represented as 50% on the plaintiff’s scale, showing that the plaintiff has failed
to prove their case to the necessary level of 51%.
Thus the crucial point is that any probability that one party’s case is true is the
complement of the probability that another party’s version is true. Thus if the
plaintiff proves their case to a probability of 55% the defendant has proved
their case to a probability of (100% - 55%), namely 45%. These percentages
for each party can be conveniently represented on their own scale of proof as
will be illustrated in later discussion.
Proposition 3: Two Sided Proof
Reasoning
It follows from Propositions 1 and 2 that the burden of proof and the standard
of proof is two sided. Each party or side to a case has their own burden of
proof and their own standard of proof. This burden and standard can be
represented on a scale of probability for each party. These are labelled here the
initiator’s scale and the responder’s scale.
These two scales can be illustrated by the common law standard of proof for
a plaintiff in a civil case. Stated in words, this requires a plaintiff to prove their
case on the balance of probabilities. By widespread agreement, this verbal
formula becomes a mathematical measure – it is treated as requiring a plaintiff
to prove their case to a standard of 51%.
To take the explanation further, we need to look at a specific happening, where
a plaintiff proves their case to a standard
of exactly 51%. This level is
significant because it is the lowest that they a plaintiff can achieve and still win
the case. Where the plaintiff proves to this minimum level of 51%, the
complementarity rule tells us that the defendant has proved their case to a level
of 49%.
This special case reveals the path for determining the standard of proof for a
defendant. This is the minimum level of certainty that a defendant must achieve
in order to win by blocking the plaintiff’s claim. Clearly this level is 50%. At
this level the plaintiff also achieves 50% and also just fails to prove their case.
In this way Propositions 1 and 2 enable us to identify the standard of proof for
a responding party such as a defendant.
Formula
The method of deriving a standard of proof for one party from the standard of
proof for the other party can be expressed in a formula. Assume Party 1 has
to prove something to a standard of X%. In this case Party 2 has to disprove
that something to a standard of (100-[X+1])%, which equals (101-X)%.
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