8.5 Common Cause Analysis
9.1.5 Semantics of Causal Data Representation
AcciMaps offer a bit more informal way of conducting occurrence analysis than WBA. That means results of AcciMaps tend to differ more between au- thors than results from WBA. The more formal semantics of Why-Because Graphs allows for better semantics in data formats and algorithmic pro- cessing. In contrast, non-rigid defined cause-effect relationships, as they are used in AcciMaps, would result in non-rigid defined relationships in data formats. Which means that the comparison of two non-identical syntactical elements, such as edges in a graph, will have different meanings, but would be equal according to syntax.
The causal semantics of WBA, and the semantically well-defined syntax of WBGs, do not impose assumptions other than that systems described using WBGs adhere to the laws of causality3. WBAs semantics have a range of benefits . The focus here is to develop algorithms which compare properties in different WBGs. The algorithms are designed to deliver results which also have well-defined semantics, which are based on the semantics of WBA. Important for determining similarity between WBGs are the Counterfactual Test and the Counterfactual Conclusion, see paragraphs below. The Causal Sufficiency Test is not part of the causal reasoning to determine similarities in WBGs.
The Counterfactual Test and Necessary Causal Factors (NCF) The Counterfactual Test is one of the core principles of WBA.
To determine if two factors are causally related, one being the cause of the other, the counterfactual test asks the following question: If factor A had not been, could factor B have happened? If the answer is No, B could not have happened if A had not happened, then A must be necessary for B to happen.
If the Counterfactual Test has determined that A is necessary for B to happen, we term it that A is a necessary causal factor (NCF) for B.
In the real world A and B did happen. The counterfactual test is a what- if question which assumes that B did not happen contrary to fact, hence the name.
The question assumes that all other circumstances in which A and B take place remain the same, as far as possible. So the question, as stated above should be added by the phrase ”all else remaining equal”.
This is based on the nearest possible world semantics . The nearest possible worlds semantics assumes the existence of other worlds, some like ours, some not. If we have the ability to compare other possible worlds with our own and order them according to similarity then we can find the nearest possible world W in which B did not happen. If A did not happen in W then B must be necessary for A to happen. This does not mean that there is no other possible world in which A could happen without B, but the further away such a world is from ours the less explanatory power the counterfactual test has. At some distant world from ours things may be completely different.
In a Why-Because Graph the counterfactual or NCF relation is denoted by the directed edges in the graph. The pointy end going into the effect and the stub end coming out of the cause.
WBGs usually consist of more than two factors. Two factors may be causally related without being NCFs of each other. Effects can be causes themselves and so causal paths form in a Why-Because Graph.
Assume 4 factors as pictured in 7.1. Let ncf (A, B) be the counterfactual relation between A and B, where A is the necessary causal factor (NCF) and B is the effect. The diagram 7.1 shows
• ncf(Factor1,Factor2), • ncf(Factor2,Factor3) and • ncf(Factor3,Factor4)
What does this say about the causality relation between F actor1 and F actor4?
• If F actor1 had not happened, then F actor2 could not have happened. • If F actor2 had not happened, then F actor3 could not have happened. • If F actor3 had not happened, then F actor4 could not have happened. Can we follow ncf (F actor1, F actor4)? No, we cannot, because the coun- terfactual test for F actor1 and F actor4 demands, that all else should remain
9.1. CAUSAL ANALYSIS METHOD 89 equal. If F actor3 is necessary and sufficient to cause F actor4 the presence or absence of F actor1 does not matter. Each counterfactual test is con- ducted in a different nearest possible world. F actor1 could be a necessary causal factor for F actor4, but we cannot simply draw conclusions from the three worlds and assume that the conclusions hold in a fourth world.
We can draw the conclusion that F actor1 and F actor4 are causally re- lated, but the relation identified by the Counterfactual Test is not transitive. But nevertheless there is a chain of factors and NCF-relations. F actor1 may not be a NCF for F actor4, but it is a Cause: cause(F actor1, F actor4).
Factor 1 Factor 2 NCF Factor 4 Cause Factor 3 NCF NCF
Figure 9.1: Necessary Causal Factor (NCF) chain illustrating the causal relationship between Factors 1 and 4
In 9.1 there is only one causal relation (dotted line) depicted, but of course there are many more, namely between all factors which are on the
same causal path: cause(F actor1, F actor2), cause(F actor1, F actor3), cause(F actor1, F actor4), cause(F actor2, F actor3), cause(F actor3, F actor4)and cause(F actor3, F actor4).
Causal Sufficiency and Causal Completeness
There are two other criteria used in WBA. The Counterfactual Test es- tablishes necessary causal relations between cause and effect. The Causal Sufficiency test asks another question. If C1, C2 and C3 are all causes and NCFs for effect E, then the question is if C1, C2 and C3 are sufficient to cause E. If E must happen if C1, C2 and C3 happen, then C1, C2 and C3 are causally sufficient for E.
Both tests together form the Causal Completeness test. A WBG is correct and relatively complete if all its factors pass the Causal Completeness test. For the automatic common cause analysis the Causal Sufficiency Test is only of relevance insofar as I will assume that all WBGs processed are correct according to the Causal Completeness Test.