Determinism is not a defining feature of counterfactuals, you can make a stochastic theory of counterfactuals that is a strict generalisation of SEM-style deterministic counterfactuals. See Pearl, Causality (2009), p. 220 “counterfactuals with intrinsic nondeterminism” for the basic idea. It’s a brief discussion and doesn’t really develop the theory but, trust me, such a theory is possible. The basic idea is contained in “the mechanism equations ui=fi(pai,ui) lose their deterministic character and hence should be made stochastic.”
This doesn’t work in social science. Quoting the book:
This evaluation can, of course, be implemented in ordinary causal Bayesian networks (i.e., not only in ones that represent intrinsic nondeterminism), but in that case the results computed would not represent the probability of the counterfactual Yx = y. Such evaluation amounts to assuming that units are homogeneous, with each possessing the stochastic properties of the population—namely, P( Vi I pai , u) = P( Vi I pai). Such an assumption may be adequate in quantum-level phenomena, where units stands for specific experimental conditions, but it will not be adequate in macroscopic phenomena, where units may differ appreciably from each other.
Pearl is distinguishing “intrinsically nondeterministic” from “ordinary” Bayesian networks, and he is saying that we shouldn’t mix up the two (though I think it would be easier to avoid this with a clearer explanation of the difference).
Three questions:
Do we need determinism to define counterfactuals?
No
Is uncertainty represented in causal Bayesian networks typically used in social science limited to “intrinsic nondeterminism”?
No, and so we should be careful not to mix them up with “intrinsically nondeterministic” Bayesian networks
Is there no intrinsic nondeterminism in any causal Bayesian network relevant to social science?
I doubt it
More importantly, the thing you can do with counterfactual models that you can’t do with “ordinary” causal Bayesian networks is you can condition on the results of an action and then change the action (called “abduction”; this is why it would be helpful to have a better explanation of the difference between the two!). This will usually leave a bunch of uncertainty about stuff, which may or may not be intrinsic. You definitely don’t need determinism to do abduction, and I submit that our attitude towards the question of whether the leftover uncertainty is “intrinsic” should often be the same as our usual attitude toward this question: who cares?
Is there no intrinsic nondeterminism in any causal Bayesian network relevant to social science?
I doubt it
The intrinsic quantum nondeterminism probably mostly gets washed away due to enormous averages. Of course chaos theory means that it eventually gets relevant, but by the time it gets to relevant magnitudes, the standard epistemic uncertainty has already overwhelmed the picture. So I think in comparison to standard epistemic uncertainty, any intrinsic nondeterminism will be negligible in social science.
More importantly, the thing you can do with counterfactual models that you can’t do with “ordinary” causal Bayesian networks is you can condition on the results of an action and then change the action (called “abduction”; this is why it would be helpful to have a better explanation of the difference between the two!). This will usually leave a bunch of uncertainty about stuff, which may or may not be intrinsic.
I know and agree.
Do we need determinism to define counterfactuals?
No
[...]
You definitely don’t need determinism to do abduction, and I submit that our attitude towards the question of whether the leftover uncertainty is “intrinsic” should often be the same as our usual attitude toward this question: who cares?
I sort of have some problems with/objections to counterfactuals in the presence of intrinsic nondeterminism. E.g.YX=X might not be equal to Y (and per chaos theory, would under many cicumstances never be equal or even particularly close). But since intrinsic nondeterminism isn’t relevant for social science anyway, I just skipped past them.
Determinism is not a defining feature of counterfactuals, you can make a stochastic theory of counterfactuals that is a strict generalisation of SEM-style deterministic counterfactuals. See Pearl, Causality (2009), p. 220 “counterfactuals with intrinsic nondeterminism” for the basic idea. It’s a brief discussion and doesn’t really develop the theory but, trust me, such a theory is possible. The basic idea is contained in “the mechanism equations ui=fi(pai,ui) lose their deterministic character and hence should be made stochastic.”
This doesn’t work in social science. Quoting the book:
Emphasis added.
Pearl is distinguishing “intrinsically nondeterministic” from “ordinary” Bayesian networks, and he is saying that we shouldn’t mix up the two (though I think it would be easier to avoid this with a clearer explanation of the difference).
Three questions:
Do we need determinism to define counterfactuals?
No
Is uncertainty represented in causal Bayesian networks typically used in social science limited to “intrinsic nondeterminism”?
No, and so we should be careful not to mix them up with “intrinsically nondeterministic” Bayesian networks
Is there no intrinsic nondeterminism in any causal Bayesian network relevant to social science?
I doubt it
More importantly, the thing you can do with counterfactual models that you can’t do with “ordinary” causal Bayesian networks is you can condition on the results of an action and then change the action (called “abduction”; this is why it would be helpful to have a better explanation of the difference between the two!). This will usually leave a bunch of uncertainty about stuff, which may or may not be intrinsic. You definitely don’t need determinism to do abduction, and I submit that our attitude towards the question of whether the leftover uncertainty is “intrinsic” should often be the same as our usual attitude toward this question: who cares?
The intrinsic quantum nondeterminism probably mostly gets washed away due to enormous averages. Of course chaos theory means that it eventually gets relevant, but by the time it gets to relevant magnitudes, the standard epistemic uncertainty has already overwhelmed the picture. So I think in comparison to standard epistemic uncertainty, any intrinsic nondeterminism will be negligible in social science.
I know and agree.
I sort of have some problems with/objections to counterfactuals in the presence of intrinsic nondeterminism. E.g.YX=X might not be equal to Y (and per chaos theory, would under many cicumstances never be equal or even particularly close). But since intrinsic nondeterminism isn’t relevant for social science anyway, I just skipped past them.
Does chaos theory apply at the micro-scale (quantum phenomena) or at the macro-scale?
Chaos theory applies at all scales. It turns micro-scale uncertainty into macro-scale uncertainty at an exponential rate.