In the previous post on LDSL, I argued that an important part of causal inference is to look at the larger things. This implies a method of comparison to rank things by magnitude. [1]
Homogenous comparison
When the things to rank are homogenous, ranking them tends to be easy, because one can set them up as opposing forces and see which one dominates. A classic example is ranking objects by weight, where an old-school balance scale makes the gravity of the objects oppose each other, thereby lifting up the lighter one.
Direct opposition is not the only method of measurement. Alternatively, one can set up the things to both influence a standardized measurement instrument, and then compare their influence on that instrument. For instance, to compare the weight of things, one can try lifting each thing, and feeling which one requires more force to lift.
Inhomogenous comparison
In order to apply the method of root cause analysis I suggested, one doesn’t just need to be able to compare equivalent things, but also to compare inequivalent things. For instance, to figure out the biggest factors to investigate for why an election went a certain way, it is not just enough to understand the vote counts in individual voting districts. It is also necessary to compare the importance across different kinds of issues, like scandals, politician positions, politician traits, and an endless number of domains that you wouldn’t even think about because they are obviously too unimportant to matter.
As far as I know, this sort of inhomogenous comparison inherently carries some subjectivity to it. What’s most, an apple or an orange? I can’t see it making sense to declare anything specific to be the correct answer here.
Yet, what’s most, a piece of dust or a tank? Obviously a tank. When you have qualitatively different things, but they differ by orders of magnitude, it seems much more likely that there’s a sensible ordering to things. A primitive way we could think about this is to imagine something like a principle component analysis over the different ways of ordering things, taking the overall “general factor”. Yet this is somewhat unsatisfying, since presumably the resulting order depends a lot on what comparison methods we include, and it’s unclear what the “meaning” of the resulting ordering is, causally speaking.
One solution that makes sense to me is to think in terms of diminishment rather than magnitude. Even small things like blankets can produce dust as a side-effect; meanwhile a tank needs an entire factory to be produced, and is part of an intentional preparation for war by an industrial state. Generally, larger things produce smaller things, a principle that is particular clear in cases like physics where laws such as conservation of mass or energy means that it is impossible for smaller things to produce larger things without external support. The more broadly we can extend these principles, the more effectively we can reason about root causes.
[LDSL#5] Comparison and magnitude/diminishment
This post is also available on my Substack.
In the previous post on LDSL, I argued that an important part of causal inference is to look at the larger things. This implies a method of comparison to rank things by magnitude. [1]
Homogenous comparison
When the things to rank are homogenous, ranking them tends to be easy, because one can set them up as opposing forces and see which one dominates. A classic example is ranking objects by weight, where an old-school balance scale makes the gravity of the objects oppose each other, thereby lifting up the lighter one.
Direct opposition is not the only method of measurement. Alternatively, one can set up the things to both influence a standardized measurement instrument, and then compare their influence on that instrument. For instance, to compare the weight of things, one can try lifting each thing, and feeling which one requires more force to lift.
Inhomogenous comparison
In order to apply the method of root cause analysis I suggested, one doesn’t just need to be able to compare equivalent things, but also to compare inequivalent things. For instance, to figure out the biggest factors to investigate for why an election went a certain way, it is not just enough to understand the vote counts in individual voting districts. It is also necessary to compare the importance across different kinds of issues, like scandals, politician positions, politician traits, and an endless number of domains that you wouldn’t even think about because they are obviously too unimportant to matter.
As far as I know, this sort of inhomogenous comparison inherently carries some subjectivity to it. What’s most, an apple or an orange? I can’t see it making sense to declare anything specific to be the correct answer here.
Yet, what’s most, a piece of dust or a tank? Obviously a tank. When you have qualitatively different things, but they differ by orders of magnitude, it seems much more likely that there’s a sensible ordering to things. A primitive way we could think about this is to imagine something like a principle component analysis over the different ways of ordering things, taking the overall “general factor”. Yet this is somewhat unsatisfying, since presumably the resulting order depends a lot on what comparison methods we include, and it’s unclear what the “meaning” of the resulting ordering is, causally speaking.
One solution that makes sense to me is to think in terms of diminishment rather than magnitude. Even small things like blankets can produce dust as a side-effect; meanwhile a tank needs an entire factory to be produced, and is part of an intentional preparation for war by an industrial state. Generally, larger things produce smaller things, a principle that is particular clear in cases like physics where laws such as conservation of mass or energy means that it is impossible for smaller things to produce larger things without external support. The more broadly we can extend these principles, the more effectively we can reason about root causes.
Ranking is not the only question relevant for measurement. There is also the question of quantification, which I will address in a later post.