Thanks Andrew, I have previously contemplated creating a thread assigning probability for each piece of evidence and I was going to use a percentage number and let the Forum debate the odds of each individual piece of evidence but with the rabid CT defenders that are members here, I decided that coming to a fair conclusion would not be possible. Perhaps in the future?
Btw you say that each item would be less than 1/3 which could be true of some, but specific pieces of evidence like Oswald's rifle, the murder weapon, IMO would be a heck of a lot more.
JohnM
I simplified it a bit. The 1/3 figure is the probability that the fact is not true if there was just that one piece of evidence. In other words 66.7% of the time with such a piece of evidence alone, the posited fact could be expected to be true.
This takes into account the various ways that the fact may not be true, including the possibility that the evidence was fabricated by parties unknown or was the result of a deliberate lie, as well as the possibility that the person may have had poor observational skills etc.
Obviously this will vary from piece to piece and, as you point out, the items of evidence against Oswald would be considerably greater.
If the probability of probative evidence being false is close to 1/2 it is not probative at all so I used 1/3 as the highest probability that probative evidence is wrong.
The point is not to quantify the probability but to show that no matter how large the improbability of a false conclusion from an individual piece of probative evidence is if you have enough pieces and they are all independent of each other, you can remove all reasonable doubt. I set 1/3 as the highest level of improbability you could have and still consider the evidence as probative.
If one has ten such pieces of evidence that are completely independent of each other, and you assume a probability of a false positive of p for each item, the probability that the posited fact is true is (1-p^10) (ie. 1 minus the probability of all ten items being false: p to the 10th power). Even assuming a high chance of 1/3 that each individual piece is false, there would be only one chance in 59,049 that all 10 pieces could exist and the fact not be true: 1-(1/3)^10=1-1/59,049. Obviously, then, the chance that each item leads to a correct conclusion is much greater than the initial assumption of 2/3. It approaches 100%.
Even if a few of the items are not reliable (e.g. the witness did not actually make the observation claimed), the number of ways of the remaining items existing and the fact is not true is still small compared to the number of ways of having the number of ways of having 8 of the 10 being true.
Where it becomes more of a mathematical exercise is when you are analyzing pieces of evidence that are probative of an event that has a finite number ways of occurring and you have evidence that does not completely agree.
For example: the fact to be determined is whether a person wore a specific colour of hat and there are 20 witness statements about the colour, not all of which agree e.g. 15 say black, 2 say blue, 1 says brown, 1 says green and 1 says yellow. This is an either/or question so the evidence can be analysed using a binomial distribution. The binomial distribution is explained
here.