A helpful overview of the rarity of Rhesa Shipping causation difficulties and at paragraph 6 some guidance on how to approach the issues.

Thomas L.J. said,

1 These two appeals were heard together because they raise an issue as to the approach the judge was entitled to take to the determination of proof of causation where alternative mechanisms of causation were put before the court. In each case the sole issue before the court was whether the respondent to the appeal who had suffered the damage could prove on a balance of probabilities that a defect had caused the damage sustained; each appellant contended that the judge had adopted a train of reasoning which the House of Lords made clear in Rhesa Shipping Co SA v Edmunds (The Popi M) [1985] 1 W.L.R. 948 was impermissible.

4 …The Popi M was a very unusual case and as these two appeals demonstrate, the difficulties identified in that case will not normally arise.

In the vast majority of cases where the judge has before him the issue of causation of a particular event, the parties will put before the judges two or more competing explanations as to how the event occurred, which though they may be uncommon, are not improbable.

In such cases, it is, as was accepted before us by the appellants, a permissible and logical train of reasoning for a judge, having eliminated all of the causes of the loss but one, to ask himself whether, on the balance of probabilities, that one cause was the cause of the event.

What is impermissible is for a judge to conclude in the case of a series of improbable causes that the least improbable or least unlikely is nonetheless the cause of the event; such cases are those where there may be very real uncertainty about the relevant factual background (as where a vessel was at the bottom of the sea) or the evidence might be highly unsatisfactory. In that type of case the process of elimination can result in arriving at the least improbable cause and not the probable cause. …

6 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.

Edited for ease of reading. See the other cases listed under this tag.