Section 58 Conspicuous absence

This metric can be calculated on the basis only of structural information, with no knowledge of the contents or nature of the causal links.

The basic idea is to look at the lack of edges: node pairs (aka variable pairs) which could have an edge (aka arrow) but don’t, or have only a thin edge, i.e. with very few mentions. The made-up example below is supposed to be built up on the basis of edge information derived from say 15 separate respondents. Is the low number of mentions of the arrow between “better crops including feedstuffs” and “healthier pigs” (below) understandable because they were anyway rarely mentioned together by the different respondents: maybe respondents tended to talk about the pigs, or the crops, but not both? Or is it conspicuous by its absence? We can look at the 15 individual “mini-maps” produced by the 15 respondents. Did those two nodes in fact appear together in the many of the respondents’ mini-maps but without an edge between them? This is something that we can not tell just by looking at the map, but a confusion-matrix-type structural analysis can tell us.

One could build a global score for each edge, to complement the score for the frequency of mentions: so, 50% = this edge is present in 50% of the mini-maps in which both nodes were mentioned in some way or other. So if it turned out that “better crops” and “healthier pigs” appeared together in only two mini-maps, it would get a score of 100% and we would take it more seriously than if it had a score of say 10%. (We could also go on to look at all the arrows which are not in the map and talk about how much they are lacking - a kind of negative causal link.)

The algorithm calculates this score by calculating the individual respondent-level adjacency matrices for the edges mentioned by each respondent, but scoring for absence rather than presence of edges. So each adjacency matrix only has a 1 for pairs of nodes which are mentioned by the respondent but for which no edge was mentioned. Then combine them into one large adjacency matrix of “anti-causality”. The trouble is that I am not sure about the details -– not sure if the score should really be punishing situations when people in group 1 say that X leads to Z, and group 2 say that it leads to Y which is between X and Z -– that needs some more thought. In this case, you couldn’t really say that arrows from X to Z are conspicuously absent, more that these people are thinking in a more detailed way.)

In the same way, you can look at the total lack of an arrow between Better Communication and Better Wellbeing and ask aha, is this because they were never mentioned together? Or is its absence more conspicuous?