Counterfactual Scenarios in Causal Analysis

• Counterfactual scenarios are hypothetical worlds that alter antecedents to reveal causal relationships using structured models.
• They integrate methods from causal inference, planning, and stress testing through frameworks like structural causal models and backtracking.
• Applications span AI explanations, macroeconomic policy, and time series analysis, enhancing both interpretability and decision-making.

Counterfactual scenarios are hypothetical worlds in which some antecedent differs from what actually occurred and one asks what consequences would follow under that altered condition. Across contemporary work, they appear as counterfactual conditionals in language, alternate treatment assignments in causal inference, hypothetical past interventions in time series, altered planning problems, modified policy paths in macroeconomics, and adverse but plausible stress narratives in finance (Li et al., 2023, Butler et al., 2024, Wang, 2024, Soleimani, 26 Nov 2025). Much of the modern literature begins from structural causal models and the abduction–action–prediction pattern, but recent work also emphasizes backtracking to earlier causes, naturalness and feasibility constraints, product-space formalisms that separate counterfactuality from intervention, and domain-specific notions of realism (Kügelgen et al., 2022, Hao et al., 2024, Park et al., 1 Jan 2026).

1. Conceptual range and basic uses

In the most general sense, a counterfactual scenario is a representation of “what would happen if” some condition were different from actuality. In psycholinguistic and language-model evaluations, the defining form is a proposition that is false in the real world but assumed true in a hypothetical world, together with consequences that follow inside that hypothetical world; the canonical contrast is between real-world completions and counterfactual-world completions such as “If cats were vegetarians” followed by a consequence involving cabbages rather than fish (Li et al., 2023). In vector autoregressive time series, a counterfactual scenario is a hypothetical past intervention on a previously observed realization, followed by the question of what the future would have looked like under that past change (Butler et al., 2024).

The same notion is instantiated differently in planning and decision systems. In automated planning, counterfactual scenarios are minimal modifications to a planning problem $P=\{F,A,I,G\}$ such that the modified problem admits plans satisfying a desired $\mathrm{LTL}_f$ specification $\psi$; this is explicitly contrasted with earlier counterfactual explanations that modify an existing plan rather than the problem itself (Gigante et al., 29 Aug 2025). In power-system optimisation, the scenario is a minimally perturbed demand profile that would have moved the optimal dispatch into a user-specified region, such as dispatching a generator above a threshold or committing a unit at a given time (Fritz et al., 4 Dec 2025). In macro-financial stress testing, a counterfactual scenario is a structured macroeconomic shock vector for GDP growth, inflation, and policy rates, generated for a fixed horizon and mapped into portfolio losses (Soleimani, 26 Nov 2025).

These uses share a common feature: the scenario is not merely an alternative label or outcome. It is an alternate world specification tied to a generative, causal, logical, or optimisation structure. This suggests that “scenario” in this literature usually denotes a structured alternate state of affairs rather than an unconstrained perturbation.

2. Structural, potential-outcome, and measure-theoretic foundations

Two classical foundations recur throughout the literature: the Potential Outcome Model and the Structural Causal Model. In the Potential Outcome Model, counterfactuals are unobserved potential outcomes $Y(1)$ and $Y(0)$, with identification resting on assumptions such as SUTVA, consistency, positivity, and ignorability (Kang et al., 2024). In the Structural Causal Model, one specifies endogenous variables $\mathbf{V}$, exogenous variables $\mathbf{U}$, and structural assignments $\mathbf{F}$, often written componentwise as

$X_i := f_i(pa_i, U_i),$

and counterfactual reasoning follows Pearl’s abduction–action–prediction sequence (Kang et al., 2024, Hao et al., 2024).

This interventionist foundation has been extended in several directions. A continuous-time formulation based on local independence graphs treats a counterfactual scenario as a new probability law $P_\theta$ on the same sample space, characterized by a martingale problem and linked to the factual law through a likelihood-ratio stochastic differential equation; identification then depends on short-term prediction structure encoded in local independence graphs (Røysland, 2011). At a still broader level, counterfactual probability spaces and counterfactual causal spaces represent factual and counterfactual worlds on product measurable spaces such as

$\mathrm{LTL}_f$0

with shared information between worlds encoded in the probability measure $\mathrm{LTL}_f$1 and, after intervention, in causal kernels $\mathrm{LTL}_f$2 (Park et al., 1 Jan 2026). In that framework, counterfactuals and interventions are treated as orthogonal concepts rather than points on a single “ladder,” and a defining axiom is that there is no causal effect across worlds (Park et al., 1 Jan 2026).

These extensions matter because they broaden the admissible semantics of counterfactual scenarios. Rather than requiring every counterfactual to be an intervention in an SCM, they allow multiworld probability constructions, continuous-time change-of-measure formulations, and varying degrees of shared information between factual and counterfactual worlds.

3. Backtracking, naturalness, and feasibility

A central recent development is the critique of purely surgical interventions. In standard Pearl-style semantics, if one wants $\mathrm{LTL}_f$3 to take a new value $\mathrm{LTL}_f$4, one applies $\mathrm{LTL}_f$5 while keeping its causal ancestors fixed. The backtracking literature argues that this produces counterfactual worlds by “small miracles”: the exogenous context is held fixed, but the laws are locally broken to force the antecedent (Kügelgen et al., 2022). Backtracking counterfactuals reverse this design. The causal laws remain unchanged, the exogenous variables are allowed to change, and the counterfactual world is generated by altered upstream conditions. Formally, the key object is a backtracking conditional

$\mathrm{LTL}_f$6

which encodes similarity between factual and counterfactual exogenous states; desirable properties include preference for closeness, symmetry, decomposability, and distance-based constructions such as

$\mathrm{LTL}_f$7

Under this semantics, computation proceeds by cross-world abduction, marginalization over factual exogenous variables, and prediction in the unchanged model (Kügelgen et al., 2022).

“Natural counterfactuals” refine this idea by permitting only the amount of backtracking needed to return a counterfactual point to a realistic region of the observed distribution. The distinction is explicit: $\mathrm{LTL}_f$8 denotes a direct intervention, whereas $\mathrm{LTL}_f$9 denotes an intended counterfactual change that may be realized through ancestor interventions (Hao et al., 2024). The generation problem is posed as Feasible Intervention Optimization, with a minimal-change objective over ancestor variables and a naturalness constraint. In the implemented method, the distance is the $\psi$0 norm on ancestor variables, and naturalness is enforced by a conditional CDF criterion,

$\psi$1

Larger $\psi$2 imposes a stricter notion of naturalness and therefore more forceful backtracking (Hao et al., 2024).

The key conceptual point is that backtracking is not arbitrary rewriting of the past. In the “necessary backtracking” formulation, one backtracks only when the direct intervention would otherwise be unnatural, infeasible, or out of distribution; if the direct intervention is already natural, the method collapses to ordinary non-backtracking counterfactuals (Hao et al., 2024). This suggests a general shift from purely law-breaking counterfactual surgery toward minimally altered, distribution-respecting alternate histories.

4. Temporal, spatio-temporal, and multiagent scenarios

Time-indexed systems impose additional structure because the scenario typically concerns alternate histories rather than isolated variables. In vector autoregressive models, the factual process is

$\psi$3

interpreted as an SCM on the time-unfolded graph (Butler et al., 2024). A counterfactual scenario is a hypothetical intervention during a past interval, with the exogenous noise realization kept fixed across factual and counterfactual worlds. Because the model is linear, the downstream effect of a perturbation propagates exactly through the total causal effect matrices $\psi$4, which satisfy

$\psi$5

This yields exact counterfactual trajectories and total causal effects of past interventions (Butler et al., 2024).

When multiple units interact across space and time, the main complication is interference. The spatio-temporal overview emphasizes that classical POM and standard SCM are strained by systems in which one unit’s treatment affects another unit’s outcome and today’s intervention affects future states. Its proposed unifying graphical representation is the Spatio-Temporal Bayesian Network, with factorization over time-indexed nodes and a temporal assumption that causes precede or parallel their effects (Kang et al., 2024). Counterfactual inference is then organized recursively through “Forward Counterfactual Inference,” which searches causal pathways, back-door structures, and mediator layers in the time-indexed graph (Kang et al., 2024).

A related multiagent formulation models counterfactual scenarios as full future trajectories under alternate intervention histories rather than as one-step alternate outcomes. The GVCRN framework estimates individual treatment effects in observational multiagent systems by learning latent confounders $\psi$6, forecasting future covariates $\psi$7, forecasting future outcomes $\psi$8, and rolling these predictions forward over time (Fujii et al., 2022). This design is motivated by the claim that in multiagent systems the intervention changes future interactions among agents, which then changes later outcomes. The practical consequence is that realistic counterfactual scenarios require joint modeling of treatment, latent confounding, future covariates, and long-term outcomes (Fujii et al., 2022).

5. Explanations, planning, and closed-loop control

In explainable AI, the counterfactual scenario is often an actionable modification to inputs or environment conditions that would change a decision. A recent formulation replaces fixed mutable-feature sets with user-defined counterfactual templates $\psi$9, specified at inference time. In FCEGAN, the generator receives $Y(1)$0 and outputs $Y(1)$1, after which immutable coordinates are reset to their original values. This permits black-box counterfactual explanations without retraining or per-instance optimisation, using historical predictions rather than model internals (Hellemans et al., 24 Feb 2025). The design goal is flexibility under heterogeneous real-world constraints rather than a universal recourse policy.

Planning work generalizes this explanatory idea from instances to domains. Given a planning problem $Y(1)$2, an $Y(1)$3 formula $Y(1)$4, and a possible-change relation $Y(1)$5, an existential counterfactual scenario seeks the minimally modified planning problem such that there exists a plan satisfying $Y(1)$6, whereas a universal counterfactual scenario seeks the minimally modified planning problem such that all valid plans satisfy $Y(1)$7, with non-emptiness required to avoid vacuity (Gigante et al., 29 Aug 2025). For the main concrete edit classes—initial states, goals, and action preconditions—the generation problem is often no harder asymptotically than planning itself (Gigante et al., 29 Aug 2025).

In optimisation-based infrastructures, the same pattern appears with domain-specific mutable inputs. In DC Optimal Power Flow and Unit Commitment, counterfactual explanations are bilevel optimisation problems that perturb spatial or temporal demand profiles minimally in the $Y(1)$8 norm so that the lower-level optimum enters a user-specified solution region (Fritz et al., 4 Dec 2025). The counterfactual scenario thereby identifies not only an alternate optimal solution but also which demand changes and which constraint families—such as congestion or ramping—were operative (Fritz et al., 4 Dec 2025).

Closed-loop generative control systems add another layer: the scenario must remain realistic while changing risk or intent. CounterScene generates safety-critical driving scenarios by identifying the causally critical agent, modeling inter-agent dependencies with a causal interaction graph, and applying stage-adaptive counterfactual guidance that removes spatial and temporal safety margins from that single agent while allowing the world model to propagate the consequences (Jing et al., 22 Mar 2026). In LLM-based autonomous control, the SCM is explicit: $Y(1)$9 where $Y(0)$0 is a user prompt, $Y(0)$1 an action sequence, $Y(0)$2 environment feedback, and $Y(0)$3 the report. Conformal Counterfactual Generation then calibrates sets of counterfactual reports so that, with high probability, at least one generated candidate is a good enough approximation of the true counterfactual outcome (Farzaneh et al., 27 Jan 2026).

6. Counterfactual scenarios in policy, learning, and stress testing

Counterfactual scenarios are also used to learn decision rules or evaluate policy under shifts not observed in the training distribution. In semiparametric counterfactual regression, the observed data are $Y(0)$4, the intervention is an incremental shift of treatment odds,

$Y(0)$5

and the target estimand is the solution of a constrained stochastic optimisation problem for the counterfactual regression risk (Kim, 3 Apr 2025). Efficient influence functions convert the unobserved counterfactual objective into an estimable one, and the resulting estimators can achieve $Y(0)$6-consistency and asymptotic normality under product-rate nuisance conditions (Kim, 3 Apr 2025).

In offline reinforcement learning, the Counterfactual Reasoning Decision Transformer augments the factual dataset with generated counterfactual experiences. A Treatment model identifies low-probability alternative actions, an Outcome model predicts the next state and return-to-go under those actions, and uncertainty plus return-improvement filters discard unreliable counterfactual branches before the Decision Transformer is trained jointly on factual and counterfactual data (Nguyen et al., 14 May 2025). The stated motivation is to reason beyond the exact offline dataset, especially when optimal trajectories are scarce (Nguyen et al., 14 May 2025).

Macroeconomic counterfactual scenarios can be defined as policy path deviations without specifying a full structural model. In the SVMA-based framework, a hypothetical trajectory sets the policy variable on an alternative path $Y(0)$7, whereas a policy intervention forces the policy variable to be unresponsive to a shock by zeroing out the systematic response of the interest rate (Wang, 2024). The resulting counterfactual parameters are given analytically in terms of impulse responses and Moore–Penrose inverses, and identified with external instruments in a projection-based method connected to Local Projections (Wang, 2024).

Stress testing uses a different but related construction. LLM-generated macro-financial scenarios specify country, title, GDP growth, inflation, interest rate, rationale, and risk sectors for severe but plausible Q4 2026 narratives, and are mapped into Value-at-Risk and Expected Shortfall through a three-channel factor-based translator (Soleimani, 26 Nov 2025). The scenario itself is therefore a structured counterfactual macro path rather than a replay of a historical episode.

7. Identifiability, evaluation, and recurring controversies

A persistent issue is whether a counterfactual scenario is identifiable from observed data or merely plausible. For high-dimensional outcomes, observational equivalence can support multiple mechanisms with different counterfactuals. One recent resolution uses continuous-time flows and dynamic optimal transport: if the causal mechanism is the unique OT map $Y(0)$8 for a convex potential $Y(0)$9, then the induced counterfactual transport

$\mathbf{V}$0

is unique, monotone, and rank-preserving under stated regularity conditions; the paper extends this identifiability logic to Markovian settings and to IV, backdoor, and frontdoor cases in non-Markovian settings (Ribeiro et al., 9 Oct 2025). This directly addresses the objection that many learned counterfactual maps lack a causal identification story.

Evaluation raises a different problem. In scenario modeling, the realized world usually differs from the modeled scenario, so the raw discrepancy between projection and observation mixes scenario deviation with model miscalibration. The relevant quantity is the counterfactual model error

$\mathbf{V}$1

not the difference between the scenario projection and the realized outcome at $\mathbf{V}$2 (Howerton et al., 30 Nov 2025). Three approaches are compared: evaluating only retrospectively plausible scenarios, inferring the error distribution directly by rerunning the model at the realized scenario, and estimating the observations in the modeled scenarios. The paper recommends the latter two over the first, with the preferred choice depending on whether one can model the counterfactual observation well or instead trust the mechanistic model to capture the relevant nonlinearities (Howerton et al., 30 Nov 2025).

Several controversies recur across domains. One concerns semantics: counterfactuals need not be reducible to interventions, as argued by the counterfactual-spaces framework, which treats counterfactuality as a property of product-world probability spaces and interventions as properties of causal kernels (Park et al., 1 Jan 2026). Another concerns realism: purely surgical changes may leave the data manifold, motivating natural and backtracking counterfactuals (Hao et al., 2024, Kügelgen et al., 2022). A third concerns competence claims in language systems: models can appear to reason counterfactually by overriding world knowledge, yet much of the effect can be driven by lexical cues, and when both world knowledge and lexical associations are mitigated, only GPT-3 showed some sensitivity to the linguistic nuances of counterfactual marking (Li et al., 2023). Finally, quantum theory challenges truth-valued classical counterfactual logic. A recent formalism therefore treats measurement settings as antecedents and replaces truth values with counterfactual probabilities, or “supposabilities,” defined by averaging over fixed classical fixtures outside the causal future of the antecedent (Banerjee et al., 2 Oct 2025).

Taken together, these developments show that counterfactual scenarios are not a single technique but a family of formal objects whose meaning depends on how alternate worlds are linked to the factual one: by shared exogenous noise, by backtracked upstream conditions, by product-world probability structure, by optimization constraints, or by learned transport maps. The common scientific demand is that the scenario be not only hypothetical but also structurally interpretable, feasible within the chosen model class, and evaluable against explicit criteria of identifiability, realism, or calibration.