"If a legal rule requires a fact to be proved (a 'fact in issue'), a judge or jury must decide whether or not it happened. There is no room for a finding that it might have happened. The law operates a binary system in which the only values are 0 and 1. The fact either happened or it did not. If the tribunal is left in doubt, the doubt is resolved by a rule that one party or the other carries the burden of proof. If the party who bears the burden of proof fails to discharge it, a value of 0 is returned and the fact is treated as not having happened. If he does discharge it, a value of 1 is returned and the fact is treated as having happened."
"The balance of probability standard means that a court is satisfied an event occurred if the court considers that, on the evidence, the occurrence of the event was more likely than not. When assessing the probabilities the court will have in mind as a factor, to whatever extent is appropriate in the particular case, that the more serious the allegation the less likely it is that the event occurred and, hence, the stronger should be the evidence before the court concludes that the allegation is established on the balance of probability. Fraud is usually less likely than negligence. Deliberate physical injury is usually less likely than accidental physical injury. A stepfather is usually less likely to have repeatedly raped and had non-consensual oral sex with his under age stepdaughter than on some occasion to have lost his temper and slapped her. Built into the preponderance of probability standard is a generous degree of flexibility in respect of the seriousness of the allegation. Although the result is much the same, this does not mean that where a serious allegation is in issue the standard of proof required is higher. It means only that the inherent probability or improbability of an event is itself a matter to be taken into account when weighing the probabilities and deciding whether, on balance, the event occurred. The more improbable the event, the stronger must be the evidence that it did occur before, on the balance of probability, its occurrence will be established."
"It would need more cogent evidence to satisfy [a judge] that the creature seen walking in Regent's Park was more likely than not to have been a lioness than to be satisfied to the same standard of probability that it was an Alsatian."
"If the evidence is such that the tribunal can say 'we think it more probable than not' the burden is discharged, but if the probabilities are equal it is not."
"My Lords, if the judiciary in this country regularly found themselves in this state of mind, our civil and family justice systems would rapidly grind to a halt. In this country we do not require documentary proof. We rely heavily on oral evidence, especially from those who were present when the alleged events took place. Day after day, up and down the country, on issues large and small, judges are making up their minds whom to believe. They are guided by many things, including the inherent probabilities, any contemporaneous documentation or records, any circumstantial evidence tending to support one account rather than the other, and their overall impression of the characters and motivations of the witnesses. The task is a difficult one. It must be performed without prejudice and preconceived ideas. But it is the task which we are paid to perform to the best of our ability.
In our legal system, if a judge finds it more likely than not that something did take place, then it is treated as having taken place. If he finds it more likely than not that it did not take place, then it is treated as not having taken place. He is not allowed to sit on the fence. He has to find for one side or the other. Sometimes the burden of proof will come to his rescue: the party with the burden of showing that something took place will not have satisfied him that it did. But generally speaking a judge is able to make up his mind where the truth lies without needing to rely upon the burden of proof."
(Paragraphs 31 and 32, judgment.)
"How often have I said to you that, when you have eliminated the impossible, whatever remains, however improbable, must be the truth?"
"It is, no doubt, on the basis of this well-known but unjudicial dictum that Bingham J decided to accept the shipowners' submarine theory, even though he regarded it, for seven cogent reasons, as extremely improbable."
"What is not acceptable, at the very least in a case like the current one, is to identify that there are, say, (as here) five possible causes, rank them each in percentage terms as possibilities and then select the possibility with the highest percentage as the probable cause. The only circumstances in which it would be legitimate would be if the highest ranked cause was the one which on all the evidence the judge was satisfied was the probable cause of the incident or loss in question…I consider that it is dangerous and generally a fruitless occupation to seek to rank possibilities or probabilities in percentage terms in any event. If there are five possibilities of which four are remote or extremely improbable, that conclusion may go to support a judge's finding that the remaining 'possibility' is in fact the probable cause or explanation for the event in question."
"As a matter of common sense it will usually be safe for a judge to conclude, where there are two competing theories before him neither of which is improbable, that having rejected one it is logical to accept the other as being the cause on the balance of probabilities. It was accepted in the course of argument on behalf of the appellant that, as a matter of principle, if there were only three possible causes of an event, then it was permissible for a judge to approach the matter by analysing each of those causes. If he ranked those causes in terms of probability and concluded that one was more probable than the others, then, provided those were the only three possible causes, he was entitled to conclude that the one he considered most probable, was the probable cause of the event provided it was not improbable."