Section 20 The rule for merging arrows. Weight of evidence.
We already saw that the rules for joining causal maps can result in a map in which there is more than one arrow from a variable C to a variable E. And we discussed how to calculate a single function which combines these influences. It can be more convenient to replace this set of arrows with a single one, encoding the same combined influence, and also encoding a new attribute which we can call “evidence”, “number of mentions” or similar.
So if we hear:
heart disease increases strongly with alcohol consumption
and again exactly the same thing:
… and have already combined this into a single map: … we can show this as a single arrow:heart disease increases strongly with alcohol consumption
We will also consider that this link is now in some sense has more evidence.
Later we will see that it would be usual also to show this visually e.g. by using a thicker arrow.
20.1 Problems with evidence
We would probably also want to in some sense increase the “evidence” for a link if we had similar but not identical pieces of information, e.g. that the effect of C on E was on the one hand “large” but on the other hand “very large”. But what if we are combining fragments of information which are not even compatible?
What if we hear:
heart disease increases with alcohol consumption
but then:
heart disease decreases with alcohol consumption
We could still record stronger “evidence” for the combined link, and by all means it is true that there is a lot of evidence about some kind of link, but that would be very problematic. What if the combined function was calculated to be in some sense zero?
Case A: there are 50 studies which suggest a strong positive link and 50 studies which suggest a strong negative link. We could combine these into a single map (see section xx) claiming a zero link but evidence of 100.
Case B: there are 100 studies which all suggest a zero link. We could combine these into a single map with a combined function claiming a zero link but evidence of 100. It’s the same map as Case A! That must be wrong.