The 'if only' thoughts generated by participants validate the idea that the majority of participants produced the same counterfactual thought as the one participants were asked to evaluate in the inference task.
So the counterfactual belief function idea needs a lot of working out if it is to rescue the idea that subjectivist Bayesian belief functions can provide a viable account of the likelihoods employed by the sciences in inductive inferences.
A comparison of actual immigrant locations with the counterfactuals gives some idea of the role of characteristics in explaining location differences.
The basic idea of counterfactual theories of causation is that the meaning of causal claims can be explained in terms of counterfactual conditionals of the form "If A had not occurred, C would not have occurred".
Rubin (1974) thus links exposability to counterfactual propositions and the idea of a hypothetical experiment.
JDM helped conceive the problem, develop the solution, discovered the idea of counterfactual machines, and helped draft the manuscript.
Note that the definition mentioned in the text represents the gut idea of the counterfactual account of causation.
Counterfactual causality was the central idea that stimulated invention of randomised experiments by Ronald A. Fisher and statistical inference on them by Fisher around 1920 and, later, by Jerzey Neyman and Egon Pearson in a somewhat different way [ 3, 17].
Thanks to work on potential outcomes and the counterfactual theory of causality stemming from the early ideas of Hume (e.g., Rubin 1974)—a number of quasi-experimental strategies have emerged that (under a set of fairly stringent assumptions) offer the possibility of estimating a causal effect from data that arises from non-experimental research designs.
Extending this idea, using the concept of counterfactuals, Laubender and Bender [ 13] proposed methods for computing such population measures taking into account the confounder distribution.
