Summary: How representations of causal events are structured can affect our perception of how strong a causal argument is. For instance, research has found that people's intuition about causal power varies as a function of a cause’s scope - the number of variables directly influenced by that cause. For example, people tend to perceive the effect of a hypothetical drug that only causes night vision (narrow scope) to be stronger than a different drug that leads to night vision and joint flexibility and glowing (wider scope). This phenomenon has been referred to as "the dilution effect" (see Stephan and Waldmann, 2023). The authors have argued that, in the absence of prior beliefs about a domain, this effect occurs regardless of whether causal relations are Generative (leading to an effect) or Preventive (preventing an effect). Other researchers have argued that the dilution effect depends on non-structural factors, such as the emotional valence of the effects. For example, a drug that prevents three negative symptoms in a patient is seen as more causally potent than a drug that prevents only one negative symptom (Sussman & Oppenheimer, 2020). Like Stephan and Waldmann (2023), this study focused solely on common cause structures where a single cause leads to one versus several different effects. In this study, we examine two novel aspects of the causal structure as potential mediators or moderators for the dilution effect. We hypothesize the effect of these elements on dilution to be at least partially independent of scope, prior beliefs about a domain, or valence. The two aspects to be studied are: 1) The type of causal relations (Generative/Preventive) in networks with the same structure otherwise. The fundamental manipulation here is similar to one of the factors in Stephan and Waldmann (2021), but the mechanistic explanation for the dilution effect and, thus, the contrasts tested are different. 2) Changing the causal structure between nodes while remaining within the same Bayes net equivalence class by comparing common cause structures with causal chains. Our novel mechanistic explanation predicts a dilution effect in causal chains that is not predicted by scope, valence, or prior beliefs about the domain. Our hypotheses revolve around assumed interactions among the effects that go beyond the information provided to participants. We predict a dilution effect only when the causal relations are Generative, making interactions between effects more likely. We expect to find this interaction-based effect in both common cause and causal chain structures, the demonstration of the latter being a novel contribution of this work. Introduction: How does the structure of causal events change our perception of causal strength in arguments? The causal structure is an important feature of causal reasoning in artificial intelligence (Pearl, 1998), human moral reasoning (Johnson & Drobny, 1985; Engleman et al., 2022), and causal cognition in general (Rehder, 2014). Among the structural aspects that have been studied, Sussman and Oppenheimer (2020) have argued that the scope of a cause (i.e., the number of effects generated by a cause) is important for its perceived causal strength, whereby greater scope results in lower perceived strength. This effect was attributed to the perceived valence of the effects, as the down-adjustment of causal strength was observed only when effects were favorable. For instance, a drug that inhibited three negative symptoms in a patient was perceived as causally stronger than a drug that inhibited one negative symptom (the “boon” condition). When the effect was harmful (the “bane” condition), the scope’s impact was reversed: greater scope was associated with lower casual strength. Using Power Theory, Stephan and Waldmann (2023) criticized this interpretation of the “Bane-Boon effect”. When the causal scenarios were abstract enough to eliminate any prior beliefs in participants (e.g., an alien on Mars eating a purple gem that introduces/prevents three vs. one attribute(s)), the effect of scope was uniform across positively and negatively valenced effects. Stephan and Waldmann (2023) offered a novel explanation for the change in perceived causal power, which they called “the dilution effect”: in causes with wider scopes (i.e., multiple effects) rather than narrower scopes (e.g., single effect), causal power is seen as “diluted” across the multiple effects. They, however, provide no explanation for why the “boon” effect was observed with non-blank priors in Sussman and Oppenheimer (2020). Adjudicating between the causal power and the Bane/Boon accounts for the dilution of causal power and therefore requires further research. Other than comparing the two accounts in a single experiment that controls for all the theorized independent variables, we suggest and test a different explanation for dilution effects: In a common cause structure, participants may assume interactions between effects. Such interactions can potentially explain each individual effect, thus reducing the perceived causative role of the common cause and diluting the latter’s estimated causal power over each effect. To the extent that this explanation is valid, a similar dilution effect should be found in other causal structures where interactions between effects are possible. For instance, causal chains with three nodes allow for assumed interactions between effects. These interactions might be considered partially “responsible” for the eventual effect, resulting in a dilution of intermediate causes. Note that the interaction account for dilution does not depend on either valance (Susman & Oppenheimer, 2020) or prior knowledge (Stephan & Waldmann, 2023). The scope of all causes in a simple chain also remains one, making scope an unlikely explanation for any observed dilution of causal power. Prior research has been limited to comparing the same type of causal structure across different numbers of effects and, therefore, cannot be directly used to compare the theoretical accounts for this possibility. By directly manipulating the structure between common cause and causal chain formats while keeping network nodes the same, we examine whether dilution happens in both formats. It is noteworthy that network connections assumed by participants which are not part of the provided network have been invoked as explanations for causal reasoning effects before. For instance, Park and Sloman (2013) argue that ostensible violations of the Markov Property in humans arise because of participants positing additional nodes and connections. However, such explanations have not been offered for the dilution effect. Outline This research aims to Understand the effect of causal structure on the perception of causal power in causal arguments. We limit our comparison to Chain vs. Common Cause structures, both with the same three nodes as in a control condition). The joint probability is the same for particular configurations of these two structure types (see Figure 1), allowing us to better control for background intuitions about the causal networks participants reason about. To adjudicate between Power and Bane-Boon(BB) theories, as they provide mutually exclusive predictions for the common cause and chain structures of the type to be described. To propose a novel explanation for the deficiencies observed in 1 and 2 by our Interaction account. In this account, the causal structure of relationships plays a crucial role in determining whether the dilution effect occurs, regardless of prior beliefs and valence. Different mechanisms predict different patterns of deviation from normative criteria in estimating causal power, allowing us to compare them for consistency with findings. By controlling for valence (positive or negative outcome) and prior beliefs and by manipulating these features, we aim to explore structure as a potential additional factor for determining intuitions about causal power as a function of scope. Our novel explanation suggests that the "perceived" interactions among the effects are key in determining the dilution effect. We predict that the dilution effect will only be observed when the cause inhibits the effects, making interactions between the effects less likely. Conversely, when the cause is Generative, increasing the likelihood of interactions between multiple effects, we predict that the impact of scope will be reversed, with the greater scope being associated with lower causal strength. Figure 1. The comparisons between the joint probability P(A, B, C) in a Common effect (up) and Chain (down) network in a causal (Bayes) nets. Since the joint probability in both networks is identical, we compare the two networks in different argumentative scenarios. Controlled Variables Valence Because Sussman and Oppenheimer (2020) emphasize outcome valence, we control for this factor in our scenarios. The effect for which causal power is estimated has a patently negative valence since predictions from the competing mechanistic theories are best differentiated in this condition. We nonetheless ask participants to indicate outcome valence, thus confirming the validity of our negative valence material and allowing for statistical estimation of its impact on results. Varied Variables Prior Beliefs Because Stephan and Waldmann (2021) highlight the importance of prior domain beliefs, we use several scenarios with different degrees of expected participant familiarity. A scenario involving Aliens digesting gems was adapted from their paper to serve as the “no prior beliefs” scenario. An “economics” scenario was adapted from Rehder (2014), representing a moderate level of familiarity. Finally, we use a novel scenario about “sex work criminalization,” representing the kind of morally-charged arguments that participants tend to have prior attitudes on. Appendix A shows the text of the scenarios. We will compare the qualitative pattern of results across these scenarios to identify any potential domain differences. Network Structure This represents our central manipulation. We manipulate the causal structure as a between-subject variable to prevent causal intuitions induced by one condition from contaminating others. Chain: a Chain network where A facilitates C, which in turn facilitates B: A→C→B CC(F): a Common Cause network where C facilitates A separately facilitates B: A←C→B CC(I): a Common Cause network where C inhibits A separately inhibits B: A←C→B Control(F): a baseline for (1) and (2) in which A does not exist, and C facilitates B: C→B Control(I): a baseline for (3) in which A does not exist and C inhibits B: C→B To test the hypothesized difference between Generative and Preventive relations with respect to inviting the consideration of interactions between effects, we assume that all causal relations in our networks are single sense, i.e., the absence of a cause has no effect. This information will also be provided to participants in the instructions.