It is widely understood that statistical correlation between two variables ≠ causation. But despite this admonition, people are routinely overconfident in claiming correlations to support particular causal interpretations and are surprised by the results of randomized experiments, suggesting that they are biased & systematically underestimating the prevalence of confounds/common-causation. I speculate that in realistic causal networks or DAGs, the number of possible correlations grows faster than the number of possible causal relationships. So confounds really are that common, and since people do not think in DAGs, the imbalance also explains overconfidence.

Full article: http://www.gwern.net/Causality

Followup to:  The Fabric of Real Things, Stuff That Makes Stuff Happen

Previous meditation: "Does your rule forbid epiphenomenalist theories of consciousness that consciousness is caused by neurons, but doesn't affect those neurons in turn? The classic argument for epiphenomenal consciousness is that we can imagine a universe where people behave exactly the same way, but there's nobody home - no awareness, no consciousness, inside the brain. For all the atoms in this universe to be in the same place - for there to be no detectable difference internally, not just externally - 'consciousness' would have to be something created by the atoms in the brain, but which didn't affect those atoms in turn. It would be an effect of atoms, but not a cause of atoms. Now, I'm not so much interested in whether you think epiphenomenal theories of consciousness are true or false - rather, I want to know if you think they're impossible or meaningless a priori based on your rules."

Is it coherent to imagine a universe in which a real entity can be an effect but not a cause?

Well... there's a couple of senses in which it seems imaginable. It's important to remember that imagining things yields info primarily about what human brains can imagine. It only provides info about reality to the extent that we think imagination and reality are systematically correlated for some reason.

That said, I can certainly write a computer program in which there's a tier of objects affecting each other, and a second tier - a lower tier - of epiphenomenal objects which are affected by them, but don't affect them. For example, I could write a program to simulate some balls that bounce off each other, and then some little shadows that follow the balls around.

But then I only know about the shadows because I'm outside that whole universe, looking in. So my mind is being affected by both the balls and shadows - to observe something is to be affected by it. I know where the shadow is, because the shadow makes pixels be drawn on screen, which make my eye see pixels. If your universe has two tiers of causality - a tier with things that affect each other, and another tier of things that are affected by the first tier without affecting them - then could you know that fact from inside that universe?

Followup to: The Useful Concept of Truth

We previously asked:

What rule would restrict our beliefs to just statements that can be meaningful, without excluding a priori anything that could in principle be true?

It doesn't work to require that the belief's truth or falsity make a sensory difference. It's true, but not testable, to say that a spaceship going over the cosmological horizon of an expanding universe does not suddenly blink out of existence. It's meaningful and false, rather than meaningless, to say that on March 22nd, 2003, the particles in the center of the Sun spontaneously arranged themselves into a short-lived chocolate cake. This statement's truth or falsity has no consequences we'll ever be able to test experientally.  Nonetheless, it legitimately describes a way reality could be, but isn't; the atoms in our universe could've been arranged like that on March 22nd 2003, but they weren't.

You can't say that there has to be some way to arrange the atoms in the universe so as to make the claim true or alternatively false. Then the theory of quantum mechanics is a priori meaningless, because there's no way to arrange atoms to make it true. And if you try to substitute quantum fields instead, well, what if they discover something else tomorrow? And is it meaningless -rather than meaningful and false - to imagine that physicists are lying about quantum mechanics in a grand organized conspiracy?

Since claims are rendered true or false by how-the-universe-is, the question "What claims can be meaningful?" implies the question "What sort of reality can exist for our statements to correspond to?"

If you rephrase it this way, the question probably sounds completely fruitless and pointless, the sort of thing that a philosopher would ponder for years before producing a long, incomprehensible book that would be studied by future generations of unhappy students while being of no conceivable interest to anyone with a real job.

But while deep philosophical dilemmas such as these are never settled by philosophers, they are sometimes settled by people working on a related practical problem which happens to intersect the dilemma. There are a lot of people who think I'm being too harsh on philosophers when I express skepticism about mainstream philosophy; but in this case, at least, history clearly bears out the point. Philosophers have been discussing the nature of reality for literal millennia... and yet the people who first delineated and formalized a critical hint about the nature of reality, the people who first discovered what sort of things seem to be real,were trying to solve a completely different-sounding question.

They were trying to figure out whether you can tell the direction of cause and effect from survey data.

Please now read Causal Diagrams and Causal Models, which was modularized out so that it could act as a standalone introduction. This post involves some simple math, but causality is so basic to key future posts that it's pretty important to get at least some grasp on the math involved. Once you are finished reading, continue with the rest of this post.

Followup To: Play for a Cause, Singularity Institute $100k Challenge Grant

In the spirit of informal intellectual inquiry and friendly wagering, and with an eye toward raising a bit of money for SIAI, I offer the following two challenges to the LW community.

Challenge #1 - Bayes' Nets Skeptics' Challenge

Many LWers seem to be strong believers in the family of modeling methods variously called Bayes' Nets, belief networks, or graphical models. These methods are the topic of two SIAI-recommended books by Judea Pearl: "Probabilistic Reasoning in Intelligent Systems" and "Causality: Models, Reasoning and Inference".

The belief network paradigm has several attractive conceptual features. One feature is the ability of the networks to encode conditional independence relationships, which are intuitively natural and therefore attractive to humans. Often a naïve investigation of the statistical relationship between variables will produce nonsensical conclusions, and the idea of conditional independence can sometimes be used to unravel the mystery. A good example would be a data set relating to traffic accidents, which shows that red cars are more likely to be involved in accidents. But it's nearly absurd to believe that red cars are intrinsically more dangerous. Rather, red cars are preferred by young men, who tend to be reckless drivers. So the color of a car is not independent of the likelihood of a collision, but it is conditionally independent given the age and sex of the person driving the car. This relationship could be expressed by the following belief network:

(This started as a reply to Gary Drescher's comment here in which he proposes a Metacircular Decision Theory (MCDT); but it got way too long so I turned it into an article, which also contains some amplifications on TDT which may be of general interest.)