ideas-backwardsPseudoCausalityAndCycles

Imagine that some events repeat themselves periodically (a cycle). Now imagine that there is a predictive agent which, by observing the content of the repeating events during the second half of the previous cycle, learns what will happen during the next cycle, and adapts its behavior accordingly -- affecting its behavior during the first half of the next cycle. To understand what is happening here, we must consider at least two cycles, because the learning must occur in one cycle, and can only be applied towards predicting events in the subsequent cycle.

But what if we insist on looking at only one iteration, and rephrasing things in order to interpret that one iteration? We might overlay everything that happened in all cycles onto one single cycle. We might then say that the events in the second half of the cycle are causing the behavior of the predictive system in the first half of the cycle. It's not "really" causation, but it's something similar (i'll call this pseudo-casuation). Interestingly, pseudo-causation can be directed backwards in time.

Now imagine that the repeating events don't repeat periodically or exactly, but rather that there are only certain regularities. For instance, perhaps there are certain underlying parameters which are not directly observable, but which can be estimated by observing certain events. Now we are a lot closer to the real world. Although we have ditched the "circular" division of time into cycles, we can still use our concept of pseudo-causation, as follows.

Definition: If A causally makes B more likely to occur, then A also may be said to pseudo-causes B. But in addition, when (1) an event provides evidence which affects the estimation of some hidden parameter, and when (2) this sort of effect on the parameter estimate causes (or tends to encourage) the agent to behave in a certain way, then we say that the event pseudo-causes the agent to behave in that way.

Note that both of these conditions can be met while going backwards in time: the effect of the event upon estimation can happen in the future, and the behavior which is encouraged by that estimate can happen in the past. There is no requirement for an actual causal linkage going from event to estimation to behavior; rather, there is an actual link from event to estimation, and an actual link from estimation to behavior, but the two estimations involved may be at different times.

An example of the application of this language construct is moral hazard. In particular, imagine that the government may or may not choose to "bail out" corporations which are going bankrupt. The probability of its doing so is the hidden parameter (the hidden parameter may even drift or change every now and then, the scenario still works). Every now and then, one of these corporations gets in trouble, and then the government either does or does not bail them out, providing observers with data to update their estimates. Let's assume that agents take some undesirable activity if they believe that the probability of bail-out is sufficiently high. Now, if agents do this undesirable activity, and then later on the government bails out some corporations, the bail-out may be said to pseudo-cause the undesirable activity.

Circular pseudo-causation is possible. Back to the moral hazard example. Let's assume that the more that agents do the undesirable activity, the more likely it is that corporations get in trouble. In this case, a government bail-out pseudo-causes the undesirable activity, which made it more likely that the corporation will get in trouble; hence, the government bail-out pseudo-caused the corporation to get into trouble. More to the point, the government bail-out pseudo-caused itself.

I'm not sure how useful this is for everyday discussion -- when arguing against bail-outs, for example, it is simpler to say, "Bail-outs increase the chance of corporations failing in the future", rather than introducing the concept of pseudo-causation and then saying that "bail-outs pseudo-cause exactly the situation that the bail-out was trying to solve". But it seems theoretically interesting. Pseudo-causation is basically a language for talking about stable attractors.