Where does causation collide?

Two findings made in sequence about one past event. The first is factual cause: the Restatement (Third) of Torts fixed it in 2010 as the but-for test, conduct is a cause of harm when the harm would not have occurred absent the conduct, with the rare case of two independently sufficient causes handled separately. The second is what courts called proximate cause and the Restatement renamed scope of liability: an actor is liable only for harms that result from the risks that made the conduct tortious. Cardozo's opinion in Palsgraf in 1928 is the founding statement of that limit, framed as duty to the foreseeable plaintiff, with Andrews' dissent framing the same limit as proximate cause. California juries are instead told to ask whether the conduct was a "substantial factor", a formula the Restatement deliberately abandoned because it let fact-finders skip the counterfactual. Causation here is a verdict about a single defendant and a single harm, never a rate.[1][2][3]

Unit

One defendant's conduct and one plaintiff's harm, in a single past event

Recovery means

Not applicable, the remedy is damages once both causal findings are made

Measured by

Fact-finder's verdict on but-for cause by a preponderance of the evidence; scope of liability decided by the jury, or by the court where no reasonable jury could find the harm within the risk

The question of what it is for one thing to cause another, answered by analysis and tested against counterexamples rather than data. Hume set the terms in 1748: we never observe a necessary connexion, only constant conjunction, so a cause is an object followed by another where all objects like the first are followed by objects like the second; the felt necessity is a habit of the mind. Lewis in 1973 replaced regularity with counterfactual dependence, c causes e when e would not have occurred had c not occurred, or when a chain of such dependences links them, evaluated across the closest possible worlds. Mackie's INUS condition, introduced in 1965 and set out at length in 1974, made the ordinary cause an insufficient but non-redundant part of a condition that is itself unnecessary but sufficient: the short circuit causes the fire only together with the oxygen and the absence of a sprinkler. The distinctive feature is that these are accounts of the concept, offered for single events and for kinds alike, and pre-emption and overdetermination are their standing problems.[4][5][6]

Unit

A relation between two events, or between two kinds of event, as a concept

Recovery means

Not applicable, the criterion is whether the analysis survives pre-emption, overdetermination and the other counterexamples

Measured by

Judgments about described cases; no instrument

The effect of a treatment on a unit is the difference between what the unit's outcome would be under treatment and what it would be under control. Rubin fixed the framework in 1974 for randomised and non-randomised studies alike; Holland named it the Rubin causal model in 1986, stated the fundamental problem, that only one of the two potential outcomes is ever observed, and added the slogan "no causation without manipulation". The estimand is therefore an average over units, recoverable by randomisation or by adjustment under an assumption that treatment is as good as random given covariates. Pearl's structural causal models supply the other half: causal assumptions are drawn as a directed graph, an intervention is the do operator, and the do-calculus says when an interventional quantity can be identified from observational data. Causation in this meaning is defined by an intervention and estimated in a population; it does not say what caused this outcome in this unit.[7][8][9]

Unit

A population of units, each with a potential outcome under each treatment

Recovery means

Not applicable, the criterion is identification: whether the causal estimand can be written in terms of the distribution that was observed

Measured by

Average treatment effects from randomised or adjusted comparisons; interventional distributions identified by graphical criteria

Two constructs under one field name. Granger's 1969 definition for time series says that X causes Y when the past of X improves the prediction of Y beyond what the past of Y already gives; it is a statement about forecasting and temporal order in stationary series, and Granger himself said so, describing the relation as predictive and later complaining about papers that read it as more. The second construct is the one Angrist and Pischke codified in 2009: treat observational data as a natural experiment and recover a causal effect through an instrumental variable, a regression discontinuity or a difference in differences, with the estimand a local average treatment effect for the units the instrument moves. The first asks whether a series helps predict another; the second asks what a policy would do. Only the second is causation in the potential-outcomes meaning, and the credibility of the exclusion restriction is the whole argument.[10][11]

Unit

A pair of time series; or a sample of units on either side of a natural experiment

Recovery means

Not applicable, the criterion is whether the instrument is credible, or whether the lagged predictor adds forecasting power

Measured by

F-tests on lagged predictors in a vector autoregression; instrumental-variables and regression-discontinuity estimates of local average treatment effects

Whether an exposure causes a disease, judged from observed associations in populations where experiment is usually impossible. Bradford Hill's 1965 address listed nine viewpoints, strength, consistency, specificity, temporality, biological gradient, plausibility, coherence, experiment and analogy, as aids to the judgment of whether an association is causal, and insisted they were not criteria and that none could be required as a sine qua non. Rothman and Greenland's sufficient-component cause model gives the judgment a structure: a disease has several sufficient causes, each a set of components that together complete it, and a cause of a case is any component of the set that completed it. Most causes are therefore neither necessary nor sufficient, the fraction of cases attributable to each component can sum to more than one hundred percent, and the population attributable fraction, not the individual verdict, is the quantity of interest. Causation here is a property of an exposure across many cases, read from relative risks and dose–response.[12][13]

Unit

An exposure and a disease in a population, with each case completed by a set of component causes

Recovery means

Not applicable, the criterion is the attributable fraction: cases that would not have occurred without the exposure

Measured by

Relative risks and dose–response gradients from cohort and case–control studies; attributable fractions; judgment against Hill's viewpoints

A causal model is one that predicts not only the observed distribution but what happens under intervention, and the field's two projects are to learn such models from data and to build learners that behave like them. Peters, Janzing and Schölkopf set out causal discovery in 2017: under assumptions such as independent noise or independence of cause and mechanism, the direction of an arrow between two variables can be read from observational data, and a structural causal model entails the interventional and counterfactual distributions a purely statistical model cannot. Schölkopf and colleagues' 2021 programme of causal representation learning asks the learner to find the causal variables themselves in raw pixels or text, on the principle that mechanisms are independent and that a distribution shift changes few of them. The motivating fact is that a predictor trained on one distribution can score well by exploiting correlations that are not causes and fail when the distribution moves; prediction accuracy is not evidence that causes were learned, which is the same lesson as Granger's caveat with higher stakes. The generalization and robustness pages carry the other half of that argument.[14][15]

Unit

A learned model, the variables it represents, and the distributions it is asked to transfer to

Recovery means

Invariance, a model whose predictions survive intervention or distribution shift

Measured by

Recovered graphs scored against ground truth on benchmark data; out-of-distribution and interventional accuracy