The burden of proof in UK civil trials

Question

In UK civil trials, it is said that

1. The burden of proof is on the claimant.
2. The case will be decided ‘on the balance of probabilities’.

Are these assertions consistent? Based on the second statement, one might think that the outcome of a case will depend on whether it is more likely than not (>50%) or less likely than not (<50%) that the claimant’s allegation is correct (based on the relevant evidence). But if that is true, I don’t see how the claimant has any special ‘burden’ that they need to discharge. Sure, in order for the claimant to win, the relevant decision maker (let’s say it is a judge) needs to think that it is more likely than not that the claimant is right. But equally, in order for the defendant to win, the judge needs to think that it is more likely than not that they (the defendant) are right. So the situation is entirely symmetric!

Update: as some have commented, the claimant may lose if the judge thinks that the probability is exactly 50%. If you think, for example, that the judge’s assessments should be restricted to integer percentages (0%, 1%, 2%, etc.), this means that the claimant wins if the probability is 51% or higher, and loses if the probability is 50% or lower. This situation is very slightly asymmetric; but only very slightly! And if the judge can make more nuanced judgments (no longer restricted to integers), the asymmetry shrinks.

Answer 1

First of all, law is not mathematics and it is futile to try to assign an "exact" statistical percentage or apply Bayes' theorem in any specific case unless the facts of the case are particular enough. In the end, judges or juries (most often) do not apply a statistical model to their cases, what matters is if the evidences (by both parties) presented on one claim convince them that the claim is more likely to be true than not, that is, what they "feel" or "think" about the probability.

More probable than not means > 50%; if the fact finder finds scenarios leading to different outcomes equally likely, the claim is not proven and the party bearing the burden of proof fails.

If you want to analyze it mathematically, the burden of proof does not necessarily means that the probability of a claim favourable to the burdened party to be true in the absence of evidence is zero. Since only two values are possible as an outcome on any particular claim (as far as the burden of proof is concerned), a step function must be used to convert the probability to a judgement. The burden of proof represents the choice of that unsymmetric step function.

The burden of proof also represents the legal (not necessarily "factual" or statistical) assumption (an imposed, unquantifiable prior "probability").

Here I use the word "claim" generally, for a case to succeed there can be multiple elements or claims that all need to be proven to be more likely than not to be true, e.g. if you want to sue someone for medical bills because they crashed into you and you have a broken leg, you need to prove both that they were responsible for the crash and that the medical bills are for the broken leg, and the broken leg is a result of that crash.

The burden of proof means that if you do not provide any evidence that the leg was broken as a result of that crash, or if your evidence is very weak, or if your evidence is not stronger than the other party's counter-evidence, your case must fail; the defendant does not have to prove that the crash did not cause your broken feet.

Answer 2

These statements are consistent, because you are ignoring a third possibility: a case where the evidence is perfectly balanced, i.e., the evidence makes it neither more nor less than 50 percent likely that the claimant's allegation is true.

So imagine Plaintiff sues Defendant for trespass and presents only one piece of evidence: a hair left behind by the trespasser and matching Defendant's DNA. Defendant stipulates that someone trespassed but presents only one piece of evidence: his identical twin's DNA, which is likewise a perfect match to the sample.

It is now 50 percent likely that Defendant trespassed, and 50 percent likely that Defendant did not trespass. The parties have brought equal amounts of evidence and balanced the scales perfectly. Defendant wins because Plaintiff did not carry his burden, which was greater than Defendant's.

The difference can be seen more clearly in a scenario that is even less likely. Imagine a trial in which neither side presents any evidence at all. Again, the scales are perfectly balanced, but Defendant wins because only Plaintiff had a duty to present any evidence at all.