"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”
The Sign of Four begins with a bored Holmes mired in cocaine addiction, much to the disquiet of Dr Watson. A young woman appears. She has a mystery that needs solving. Holmes solves it. He is cured from his addiction and, by the end of the book, the young woman is set to become Mrs Watson.
Amidst all the action comes the pronouncement quoted at the start of this post. It has become one of Holmes’ most enduring dicta on the science of deduction; so enduring, in fact, that his deer-stalkered head was reared in the Court of Appeal last month. The case was Graves v Brouwer  EWCA Civ 595. It concerned a house fire, but the principles are of general application to many cases where a court is obliged to wrestle with competing theories as to causation.
Mr Brouwer and Ms Graves were next-door neighbours. Mr Brouwer was an odd man: he described himself as controlling to the point of being “anal”, a description the judge was happy to adopt. One day he decided to dispose of a small quantity of papers by burning them in the passage by the side of his house. He set them alight and then doused the ashes with a hose. Shortly thereafter, Ms Graves’ house caught fire. In due course she brought a claim against Mr Brouwer, alleging that the fire he started had somehow spread to her house.
Both parties instructed experts. They agreed that the chances of an ember containing sufficient residual energy to start a fire escaping from Mr Brouwer’s passageway and travelling to the eaves of Ms Graves house’ was small. However, the other possibilities were also not particularly attractive. One that was mentioned was “anting”, i.e. birds picking up smoldering cigarette ends and transporting them back to their nests. But there was no positive evidence of birds nesting under the eaves of Ms Graves house. The only other theory that was posited was that persons unknown had deliberately set fire to Ms Graves’ house, i.e. arson.
During cross-examination, Mr Brouwer’s expert was asked whether, if the court took the view that arson did not cause the fire, then on the balance of probabilities, the fire started by Mr Brouwer had to be the cause of the fire in the Claimant’s house, even if improbable. He replied in the affirmative.
The trial judge held that, but for the expert’s concession in cross-examination, she would have been minded to dismiss the claim on causation. But, having rejected the arson theory and the concession having being made, she felt compelled to find for the claimant on causation. She went on to find, however, that Mr Brouwer had not been negligent in the way he has carried out the “burn” and so the claim failed anyway. Both parties appealed. Ms Graves appealed the finding of negligence; Mr Brouwer cross-appealed the finding on causation.
The Court of Appeal took the opportunity to conduct a helpful exposition of the correct principles from the authorities, stretching back to the case in which Holmes made his first appearance in this field, namely The Popi M  1 WLR 948. That case was about a ship had been lost at sea. The trial judge was Bingham J (as he then was). The House of Lords held that he had fallen into error in deciding the case on causation because he had (albeit implicitly) translated Holmes’ dictum too willingly into a legal context.
What works in a fictional detective story does always not work in court of law. In practice, it is rare to be able eliminate all other possibilities. Some may exist but not have been suggested to the court; others will have been suggested but it will be impossible to eliminate them entirely due to deficiencies in the evidence. So it is incumbent upon a judge to step back and ask themselves whether a particular cause is more likely than not to be the correct one. The exercise is not one of identifying the least unlikely cause and then declaring that the correct one. If, having heard all the evidence, the judge remains of the view that the causal mechanism which establishes the claim is improbable then the claimant has failed to discharge the burden of proof and the claim must fail.
In Graves v Brouwer the Court of Appeal held, applying The Popi M, that the judge had been wrong to place the reliance she did on the expert’s answer in cross-examination. It went further. The question, it said, should not have been asked at all because it invite him to express a conclusion of question of mixed fact and law which it was the task of the judge to reach. The judge had, as a result, fallen into the same error as Bingham J in The Popi M by applying the Holmesian dictum too literally. She should have asked herself whether, all things considered, a flying ember from the fire started by Mr Brouwer was more likely than not to have caused the fire. She had not done so and hence had misdirected herself. So the Court of Appeal allowed Mr Brouwer’s appeal on causation. (It also, incidentally, upheld the judge’s finding on negligence for good measure).
Judges may think they know all they need to know about probability because they apply the balance of probabilities every day. But if a judge as capable as the late Sir Thomas Bingham can get it wrong then any judge can get it wrong. Graves v Brouwer is a useful case to use if you want to ensure that they get it right.