I am keenly interested in notions of causation, and specifically how they relate to models of complex phenomena. One reason is that complexity (i.e., feedback, multiplier effects, evolution, etc.) blurs the lines of clear causal relations. I have made the point elsewhere that causation is not something in the world that we match and/or uncover, but rather only something in our models (including mental models) that structures and orders the actions and reactions. I am therefore especially focused on the methodology of mechanisms in models and how to make them clean, and conform to how we think things happen (which is why cross-level, e.g., downward or upward, causation is something to avoid). Within a level of organization a model's causal relationships follows the rules generating behavior in that model, but the higher-order (emergent) phenomena generated by that mechanism may reveal causal relationships that violate the ones generating said phenomena. Here I outline a project that can reveal such an emergent causal inversion.

The project starts with a simple agent-based model at the microlevel. The model could be something as simple as disease spread along a network, a segregation model, or a majority imitation model. Perhaps something more sophisticated is needed to generate the desired effect, but I don't think so. As the model runs, track several variables, including both aggregate variables over the agents and properties of the macrolevel itself. This is done, as per usual, over a few hundred or thousand runs of the model to build a dataset of time-series of all these variables.

The next step is use a statistical modeling technique specifically designed to uncover causal relationships in data of this kind: Bayesian network analysis. First we build the Bayesian network of the microlevel variables using the causal relationships implied by the agent rules we specified. Then we use software to uncover (using advanced AI techniques) the structure of the Bayesian network for the macrolevel variables. We also need a reduction bridge law that translates macrostates into microstates; i.e., what microlevel variables values are consistent with which macrolevel variable values.

Once all that is complete, what we are looking for is a causal relationship in the macrolevel Bayesian network that contradicts the causal mechanisms we know are operating at the microlevel. Just to be clear (because there is a lot of confusion around the term "emergence") this is not intended to reveal how the macrolevel causes behavior at the microlevel. Causation at each level is independent, therefore such a claim is just nonsense even though such claims are often made (e.g. the level of segregation in this neighborhood caused the agent to move to another neighborhood). That is not the unintuitive contradiction we are looking for.

What we want to see is that at the macro level, the value of variable A affects the likelihood of variable X and X doesn't affect A: A->X in the Bayesian network. The variable A happens when the microstate has values a, b, and c. The variable X occurs when the microstate has values x, y, and z. Yet at the microlevel, through the rules we specified, we know that it is actually the case that x, y, and z have an affect on a, b, and c rather than the other way around. Meaning that given the data we collect from the system, the apparent causal structure at the macrolevel is incompatible with the causal structure at the microlevel. And this could all be shown in a totally formal and rigorous way.

This is important because THAT property of the macrolevel, that it has distinct causal relationships from the microlevel that it can be reduced to, is perhaps the best candidate for a truly emergent behavioral property...of a certain kind. Because the macrolevel can unambiguously be reduced to the microlevel, that is not the issue here (though the most common way to define emergence). The point is that the behavior of the variables at the macrolevel cannot be reduced to behavior of the microlevel, even though all the states can be. And it's even better because the behavior can be reduced in principle, but the reduction reveals conflicting relationships.

The microlevel is where all the real causation is in the model/data, so the apparent causal relationships in the macrolevel are "incorrect" in some sense, but not in the sense that they fail to predict future values at the macrolevel. If it were done right (i.e., if it is possible to actually get a model to generate this emergent causal inversion) then basing the macrolevel causal structure on the actual microlevel structure would make predictions worse. What this means is that macrolevel objects literally behave differently than is implied by the mechanisms that generate them. And that, I think, would be a huge success for complexity theory and the hunt for emergent phenomena.