Causality

Post date: Sep 07, 2017 2:47:52 PM

What is a cause?

Thinking about causality too broadly leads to paralyzing problems. For example, if I kick a ball and it moves, what was the proximate cause? Clearly, the kick. But what about the mass of the ball? A low mass enables me to move it. If it weighed 1000 lbs, my kick wouldn't budge it. So did the kick and the low mass jointly cause the ball to move? Probably, but this broad view of causation is just too wide to be useful.

A better idea might be to declare a cause as a direct action or intervention that results in a change in Y. This brings the definition of cause in line with what we do when we run true experiments (i.e., the ones with random assignment of cases). Ontologically, this approach is agnostic about whether causality exists out there or is just a concept.

Key assumptions

[Drawn from Morgan and Winship 2007] The key assumption we make in investigating causality is that each individual in the population has a potential outcome for each treatment state, even though each individual will only ever have one treatment state at any given point in time. More formally, suppose there is a dichotomous outcome variable y(i) that we will observe for each individual i. The potential outcomes for each individual are y1(i) and y0(i), where y1(i) indicates the outcome for individual i for the treatment state, and y0(i) indicates that individual's outcome for the control state. Because both y1(i) and y0(i) exist in theory for each individual, an individual-level causal effect can be defined as the simple difference y1(i) - y0(i). But because it is impossible to observe both y1 and y0 for any individual, the causal effect cannot be observed or directly calculated. [see footnote 1 below]

In physics, there is a way around this. We can't observe both y1 and y0 for the same individual gold atom, but all gold atoms are identical in every way. So you don't have to observe y1 and y0 for the same atom, you can apply the treatment state and control state to two different atoms and it is as if we observed it in the same atom. The thing about biological and social sciences is that no two individuals are the same.

Footnote 1. The best we can do in the social sciences is a crossover design in which each individual is exposed to both treatment and control states in succession, and with enough time in between that the effects of the cause have time to subside, yet the individual undergoes no other changes in that time. Good luck with that. Such conditions must be very rare, if they exist at all, and their existence could never be proved anyway.