Causal manipulation theorems proposed by Spirtes et al.
(1993) and Pearl (1995) in the context of directed probabilistic graphs,
such as Bayesian networks, do not model so called reversible causal
mechanisms, i.e., mechanisms that are capable of working in several
directions, depending on which of their variables are manipulated
exogenously.
An example involving reversible causal mechanisms is the power
train of a car: normally the engine moves the transmission which,
in turn, moves the wheels; when the car goes down the hill, however,
the driver may want to use the power train to slow down the car, i.e.,
let the wheels move the transmission, which then moves the engine.
Reversible causal mechanisms are modeled quite naturally in the
context of equilibrium structural equation models.
In this paper, we investigate whether Bayesian networks are
capable of representing reversible causal mechanisms.
Building on the result of Druzdzel and Simon (1993), which shows
that conditional probability tables in Bayesian networks
can be viewed as descriptions of causal mechanisms, we study the
conditions under which a conditional probability table can represent
a reversible causal mechanism.
