When evaluating DNA evidence within a likelihood ratio framework, should the propositions be exhaustive?

We seek to develop a rational approach to forming propositions when little information is available from the outset, as this often happens in casework. If propositions used when evaluating evidence are not exhaustive (in the context of the case), then there is a theoretical risk that an LR greater than one may be associated with a proposition in the numerator that - if all meaningful propositions had been considered - would in fact have a lower posterior probability after consideration of the evidence. Ideally, all propositions should be considered. However, with multiple propositions, some terms will be larger than others and for simplification very small terms can be neglected without changing the order of magnitude of the value of the evidence (i.e. LR). Our analysis shows that mathematically a contributor's DNA can be assumed to be present under both prosecution and alternative propositions (H

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