4.14 Example: probative value
Consider the following propositions from Table 4.1:
\(H_p^5\): The glass from the defendant’s clothing originated from the smashed window,
\(H_d^5\): The glass from the defendant’s clothing originated from some other source,
\(H_p^6\): The blood on the defendant’s shoes came from the claimant,
\(H_d^6\): The blood on the defendant’s shoes came from someone else.
Suppose there are also the following three pieces of scientific evidence whose probative value is to be determined:
- \(E_1\): glass analysis reveals a match between the fragments found on the defendant’s clothing and the smashed window,
- \(E_2\): DNA analysis of the blood on the defendant’s shoes does not match the claimant’s DNA,
- \(E_3\): gun shot residue particles were found on the defendant’s clothing.
Evidence \(E_1\) is highly relevant to the source level propositions \(H_p^5\)/\(H_d^5\). We expect a match if \(H_p^5\) is true. This belief translates to a probability for \(E_1\) conditioned on \(H_p^5\) of 1 or very close to 1. There might also reasonably be a match if \(H_d^5\) is true. This would occur when the same type of glass has been used for both the smashed window and the other source. One factor which will affect our expectation is how common the type of glass is in other uses, e.g. are all household windows made from that type of glass? The more common the glass, the greater the probability for \(E_1\) conditioned on \(H_d^5\). The rarer the glass is, the lower the probability for \(E_1\) conditioned on \(H_d^5\). Rarer glass types result in a greater difference between the conditional probabilities of the evidence \(E_1\) under \(H_p^5\) compared to \(H_d^5\) and therefore have higher probative value.
Evidence \(E_2\) is highly relevant to source level propositions \(H_p^6\)/\(H_d^6\). In this case, \(H_p^6\) is incompatible with the evidence: if the claimant truly is the source of the blood then a “no match” is near impossible. The only situation in which this is not true is if there has been a mistake with handling and analysing the sample, so that it becomes contaminated or is switched with another sample. With sufficient evidence-gathering and analysis protocols in place, it is assumed that this is not the case and this is background information. This belief translates into a probability for evidence \(E_2\) conditioned on proposition \(H_p^6\) of close to 0. On the other hand, we would expect “no match” if the claimant is not the source, i.e. if \(H_d^6\) is true. This is a probability for the evidence \(E_2\) conditioned on proposition \(H_d^6\) of close to 1. Since the conditional probabilities under each source level proposition are so different, this evidence clearly discriminates between them and so it has high probative value.
Evidence \(E_3\) does not appear to be relevant to either pair of competing source level propositions with the lack of contextual information given here. Since it is not relevant, then it also has no probative value for those propositions. However, it should not be dismissed outright since there may be other propositions for which it is highly probative.
This analysis shows that propositions are key in defining the probative value of scientific evidence. The same piece of evidence can have different values for its conditional probabilities depending upon the competing propositions on which it is conditioned. The same piece of evidence can also have no probative value for one set of competing propositions but may be highly probative for another.