The availability of counterfactual historical data would be too complex to compute given the statistically infinite number of parameters that determine any particular outcome. A mathematically interesting way to look at this problem is through causal inference[1][2]. In our “ordinary” history, we only see our perceptual timeline as a single function of collapsed states; what we do not observe are the innumerable counterfactual outcomes “of the multiverse” and if we could, the volume of data would make the insights useless unless we could specify the relevant alternate sets themselves that we wish to observe, and at this point it becomes a “choose your own adventure” where expectation would corrupt any meaningful observations.
Historians tend to frame events in terms of contingency vs. inevitability, structure vs. agency, and argue over whether a specific event really did “change history.” Adding counterfactual data brings a ruler to the game and suddenly history is measurable with definable relative baselines. So, for any historical event E, we can define an outcome of interest Y to define any one variable such as GDP growth or mortality. Then, the causal effect of the event becomes:
where, τ measures the affected change under the applied pressure, E[Y | do(E=1)] is the average outcome with applied positive pressure (make it happen), and E[Y | do(E=0)] is the mean outcome with negative applied pressure (make it not happen). Essentially, this determines the average change in outcome comparing the universe where it did happen, to the universe where it did not. The ‘do’ in the equation changes the measurement from what was the outcome of the sample set of did/did not happen, to if we hardcode the outcome, what are the consequences[3]?
The cleanest analysis comes from a thought experiment that forces an artificial binary formulation. Historical events rarely unfold in a happened / didn’t happen structure. Additionally, the consequences are equally multidimensional where timing, magnitude, complex event interactions, and a myriad of other factors are affected in ways often impossible to observe. For simplicity, we will adopt this binary historical model where events either occur or do not occur.
We first define as opposing states:
Yi(1) = outcome occured
Yi(0) = outcome did not occur
Introducing counterfactual data gives us in simplified form:
Event occurs
Y(1)
Event does not occur
Y(0)
One benefit of such a system would be the ability to discern which events were actually pivotal versus which were just talked about as being pivotal and what affect broad social promotion has in framing actual events versus the public’s perceptions of those events. With our newfound historical measuring stick, we can define an estimated social importance score as:
for our binary approach, or for the multidimensional case:
Essentially, counterfactual data would allow us to rank historical events by the magnitude of the causal impact.
Some key flaws in the system are the trickle down or butterfly effect, and the choice of outcome variable. What is good? What is a good outcome? Let’s say that we make a great decision that gets rid of all of the mosquitoes in North Carolina. Sign me up, right? But, then the bat population falls off and dies, and those less agreeable South Carolina mosquitoes move in, and next thing you know we (North Carolinians) are all driving on horrible roads with Gamecocks bumper-stickers. It is a slippery slope. Even with perfect binary counterfactual data, interpretation would not be trivial, and although counterfactual historical data would sharpen causal knowledge, it would not eliminate normative disagreement.
In conclusion, it is difficult to see how counterfactual data would be useful given the complexity of causation in our singular macroscopic timeline and the dynamic human perception of good versus bad outcomes. This was kind of a ridiculous question, but this was fun.
RReferences
- Cunningham, S. (2021). Potential outcomes causal model. In Causal Inference: The Mixtape. Yale University Press. ↩
- Lin, W., Dudoit, S., Nolan, D., & Speed, T. P. (2024). From urn models to box models: Making Neyman’s (1923) insights accessible. Journal of Causal Inference, 12(1), 20230073. doi.org/10.1515/jci-2023-0073 ↩
- Pearl, J. (2010). The foundations of causal inference. Sociological Methodology, 40(1), 75–149. doi.org/10.1111/j.1467-9531.2010.01228.x ↩