold than
the  individual elements for the much more serious crime of murder. This is 
intuitively unacceptable, even for a thief, if not a  murderer!

Fortunately, there is another conceptual analysis we can bring  in to
resolve the "conjunction" paradox, which, admittedly, moves away from  thinking
of the standard of "legal proof" as a quantified threshold of absolute 
probability. We may analyse 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. One criticism of this 
interpretation of the standard of "legal 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.

But one may allege there is a deeper problem with  the probabilistic
conception of the standard of "legal proof", and it is that  there does not seem
to be a satisfactory interpretation of probability that  suits the forensic
context. The only plausible candidate is the subjective  probability
according to which probability is construed as the strength of  alethic 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. 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. 50% 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 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.  The subjectivist Bayesian theory of legal
fact-finding has come under attack. 

1) ascertainment of the likelihood ratios is highly problematic.
2)  Bayesi's theory is not sensitive to the weight of evidence which,
roughly put,  is the amount of evidence that is available.
3) While Bayes's 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.The suggestion  of starting
the trial with prior odds of 50:50 can and has be criticised.
4)  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. The
impossibility of  complying with the Bayesian model undermines its
prescriptive value.
5)  Bayes's  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, i.e. , the comprehensiveness of the evidence. Some are
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. We can have a  legal
application of a general theory of  epistemology.
6) 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. 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. The reasoning -- vide  Grice,
"Aspects of reason" -- 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.

The holistic  nature of evidential reasoning as revealed by these studies
has inspired  alternative conceptual analyses that are of a non-mathematical
nature.  One alternative, already mentioned, is the explanatory or relative
plausibility  one. This analysis contends 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. 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 legal 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. Now, the  relative plausibility theory
itself is perceived to have a number of  shortcomings.
1) 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.
2) 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. 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
3) 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. 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.

But problems are fine, if legal philosophy's problems were all  solved,
legal philosophy, understood as the conceptual analysis of legalese --  as this
legalese is akin to ordinary language (alla Grice or  Hart) -- would be 
dead!

Cheers,

Speranza

REFERENCES:

Grice, The causal theory of perception, Aristotelian Society.
Grice,  Way of Words
Grice, Aspects of Reason: the John Locke Lectures, Oxford: Clarendon
Hart, The concept of law
Toulmin, Probability, in Flew, "Conceptual  Analysis".