From: Mr. Asha

Subject: The impossibility of asymmetric causation

**Statement to all:**

Apart from the innate symmetricity of structural equation systems,
the very definition for the conditional probability as
well as Bayes's law of inverse
probability unambiguously suggest the reversibility of
cause-effect relationships. ...

``*A* is a cause of *B* only when *B* can cause *A*.'' Amen.

(Quoted from Mr. Asha review of *Causality*, amazon.com, August 29, 2000)

**Author's reply**

It is instructive to compare the apparent symmetries of
Bayes rule and structural equations with the asymmetry
inherent in out conception of causation.
Bayes rule asserts that if *A* is relevant to *B*, then *B* must
be relevant to *A*, that is, if learning *A* changes the probability
of *B* then learning *B* must change the probability of *A*. This
symmetry constitutes the first of the five properties of
graphoids (*Causality*, page 11).
However, this symmetry refers to informational
relevance, not to causal relevance (as axiomatized in
*Causality*, Section 7.3.3). Bayes's rule and information
relevance deal with changes in one's beliefs about a static world;
causality deals with changes in the world itself.
My belief about the rain may change in light of reading
the barometer, but there is nothing I can do to the barometer
that will change the rain in the physical world.

The apparent symmetry of structural equations is equally deceiving.
On page 160 I explain how structural equations serve
a dual purpose, observational and interventional, and
I argue that it is the inteventional component which
distingushes structural equations from algebraic equations.
Referring to the equation *y*=b*x*+e, page 160 reads:

"Note that the operational reading just given makes no claim

about how *X* (or any other variable) will behave when we

control *Y*. This asymmetry makes the equality signs in

structural equations different from algebraic equality signs;

the former act symmetrically in relating observations on *X* and *Y*

(e.g., observing *Y*=0 implies b*x*= -e),

but they act asymmetrically when it comes to interventions

(e.g., setting *Y* to zero tells us nothing about the relation

between *x* and e). The arrows in path diagrams

make this dual role explicit, and this may account for the

insight and inferential power gained through the use of diagrams.

Although the literature on structural equation models does not explicitly acknowledge this basic interpretation of structural equations -- a puzzling phenomenon that I explain in Section 5.1 -- it is implicit in the conclusions that scientists draw from SEM studies.

Next discussion (many readers: *Errata list for
the 3rd printing of Causality*)