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Graded Causation and Defaults
Joseph Y. Halpern, Christopher Hitchcock
TL;DR
Existing accounts of actual causation face problems with preemption, isomorphic counterfactual structures, and disagreement about causal judgments. This paper adds a flexible normality ordering to structural-equation causation, using the normality of best witnesses to produce graded, comparative judgments. The framework addresses isomorphism and disagreement while leaving the choice of relevant normality factors open.
Problem
Counterfactual and structural-equation accounts do not adequately handle cases where isomorphic dependence patterns support different causal judgments or where people disagree about causation.
Method
The paper extends the Halpern–Pearl framework with a normality ordering over possible worlds and grades candidate causes according to the normality of their best witnesses.
Results
Different normality orderings allow isomorphic causal structures to yield different judgments and allow disagreement despite agreement about underlying causal structure.
Takeaways & Limitations
The framework provides a flexible way to represent varied causal judgments without settling which defaults, typicality, or normality factors should be used.
Takeaways & Limitations
The proposal does not address several putative counterexamples to the HP definition, including voting scenarios, and leaves the choice of normality ordering open.
Abstract
from arXiv · showhide
Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. A number of philosophers and computer scientists have also suggested that an appeal to such factors can help deal with problems facing existing accounts of actual causation. This paper develops a flexible formal framework for incorporating defaults, typicality, and normality into an account of actual causation. The resulting account takes actual causation to be both graded and comparative. We then show how our account would handle a number of standard cases.
1 Introduction
Actual causation is difficult to define because counterfactual and structural-equation accounts face preemption, isomorphism, and disagreement cases. The paper introduces a flexible normality-ordering framework that makes causation graded and comparative while preserving differing causal judgments.
- Actual causation concerns whether one particular event caused another and is relevant to moral and legal responsibility.
- Counterfactual accounts struggle with preemption, because an event may cause an outcome even when the outcome would have occurred through a backup cause.
- Isomorphic counterfactual-dependence patterns can yield different causal judgments, as in cases contrasting weather with a neighbor’s failure to water flowers.
- Empirical findings indicate that defaults, typicality, and normality influence people’s judgments about actual causation.
- The paper represents relevant considerations by ranking possible worlds in a flexible normality ordering rather than deciding which factors should determine causation.
- Different normality orderings can address isomorphism and disagreement, while grading causes permits one event to count as more of a cause than another.
- The proposal begins with the Halpern–Pearl definition but is intended as a recipe applicable to other structural-equation accounts.
2 Causal Models
Causal models represent variables and their dependencies with structural equations, distinguishing endogenous outcomes from exogenous conditions. Interventions modify equations, but model-variable selection remains a substantive limitation because it determines which causal claims can be expressed.
- Structural equations specify how variables depend on one another, such as whether a forest fire requires either a lightning strike or a dropped match.
- In the disjunctive model, FF equals the maximum of L and M; in the conjunctive model, FF equals their minimum.
- Structural equations are asymmetric assignment rules rather than ordinary algebraic equalities, supporting non-backtracking counterfactuals.
- The model simplifies potentially complex conditions by building them into the forest-fire equation rather than representing every factor explicitly.
- A causal model formally consists of a signature listing endogenous and exogenous variables and structural equations relating their values.
- Intervening on X by setting it to x replaces X’s equation with X = x, allowing the model to represent external interventions.
- Choosing variables determines the language of causal analysis, so omitted variables cannot be considered as causes within the model.
- The formalism does not determine the uniquely right causal model, although it can clarify disagreements between alternative models.
3 The HP Definition of Actual Causation
The Halpern–Pearl account defines actual causes through actual occurrence, counterfactual dependence under suitable contingencies, and minimality. It addresses preemption but still faces problems when structurally identical counterfactual patterns support different causal judgments.
- Naive counterfactual reasoning fails in the forest-fire case because either lightning or the match would independently suffice, yet HP counts both as actual causes.
- The HP account handles preemption by requiring a counterfactual dependence under a contingency that suppresses the backup cause.
- The HP definition treats X = x as an actual cause of ϕ only relative to a causal model and context.
- AC1 requires that both the candidate cause and the outcome actually occur.
- AC2 tests whether changing the candidate under permitted contingencies changes the outcome while controlling potentially masking side effects.
- AC3 imposes minimality, excluding inessential elements from conjunctions presented as causes.
- Other structural-equation theories use a similar strategy but differ over which model modifications and contingencies are permissible.
4 The Problem of Isomorphism
The problem of isomorphism arises because cases with isomorphic counterfactual-dependence structures can warrant different actual-causation judgments. Examples involving bogus prevention and short circuits show that structural-equation accounts, including HP, cannot capture these differences alone.
- The problem of isomorphism: Two examples illustrate isomorphic counterfactual-dependence structures yielding different actual-causation judgments.The section presents bogus prevention and short-circuit cases as illustrations of this problem.
- Bogus prevention: In the bogus-prevention case, most people judge that the bodyguard’s antidote did not cause the victim’s survival, although the HP definition says it did.Under the relevant contingency, the victim survives if and only if the bodyguard adds the antidote.
- Bogus prevention: The bogus-prevention model has structural equations isomorphic to those of the disjunctive forest-fire model.The variables for the assassin, bodyguard, and victim’s survival correspond to lightning, match, and forest fire.
- Short circuits: In the short-circuit case, most people judge that adding the antidote is not an actual cause of survival because it caused the threat it neutralized.Without the antidote, the poison would not have been added, so administering the antidote did not prevent death.
- Implication: The problem affects any account relying only on structural equations or counterfactual-dependence structure, not just the HP definition.Isomorphic structural models can correspond to different judgments about actual causation.
5 Defaults, Typicality, and Normality
The paper motivates incorporating defaults, typicality, and normality into actual-causation judgments while distinguishing their descriptive, prescriptive, and defeasible aspects. It argues that these considerations need not undermine objectivity and leaves their precise content flexible and context-sensitive.
- Core concepts: The revised account incorporates defaults, typicality, and normality as related but distinct concepts.These concepts are introduced as resources for enriching an account of actual causation.
- Core concepts: Defaults are defeasible assumptions about what happens or is the case when no additional information is given.Further information can override a default inference, as in the example of Tweety and penguins.
- Core concepts: Typicality concerns what is characteristic of a type, whereas normality can refer descriptively to statistical prevalence or prescriptively to conformity with a rule.The paper distinguishes typicality from mere frequency and separates descriptive from prescriptive senses of normality.
- Empirical motivation: Psychological and experimental-philosophy research indicates that statistical and prescriptive norms can influence counterfactual and actual-causation judgments.The cited work reports effects involving moral evaluations, negative evaluations, and other normative considerations.
- Objectivity concerns: Incorporating normality raises concerns that causation could become subjective, socially constructed, value-laden, or context-dependent.The paper treats these as worries about the consequences of adding normative considerations to causation.
- Objectivity concerns: The authors argue that causal structure remains objective while actual causation may depend on specialized judgments involving normality.They distinguish the objective structural equations from judgments of actual causation.
- Flexibility and scope: The framework is intended to represent whichever normality or default considerations are appropriate in a particular context.It does not prejudge whether prescriptive norms, statistical frequency, individual typicality, or population typicality should control judgments.
- Flexibility and scope: Defaults can represent objective or non-subjective ideas such as a system’s starting state or undisturbed evolution.The paper gives default-state and uniform-motion examples for representing event-based or system-dependent causal judgments.
6 Extended Causal Models
The paper extends causal models with a partial preorder over worlds that represents normality separately from structural counterfactual dependence. This ordering filters admissible interventions and ranks causes by the normality of their best witnesses.
- Extended models: An agent may supplement structural equations with a theory of normality or typicality, such as the claim that people typically do not put poison in coffee.The approach follows the idea that causal structure and normality can be represented together.
- Extended models: A world is a complete assignment to the model’s relevant variables, and it need not satisfy the causal equations.Worlds represent complete situations in the language determined by the endogenous variables.
- Normality ordering: The framework uses “default” and “typical” for variables or equations, reserving “normal” for comparisons among worlds.This terminology distinguishes variable-level notions from world-level rankings.
- Normality ordering: Normality is represented by a reflexive and transitive partial preorder over worlds.The ordering permits strict comparison, equality of normality, and incomparability.
- Normality ordering: The normality ordering does not determine which counterfactuals are true or which worlds are closer; the causal equations determine those counterfactuals.The model assigns structural dependence to equations and normality comparisons to the ordering.
- Revised causation: The revised causation condition requires intervention-generated worlds considered in AC2(a) to be at least as normal as the actual world.This formalizes a preference for altering atypical features to make worlds more typical.
- Graded and comparative causation: Normality ranks actual causes by comparing the normality of their best witnesses, helping explain why people typically select one cause among multiple counterfactual causes.A witness is a world demonstrating AC2(a), and a best witness is not outranked by another witness.
- Graded and comparative causation: The best-witness ranking strategy can also be adapted to other actual-causation definitions with a structure similar to HP’s.The paper illustrates this adaptability using Hall’s proposal.
7 Examples
The examples show how normality orderings make actual-causation judgments graded, comparative, and sensitive to norms, expectations, and contextual atypicality.
- 7.1 Omissions: The framework leaves unresolved how to classify borderline cases, such as holding one’s breath as an action or omission.It also assumes that relevant norms can be identified before assessing causation.
- 7.1 Omissions: Normality rankings can preserve omission as causal while making positive events much better causes.Watering and not watering may both receive causal status, but hot weather can have the more normal witness.
- 7.1 Omissions: Whether a neighbor’s omission counts as a cause depends on obligations or reasonable expectations that she would have watered the flowers.Without such an obligation or expectation, the omission is not counted as a cause.
- 7.2 Knobe effects: Subjects rated one norm-violating action 2.2 and the other −1.2, indicating different causal judgments for actions with different normative status.The experiment presented participants with one claim at a time rather than forcing a direct choice.
- 7.2 Knobe effects: When both actors were permitted to take pens, judgments became intermediate, suggesting that actual-causation attributions are partly comparative.Reduced attribution to the professor coincided with increased attribution to the administrative assistant.
- 7.3 Causes vs. background conditions: In the fire example, the match is judged a cause while oxygen is not, but atypical oxygen can make its witness comparably normal and support judging oxygen causal.The account therefore accommodates contextual changes in normality ordering, while the match may remain primary under a standing-condition interpretation.
8 Conclusion
The paper adds normality considerations to structural-equation accounts of causality, addressing isomorphism and disagreement while extending beyond the HP definition.
- 8 Conclusion: The framework incorporates normality into structural-equation theories of causality to address the problems of isomorphism and disagreement.The analysis is developed using the HP definition, but the authors state that the ideas should carry over to other structural-equation accounts.