Rating assessments by others

The purpose of the numerical rating scheme is to communicate concisely how one regards any given proposition.

The rating scheme is used to show when it is appropriate to treat a particular proposition as a hypothesis: namely, when the rating is neither 0 nor 1 and the credibility is of particular interest.

From the very definition of the numeric scheme, it is possible to indicate extremely concisely the fact that another person has expressed their evaluation of certain propositions as 0 or 1.

For example, most devoutly religious people hold certain (if not all) the tenets of their creed as absolutely true, and many are prepared to state this unequivocally if asked. We can therefore assert of such a person that their evaluation of any proposition asserting one of that person's tenets is 1.

In certain special cases, it is useful to be able to discuss other people's evaluations of certain propositions in terms of my numeric credibility evaluation scheme.

For an example, I draw upon a fictitious court case in the novel According To The Evidence by Henry Cecil. A woman has been murdered, and a man is on trial for it. This is because the man was seen on a street with the victim by another woman (who knew the victim), shortly before the time of death. The witness saw the victim and the prisoner after nightfall, by the light from a street lamp. She saw the victim clearly enough to recognize her, and the face of the man equally clearly. Though she did not know the man, when interviewed by the police she picked the man out from a large number of photographs and subsequently in an identification parade.

The witness had also heard the man seen with the victim say during their converation a certain word with a certain unusual stress, so when she attended the identification parade she was allowed to show the man she picked a piece of paper on which she had printed this word, and she confirmed that the man pronounced it with the same stress.

The outcome of the trial was going to depend very largely on the evidence of this witness. The defence barrister was relying on being able to persuade the jury that it was a case of mistaken identity, in other words that the prisoner was not the man the witness had seen on the night of the murder.

Therefore during cross-examination, the defence barrister quizzed the witness about how sure she was that the man she picked out, nw the prisoner, was indeed the man she saw with the victim shortly before the murder. He asked her about how sure she was before and after asking the man to pronounce the word on the slip of paper.

The whole scene of the dialogue with this witness in the box, presented like a scene in a play and all in rather smaller type than the main narrative in the novel, takes more than six pages. I precis the dialogue in what follows to amke my point. At one point the defence counsel (DC) asks the witness (W):

This is the sort of thing that we are led to believe is normal in real life in criminal trials in the English courts. However, the defence counsel's line of reasoning is totally bogus. If only the witness had had at her disposal my rating scheme, as the means to express her confidence in the proposition "the prisoner is the man I saw with the victim", she could put an end to this vexacious quizzing at a stroke. All she would have to say was this:
"Look, before I asked him to read out the word, I was sure with a rating of 0.9. After I he read out the word, I was sure with a rating of 0.95. So I was more sure afterwards than before, but I was very sure indeed before anyway. This line of questioning is a waste of everybody's time!"

The reason I set up this example at length was that this was a fictional redering, published in 1954, of a problem with the criminal justice system that is still with us half a century later: how to conduct fair trials of people suspected of very grave crimes when the criminal (whoever it is) has been very careful to avoid leaving clues, so that there is very little evidence and what there is is circumstantial. In the story, the prisoner is found not guilty, and is released; subsequently several more women are murdered, for the man is in fact a serial killer, and then another person kills the person who had been tried and acquitted of the murder of that one woman known to that one witness, after which the series of murders stops. Also evidence becomes available after the man's death which makes it certain that he was indeed the serial killer responsible for the murder for which he was tried.

The main point of the novel is the interesting question of how society regards, and the criminal justice system treats, any peson suspected of murdering the murderer. However, the interesting general point about rating the credibility of propositions and hypotheses, is that in court cases people (specifically jury members most of all) spend their time trying to evaluate the credibility of the statements of witnesses; but they also have to hear evidence of how reliable witnesses consider certain other information to be, notably in cases where heresay is allowed such as evidence as to what a murder victim was heard to asy before they died, for example.

This, then, is just one example of where the rating of how other people rate hypotheses is a crucial part of a terribly important public function in society. If everybody was acquainted with and understood a numerical system, it might make discussion of cases by these key participants much easier than it is.

However I know perfectly well that, with the present level of real numeracy in society, adoption of my scheme just isn't going to happen.

On the other hand for anybody who watches the TV quiz show Who Wants To Be A Millionaire and remembers the conversations have with their Phone-A-Friend, it is quite common for them to ask "how sure are you?" and for the friend to answer "about 90 per cent". Now given that 90% means 0.9, if that isn't my numeric credibility scheme in action I don't know what is...