12* - Probability Distributions and Causation

Summary

Causation and Causal Connection: A Graphical Exposition

The relations between causation and causal connection (and ultimately probabilistic dependencies) can be clarified with the help of the three kinds of graphs. Figure 12.3a, 12.3b, and 12.3c show respectively the normal, path, and connection graphs that correspond to the causal relations among the salt concentrations of the five salt basins in figure 6.3, which is reproduced in figure 12.3d. To each normal graph, there corresponds a single path graph, but a path graph may correspond to more than one normal graph. The connection principle implies that for each path graph, there is a unique connection graph: For all vertices u and v in a connection graph G_c, there is an undirected edge between u and v if and only if in a corresponding path graph G_p with the same vertices there is an edge from u to v or from v to u or there is an edge from some vertex to both u and v. If one substitutes the word “path” for the word edge, this same claim defines the unique connection graph corresponding to every normal graph.

If I (or I_g) is true, then there is a unique path graph corresponding to each connection graph that correctly represents the causal relations: For all vertices u and v in a path graph G_p, there is a directed edge from u to v if and only if in the corresponding connection graph G_c with the same vertices there is an undirected edge between u and v and for all vertices w other than v if there is an edge in Gc between w and u, then there is an edge between w…