Variation semantics: when counterfactuals in explanations of algorithmic decisions are true

We propose a new semantics for counterfactual conditionals. It is primarily motivated by the need for an adequate framework for evaluating counterfactual explanations of algorithmic decisions. We argue that orthodox Lewis-Stalnaker similarity semantics and interventionist causal modelling semantics are not adequate frameworks because they classify too many counterfactuals as true. Our proposed semantics overcomes this problem of the orthodox approaches and has further advantages, including simplicity, robustness, closeness to practice and applicability. It is based on the idea that a counterfactual `if A were the case, C would be the case' is true at an elementary possibility ω just in case C is true at all variants of ω at which A is true, other things being equal. We provide a novel explication of the idea of a variation that makes a given sentence true while leaving other things (but not necessarily all other things) equal