What is the meaning of proof beyond reasonable doubt?

This difficult question has recently been addressed in two Commonwealth jurisdictions. In the first case (R. v. Wanhalla and Court (CLW/06/46/31)), the Court of Appeal of New Zealand said that the starting point was that the accused was to be treated as innocent until the prosecution have proved his guilt.

Proof beyond reasonable doubt was a very high standard and it would only be met if, at the end of the case, the jury were sure that the accused was guilty; it was not enough for the prosecution to persuade the jury that the accused was probably guilty or even that he was very likely to be guilty. However, the jury should be told that it was virtually impossible to prove anything to an absolute certainty when dealing with the reconstruction of past events, and that the prosecution do not have to do so. A reasonable doubt was an honest and reasonable uncertainty left in their mind about the guilt of the accused after giving careful and impartial consideration to the whole of the evidence.

In the second case (R. v. Cavkic, Athanasi and Clarke (CLW/06/46/32)) the Court of Appeal of Victoria addressed the question of whether the criminal standard of proof could be expressed as a ratio (eg. 70 per cent or 80 per cent sure). The court said that the law had never proceeded on such a basis; whilst it was for a jury to determine what constituted a reasonable doubt in their minds, that task could not be seen to be undertaken by the adoption of a process which might enable them to submerge their own genuine doubts in a decision which essentially rested upon a pseudo mathematical assessment of probabilities. If the criminal standard of proof was expressed by reference to some calculation of percentages, there would be an acknowledgement of the existence of a doubt which may or may not be reasonable.