2.3.1. Participants

The experiment was conducted over the Internet to obtain a large and demographically diverse sample. A total of 1,178 people completed the experiment. The participants were sampled through the Internet platform Mechanical Turk via CloudResearch from the USA, UK, Canada, and Australia. They were paid a small amount of money for their participation (on average $6 per hour) and told that there would in addition be a $1 bonus, if they answered accurately and participated in the second half 1 week later. The following exclusion criteria were used: not having English as native language, completing the task in more than 2 standard deviations below or above the mean completion time, failing to answer at least one of 2 simple SAT comprehension questions correctly in a warm-up phase, and answering ‘not seriously at all’ to the question ‘How seriously do you take your participation’ at the beginning of the study. The final sample for Session 1 consisted of 977 participants. Of these 977 participants, 787 (80.56%) participated in Session 2, 1 week later. To fit the Conflict model, data from both sessions are required. Thus, our analyses are focused on the latter participants.

Mean age of these 787 participants was 42.5 years, ranging from 19 to 91.Footnote ⁵ Among these, 40.53% self-identified as male; 57.18% as female; 11 participants indicated that they were non-binary, and 7 participants preferred not to reveal their gender. 70.65% indicated that the highest level of education that they had completed was an undergraduate degree or higher. Applying the exclusion criteria had a minimal effect on the demographic variables. For the analysis, we focus on the 769 participants who had participated in both sessions and who self-identified as either male or female to compare with previously reported gender effects.

2.3.2. Design

Each session had a within-participants design with the following factors varying within participant: consequence (smaller vs. greater) and norm (proscriptive vs. prescriptive). To allow for 3 trial replications for each of the 4 CNI conditions (3 $\times$ 4), each participant in total worked through 12 scenarios within a session. Across the 2 sessions, the following factor was varied within participant: causal structure (intended means vs. foreseeable side-effect). The same 12 background scenarios appeared in both sessions, but each scenario was presented in the intended means version in one session and the foreseeable side-effect version in the other session. In total, there were 24 items (12 scenarios × 2 causal structures) and 8 within-participant conditions (4 CNI conditions × 2 causal structures).

2.3.3. Materials and procedures

Participants were presented with the 4 CNI conditions across 12 background scenarios in random order and with random assignment of condition to scenario. Six of these scenarios (the Transplant, Vaccine, Bishop, Immune Deficiency, Dialysis, and Rwanda) were based on Gawronski et al. (Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017) and Körner et al. (Reference Körner, Deutsch and Gawronski2020) but further modified. Two scenarios (Hospital, Sinking Boat) were based on Moore et al. (Reference Moore, Clark and Kane2008) but further modified and 4 scenarios were new (Welfare, Carcrash, Undercover, Avalanche Disaster).Footnote ⁶

An example of the scenarios is displayed in Table 3. While the scenarios followed the form of the scenarios in Gawronski et al. (Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017) and Körner et al. (Reference Körner, Deutsch and Gawronski2020) to implement the CNI conditions, we chose to replace some scenarios because the proposed action had the flavor of murder (e.g., shoving a person from the edge of a building in the Construction site scenario, or adding peanut oil that would kill a person with an allergy to a dish in the Peanuts scenario). In these cases, the proposed action did not fall within the purview of the professional duties of the agent described (construction worker, the head of a restaurant). In other cases, scenarios from Gawronski et al. (Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017) and Körner et al. (Reference Körner, Deutsch and Gawronski2020) were replaced, because they depicted situations involving special norms (e.g., like torturing a guilty victim in the Torture scenario, and not negotiating with terrorists in the Abduction scenario). Others were replaced, because they did not permit us to parallelize the ratio of victims saved and sacrificed (e.g., the Assisted Suicide scenario and the Mother scenario), or because the victim had personal relationships to the agent deciding over the sacrifice (the Mother scenario).

Table 3 CNI conditions as implemented in one of the scenarios

Note: Example of a CNI scenario in both the intended means and foreseeable side-effect conditions. First, a shared cover story is presented. Next, the continuations implementing the intended means vs. foreseeable side-effect conditions are displayed. Finally, the invariant choice is depicted along with the 3 response options (Action vs. Inaction vs. Skip). The words ‘the action’ were colored in blue. The ProGreater, ProSmaller, PreGreater, and PreSmaller abbreviations are defined in Table 1. In the Proscriptive condition, what Figures 1–3 label as “Action” [“Inaction”] corresponds to responding “Yes” [“No”] to whether it is acceptable to carry out the action; in the Prescriptive condition, it corresponds to responding “Yes” [“No”] to whether it is acceptable to prevent the action.

Rosas and Koenigs (Reference Rosas and Koenigs2014) criticize past sacrificial dilemma research for introducing confounds like fated victims, who would die irrespectively of the sacrifice, guilty victims, who deserve to be sacrificed due to their own immoral behavior, and selfish reasons for selecting the ‘utilitarian option’. We carefully modified the scenarios to avoid these confounds. Across all scenarios, we further parallelized (1) the ratio of victims saved and sacrificed (5 vs. 1), (2) the probability terms describing how likely the outcomes of action/inaction would be, and (3) the way in which the smaller benefits were implemented in the ProSmaller and PreSmaller conditions, so that the gain of sacrificing an innocent person was trivially less than the cost of the sacrifice across all scenarios. Finally, we implemented a foreseeable side-effect and an intended means version of each scenario described below.

As already mentioned, the scenarios involve a manipulation of norms (proscriptive vs. prescriptive). Baron and Goodwin (Reference Baron and Goodwin2020) criticized the implementation of prescriptive norms in Gawronski et al. (Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017) for requiring participants to interfere with the preselected action of another person, who in some cases was depicted as the participants’ colleague or superior, which in turn raises unintended prospects of hurting this person’s feelings, violating lines of authority, or risking retaliatory actions. To circumvent this problem, we chose to implement the prescriptive norm condition differently (see also Henning and Hütter, Reference Hennig and Hütter2020, Reference Hennig and Hütter2021 for a related solution). In our implementation, we stipulated that a person lower in the professional hierarchy (e.g., an assistant to the participant) had preselected the presented action in the prescriptive condition under the assumption that this was what the participant wanted. If unhappy with this preselection, participants could reverse the planned action without going against the will of another agent. Note that while deontologists, such as Kamm (Reference Kamm2007), weigh negative rights (not to be harmed) stronger than positive rights (to be aided), this distinction does not carry over to the contrast between proscriptive and prescriptive norms under the present implementation. For what we label as ‘prescriptive norms’ here are not new deontological norms (e.g., norms to aid), but just the old deontological norms against sacrificial harm, which are now applied in a context in which accepting the harm is a default set by an assistant. As a validation, Appendix B presents an analysis of action/inaction responses in the congruent trials, which are neither predicted by Utilitarianism nor Deontology. In Baron and Goodwin (Reference Baron and Goodwin2020, Reference Baron and Goodwin2021) and Gawronski et al. (Reference Gawronski, Conway, Hütter, Luke, Armstrong and Friesdorf2020), such responses are denoted as ‘perverse’, but we here prefer the less value-laden term ‘abnormality rates’, which indicates that the response pattern goes against the expectations of ‘normality’ and is in this sense a form of pathological response–while remaining neutral on its etiology. In this analysis it is found that the modified scenarios do indeed reduce the rates of abnormal responses and that further modeling can reveal one mechanism leading to abnormal responses (see Appendix B).

Table 3 illustrates how the CNI conditions were implemented. Intended means scenarios follow the structure of a causal chain, in which the sacrifice of 1 person (C₂) as an act is presented as the only causal means for saving the 5 people (E₁).

Foreseeable side-effect scenarios follow the causal structure of a common cause, where the intended action has 2 effects; the intended outcome (E₁ = saving 5 people) and an unintended but foreseen side-effect (E₂ = killing 1 person).

The distinction is conceptually similar to the direct versus indirect harm distinction in Royzman and Baron (Reference Royzman and Baron2002) and the distinction between instrumentality and non-instrumentality in Fahrenwaldt et al. (Reference Fahrenwaldt, Olsen, Rahal and Fiedler2025). In the intended means condition, the harm is direct since there would be no way to get the desired outcome if the harm did not occur. In this case, the victim’s mind or body is used as an instrument to save others. In the foreseeable side-effect condition, the harm is indirect and obtaining the desired outcome is not required to occur. Rather, harm to the victim is a side-effect of the agent’s action.

Note, the direct form of harm in our scenarios does not take the form of direct use of personal force (e.g., pushing, smothering) as in Greene et al. (Reference Greene, Sommerville, Nystrom, Darley and Cohen2001) and Greene (Reference Greene2013). Often these two factors (i.e., use of the victim as an instrument and direct personal harm) are coupled in studies (Fahrenwaldt et al., Reference Fahrenwaldt, Olsen, Rahal and Fiedler2025). Yet, our manipulation does involve a coupling of causal structure with a difference in outcome certainty. In intended means scenarios, we state that the sacrificed person ‘will die’ if the intervention succeeds, because the sacrifice is presented as the only available means (if the goal is achieved, the sacrifice must have occurred). In foreseeable side-effect scenarios, we state the sacrificed person ‘will highly likely die’, since the sacrifice is a predicted consequence of a common cause intervention (which permits that the intervention succeeds but the prediction fails because the side-effect is prevented).Footnote ⁷

2.3.3.1. Presentation of scenarios

The order of the scenarios and the CNI conditions within scenarios were randomized for each participant anew.Footnote ⁸ Following Gawronski et al. (Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017), participants were given an instruction asking participants to pay close attention to small details in scenarios that seem similar and warning them that some of the scenarios may be unpleasant to think about since they related to difficult real-life issues. In addition, participants were given the following instructions for use of the skip option: ‘There is now also the option to “skip” a moral decision for cases, where you are undecided about whether the described action is morally acceptable or inacceptable. Please do not use the “skip” option more than 2 times’.

In each of the 2 sessions, participants first completed 2 practice items and then completed the moral judgments either for the intended means or foreseeable side-effect condition (with the order of these 2 causal structures randomized for each participant). The 12 background scenarios were presented in random order with random assignment of scenario to CNI condition. Experiment 1 followed Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015) and Conway et al. (Reference Conway, Goldstein-Greenwood, Polacek and Greene2018a) in measuring a range of covariates, which are categorized as egoistic or altruistic in Table 4.

Table 4 Overview of Experiment 1

Note: Session 1 and Session 2 were separated by one week. Participants who were randomly assigned to intended means in Session 1 saw the CNI scenarios in the foreseeable side-effects condition in Session 2 as a within-participant manipulation and vice versa. Blocks with covariates₂ were presented in random order. ‘Greater good scenarios’ = scenarios from Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015). ‘IWAH’ = identification with all of humanity. ‘IWAC’ = identification with local community. ‘IWAA’ = identification with own nationality, which in previous studies was restricted to Americans but is here tailored to each participant’s home country.

2.3.4. Altruistic vs. egoistic covariates

The self versus other sacrifice options in Table 4 refer to a switch version of the run-away-Trolley (Huebner and Hauser, Reference Huebner and Hauser2011; Thomson, Reference Thomson2008) in which participants are presented with the third option of sacrificing themselves in addition to the 2 classical options of action and inaction. Participants’ level of psychopathy was probed via Levenson et al.’s (Reference Levenson, Kiehl and Fitzpatrick1995) subscale for primary psychopathy in a noninstitutionalized population. The subscale consists of 16 Likert-scaled items (e.g., ‘For me, what’s right is whatever I can get away with’), some of which are reverse-coded (α = .91). Participants’ empathy was measured via the Empathic Concern Subscale of the Interpersonal Reactivity Index (Davis, Reference Davis1980), which consists of 7 Likert-scaled items (e.g., ‘I often have tender, concerned feelings for people less fortunate than me’), some of which are reverse-coded (α = .89).

The Identification with All Humanity Scale from McFarland et al. (Reference McFarland, Webb and Brown2012) was used, which consists of 9 items (e.g., ‘How much would you say you care (feel upset, want to help) when bad things happen to a) people in my community, b) people from your home country, and c) people anywhere in the world’). In each case, participants indicate how much they identify with all of humanity (IWAH), their local community (IWAC), or with people from their home country (IWAA). The IWAH (α = .91), IWAC (α = .88), and IWAA (α = .91) items were then presented as the final task with participants’ preselected home country used for the IWAA items. In Table 4, IWAH is listed as falling under the ‘altruistic covariates’. The IWAC and IWAA items were used as control items.

Participants’ adherence to psychological, moral, and rational egoism was measured with 3 items from Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015). Psychological egoism is the view that deep down people are always motivated by their self-interests in the end. Rational Egoism is the view that promoting one’s own self-interest is the only rational thing to do. Moral Egoism is the view that promoting one’s own self-interest is the only moral thing to do. The Greater Good scenarios were also based on Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015). In these scenarios participants are presented with 7 dilemmas involving conflicts between self-interested and altruistic actions (α = .70). In a typical scenario, participants have the choice of either using money on their own luxury needs or on saving the lives of strangers in remote, developing countries. The task asks participants to judge how wrong they find the self-interested choice, which either privileges themselves, their family, or country over the urgent needs of distant strangers, on a 5-point Likert scale from (‘Not at all wrong’) to (‘Very wrong’).

2.3.5. The scorekeeping task

To elicit commitments to competing norms, a scorekeeping task was employed (following Skovgaard-Olsen, Reference Skovgaard-Olsen2026; Skovgaard-Olsen and Cantwell, Reference Skovgaard-Olsen and Cantwell2023; Skovgaard-Olsen et al., Reference Skovgaard-Olsen, Kellen, Hahn and Klauer2019). Across the 2 sessions, participants encountered 3 pairs of fictive participants who had given competing solutions to the tasks that the participants had just completed and who were criticizing one another. For each of the 2 causal structures, one of these fictive participants was defending the deontological solution and the other was defending the utilitarian solution. In addition, participants encountered a pair of fictive participants disagreeing over whether performing the self-sacrificing greater good deed in the Greater Good scenarios from Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015) was morally permissible (but supererogatory) or morally obligatory. For each of the 3 pairs, participants judged whether the 2 presented criticism were compelling (‘yes’ vs. ‘no’) and selected the fictive peer whose task completion should be approved (see Table 5).

Table 5 Scorekeeping judgments

Note: The table provides an overview of the scorekeeping judgments that participants made across 2 sessions: approving HITs and accepting criticism for each member of the 3 pairs. In Session 1 (week 1), participants made scorekeeping judgments for the CNI scenarios in the intended means or foreseeable side-effect condition (depending on random assignment). In Session 2 (week 2) participants made scorekeeping judgments for the CNI scenarios in the remaining foreseeable side-effect or intended means condition and for the Greater Good scenarios. On Mechanical Turk, tasks for participants are called ‘HITs’ (‘Human Intelligence Tasks’), which is a label that is familiar to the participants.

2.3.5.1. Procedure

Participants were randomly assigned to a pair of fictive peers presented via pictorial avatars and first names with the avatar’s gender (male vs. female) and race (Caucasian vs. person of color) held constant within a pair. To illustrate the Scorekeeping Task, we here consider its application to the CNI scenarios. Participants were told that a pair of fictive peers had completed the same task as the one they just finished but that the 2 peers responded very differently. Participants were then presented with one of the scenarios either in intended means or foreseeable side-effect condition (depending on which they had just completed). Then followed (on separate pages) the information illustrated in Table 6.

Table 6 The scorekeeping task, the 2 conflicting responses

Note: In the upper half, the left side shows the fictive participants’ response; the right side shows his/her criticism of his/her peer opponent. The avatars and names were randomly varied such that gender (male vs. female) and race (Caucasian vs. person of color) were kept constant within a pair. This pair illustrates the opposition between Utilitarianism and Deontology.

On Mechanical Turk, tasks are described as ‘HITs’ (‘Human Intelligence Tasks’) to participants and the approval of HITs determine whether a participant is paid. Since participants are financially rewarded by approvals of HITs and build up a reputation by completing these tasks, the approval of HITs was used as an ecologically valid sanctioning measure in Skovgaard-Olsen et al. (Reference Skovgaard-Olsen, Kellen, Hahn and Klauer2019) that participants are motivated to reason about. Here we adopted this measure as well. After the presentation of the criticism, participants were asked whether they found the given criticism compelling (‘yes’ vs. ‘no’). Finally, participants were presented with a page in which both responses were repeated with the instruction that they should indicate whose ‘HIT’ on Mechanical Turk should be approved after having seen, e.g., Natalie’s and Emma’s mutual criticism.

2.4.1. Latent class analysis

In Appendix A, a latent class model is outlined, which was fitted to the scorekeeping judgments to classify participants into latent classes. This analysis was repeated for 2, 3, and 4 class solutions, each representing a distinct qualitative pattern. Table 7 compares the model fits of these solutions via information criteria. Substantially, the model favored by these criteria is evaluated on whether it yields theoretically meaningful class profiles.

Table 7 Latent class models

Notes. The number of classes refers to the number of distinct qualitative patterns identified by the latent class analysis. LOOIC = leave-one-out cross-validation information criterion. WAIC = Watanabe-Akaike information criterion. ‘elpd’ = expected log predictive density is a measure of the expected out-of-sample predictive accuracy. Note that information criteria can take both positive and negative values and that the lowest value indicates the best performance.

The information criteria which assess the expected out-of-sample predictive accuracy of the fitted models indicate that a model with 4 classes best fit the data (since it has lower values on the information criteria). Figure 4 displays the posterior median and 95% HDI of participants’ scorekeeping performance as a function of their assigned latent class.

Figure 4 Latent classes and the scorekeeping task.

Note: Posterior median estimates with 95% HDI error bars for parameter estimates of the 4-class model. Rows: Criticism (top) vs. HIT approval (bottom). Columns: GreaterGood, IntendedMeans, and SideEffect avatar pairs. Colors (evaluation targets): Deontological avatar; Obligatory GreaterGood avatar; Permissible GreaterGood avatar; Utilitarianism avatar. X-axis (latent classes): Altruism accepts obligatory GreaterGood deed; Deontology always rejects sacrifices; DoubleEffect rejects sacrifices for intended means but accepts sacrifices for side-effects; Utilitarianism always accepts sacrifices.

As Figure 4 shows, it was possible to separate the following latent classes. First, a class of Deontology (N = 426, 54.1%), whose members accepted the HIT of Deontology across both the intended means and the foreseeable side-effect conditions, and had the highest posterior probability of accepting the criticism of Utilitarianism. Second, a class of Utilitarianism (N = 171, 21.7%), with the converse behavior. Third, a class of participants (N = 82, 10.4%), whose members sided with Deontology for intended means and Utilitarianism for foreseeable side-effect was identified. Due to this distinctive switching behavior, this third latent class was interpreted as following the Doctrine of DoubleEffect. Finally, a fourth latent class (N = 108, 13.7%) was identified exhibiting neither strong inclinations toward Utilitarianism nor toward Deontology. Instead, members of this latent class stood out by accepting that the altruistic deed was morally obligatory in the Greater Good scenarios. In contrast, the other 3 latent classes merely viewed the altruistic deed as morally permissible in the Greater Good scenarios. For this reason, we selected the label ‘Altruism’ for this fourth latent class.

To further validate the designation of ‘Altruism’ to the fourth latent class, participants’ performance on all the greater good scenarios were investigated as a function of their latent class (see Figure 5). For this analysis, a Bayesian linear regression model was fitted with the latent classes as predictor and a sum-score for the performance on the Greater Good scenarios as dependent variable, which had been transformed to range within the interval [0,1], with higher values indicating a preference for the altruistic deed over the self-interested option. Bayesian regression models here and throughout the paper were fitted using the R package brms (Bürkner, Reference Bürkner2017). The R-package tidybayes (Kay, Reference Kay2023) was used to calculate the 95% HDI and display the posterior distributions in Figure 5.

Figure 5 Greater good judgments across latent classes.

Note: The black dot and line indicates the posterior median and 95%-HDI. The sum score for the greater good scenarios was transformed to range within the unit interval.

As shown in Figure 5, the latent class of Altruism had a higher posterior probability of finding the choice of the self-interested action over the altruistic deed wrong across Greater Good scenarios. Among the remaining 3 latent classes, Utilitarianism did not differ from the latent class of DoubleEffect but had a higher posterior probability of finding the self-interested action wrong than Deontology.

In Appendix B, a self-sacrifice version of the switch Trolley scenario was analyzed and it is found that the participants in the latent classes had differential preferences for sacrificing a stranger, do nothing, or sacrifice themselves to save 5 people. Participants in the latent class of Utilitarianism and Doctrine of Double Effect showed the strongest preference for sacrificing a stranger, whereas participants in the latent class of Deontology preferred to do nothing and participants in the Altruism latent class preferred to sacrifice themselves.

2.4.2. Multinomial processing tree models

Next, participants’ moral judgments were analyzed via 4 models (Table 8). These models were fitted to estimate individual MPT parameters but they aggregate over items and trial replications to be less sensitive to scenario-specific content effects. While the hierarchical model could be extended to include random scenario effects (Matzke et al., Reference Matzke, Dolan, Batchelder and Wagenmakers2013) to assess interactions between scenarios and experimental conditions, such analyses would require substantially larger within-participant designs.

Table 8 Model comparison

Note: ‘Pro>’ = ProGreater, ‘Pro<’ = ProSmaller, ‘Pre>’ = PreGreater, ‘Pre<’ = PreSmaller. See Appendix A.

CNIS₆ and CNIS₁₄ extend the CNI model by a skip option. CNIS₁₄ differs from CNIS₆ in that it does not impose an invariance assumption for the C and N parameters across the CNI conditions (ProGreater, ProSmaller, PreGreater, PreSmaller) implicit in the CNI model of Gawronski et al. (Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017). In each case, separate C and N parameters were estimated for the intended means and foreseeable side-effect conditions. Appendix A contains further details on their implementation in R and the Bayesian estimation of their model parameters. In Skovgaard-Olsen and Klauer (Reference Skovgaard-Olsen and Klauer2024), CNIS₁₄ was found to be superior to CNIS₆.Footnote ¹⁰ Here, these 2 models are further contrasted with a new Conflict model which was implemented in different variations in a model fitting exercise. In Table 8, we only report the best performing version. In CNIS-Conflict_14a, it is tested whether adding a conflict architecture to the CNI model results in a better performing model.Footnote ¹¹ CNIS-Conflict-latent_14a is identical to this model but allows for latent group-specific means of the estimated MPT parameters based on the 4 latent classes in the scorekeeping phase.

Figure 6 compares the observed response frequencies and the posterior predictive behavior of the models. As shown, severe misfits between the observed response proportions and CNIS₆ were found. One example is that the model predicts an equal observed rate of skip responses based on (1−C) $\times$ (1−N) $\times$ S, in each type of scenario within the intended means and foreseeable side-effect conditions. It is thereby unable to account for the asymmetries between rates of skip responses between congruent and incongruent items. In addition, forcing C and N parameters to remain constant across conditions limits the model’s ability to fit the data. In contrast, the 3 other models perform increasingly well. All 3 models are also able to capture the asymmetry between skip responses across congruent and incongruent conditions. But unlike CNIS_14, the conflict models can capture this asymmetry by separately modeling skip responses that arise as the result of conflict detection, whereas CNIS₁₄ is forced to adjust the C _j and N _k parameters to make the activation of the (1−C _j ) $\times$ (1−N _k ) $\times$ S differ between conditions. The best fit is obtained with CNIS-Conflict-latent_14a.

Figure 6 Posterior predictive predictions.

Note: Observed response frequencies (blue bars) and posterior predictive frequencies (red points) for 4 models: CNIS₆ and CNIS₁₄ (top row), CNIS-Conflict_14a and CNIS-Conflict-latent_14a (bottom row). Columns correspond to the 4 CNI scenarios: Pre $<$ , Pre $>$ , Pro $>$ , Pro $<$ , where $>$ indicates that the benefit of the sacrifice is greater than the costs. Columns within panels show response type (action, inaction, skip), and panels are split by causal structure (intended means vs. foreseeable side-effect).

2.4.3. Model comparison

In Table 9, a formal model comparison is made of these 4 models based on (1) the expected out-of-sample predictive accuracy (assessed via information criteria) and (2) a test of whether there are statistically significant misfits of the models as indicated by the posterior predictive checks (T₁, T₂) proposed in Klauer (Reference Klauer2010), where a small (Bayesian) p value for each indicates that the model fails to capture an aspect of the data.

Table 9 Model comparison

Note: Model comparison indices. LOOIC = leave-one-out cross-validation information criterion. WAIC = Watanabe-Akaike information criterion. ‘elpd’ = expected log predictive density is a measure of the expected out-of-sample predictive accuracy. The test statistics T₁ and T₂ represent Bayesian p values and are based on the posterior predictive model checks in Klauer (Reference Klauer2010).

As in Skovgaard-Olsen and Klauer (Reference Skovgaard-Olsen and Klauer2024), it was found that the CNI model of Gawronski et al. (Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017) extended with a skip parameter (CNIS₆) had a worse fit to the data than a version of the same model (CNIS₁₄), which permitted violations of the invariance assumption by estimating separate C and N parameters for the different CNI conditions. In addition, Table 9 shows that this model in turn was outperformed by models with the Conflict architecture.

LOOIC is an information criterion which is based on the expected out-of-sample predictive accuracy of the models. Lower LOOIC values indicate a better fit in the light of the parsimony vs. fit trade-off. Using this criterion, it was found that despite its extra structure, the Conflict model with the latent classes provides the best trade-off between parsimony and data fit. Similarly, it was found that only the conflict models were able to pass the posterior predictive check for the aggregate outcome frequencies (T₁) proposed in Klauer (Reference Klauer2010).Footnote ¹²

2.4.4. Analysis of parameter estimates

Figure 7 displays the posterior median parameter estimates of the CNIS-Conflict-latent₁₄ model_, with C and N parameters averaged across the CNI conditions.

Figure 7 Model parameters by latent classes.

Note: Posterior median estimates with 95% HDI error bars for the parameter estimates of CNIS-Conflict-latent_14a by latent class. Conflict indicates detection of response conflict in incongruent dilemmas; Resolution indicates successful conflict resolution toward action or inaction; Skip indicates a guessing response that is not sensitive to the presence/absence of detected conflicts. ${\mathrm{N}}_{\mathrm{intend}}$ = ${\mathrm{N}}_{\mathrm{intend}}^{\mathrm{avg}}$ . ${\mathrm{N}}_{\mathrm{side}}$ = ${\mathrm{N}}_{\mathrm{side}}^{\mathrm{avg}}$ . ${\mathrm{C}}_{\mathrm{intend}}$ = ${\mathrm{C}}_{\mathrm{intend}}^{\mathrm{avg}}$ . ${\mathrm{C}}_{\mathrm{side}}$ = ${\mathrm{C}}_{\mathrm{side}}^{\mathrm{avg}}$ .

The posterior parameters follow expected qualitative patterns such as ${\mathrm{N}}_{intend}^{Deontology}$ > ${\mathrm{N}}_{intend}^{Utilitarianism}$ , ${\mathrm{N}}_{intend}^{DoubleEffekt}$ > ${\mathrm{N}}_{intend}^{Utilitarianism}$ , ${\mathrm{N}}_{side}^{Deontology}$ > ${\mathrm{N}}_{side}^{Utilitarianism}$ , ${\mathrm{N}}_{side}^{Deontology}$ > ${\mathrm{N}}_{side}^{DoubleEffect}$ , ${\mathrm{C}}_{intend}^{Deontology}$ < ${\mathrm{C}}_{intend}^{Utilitarianism}$ . In words: the latent classes Deontology and DoubleEffect had higher averaged N parameters for intended means than Utilitarianism and Deontology had higher averaged N parameter for foreseeable side-effect than Utilitarianism. Conversely, the latent class of Utilitarianism had higher averaged C parameters than Deontology for intended means. Table 10 reports for each parameter displayed in Figure 7 those pairwise contrasts between latent classes for which the 95% HDI of the contrasts excluded zero, that is, for which credible differences between the two classes were found.

Table 10 Contrasts in class-specific means

Note: The posterior median of the contrast effect is reported along with the 95% HDI in square brackets. Only contrasts effects for which the 95% HDI does not include zero are reported. The contrasts were calculated based on the differences in 10,000 random posterior draws. ‘avg’ = average of the parameters.

In addition to these effects in the differences of the C and N parameters across the latent classes, Table 10 also shows that the latent class of Deontology had a higher inaction bias than Utilitarianism and Altruism and that strong differences in the Conflict parameter emerged between Utilitarianism and Deontology. Table 11 reports effects of causal structure (intended means vs. foreseeable side-effect).

Table 11 Contrasts in the CNIS-Conflict-latent_14a parameters

Note: The contrasts were calculated based on the differences in 10,000 random posterior draws of the mean parameters. In each case, the posterior median of the contrast effect is reported along with the 95% HDI in square brackets. Only contrasts effects where the 95% HDI crosses zero are reported. ‘avg’ = average of the parameters.

To simplify the interpretation of model parameters, Table 11 presents the averaged C and N parameters. In Appendix B, we show, however, that the data replicated the pattern reported in Skovgaard-Olsen and Klauer (Reference Skovgaard-Olsen and Klauer2024) of showing strong violations of the invariance assumption in the individual C and N parameters, in violation of the CNI model.

As Table 11 shows, the manipulation of the intended-means and foreseeable side-effect in the CNI scenarios influenced the estimated C and N parameters within all latent classes albeit to different extents. This stands in tension with the fact that only the latent class of DoubleEffect explicitly committed to a difference between intended means and foreseeable side-effect in their scorekeeping behavior (Figure 4). In the general discussion, we will return to this issue and discuss the repercussions of this finding for the psychological interpretation of the Doctrine of Double Effect.

As a distinguishing feature, the Conflict model has a conflict detection parameter (Con) for the case that both the latent states represented by the C and N parameters are activated at the same time. As a first step in validating whether this parameter indeed captures experienced conflict, we tested whether the estimated Con parameters could predict participants’ self-criticism in the Scorekeeping Task. Self-criticism in the Scorekeeping Task occurs when participants accept the criticism of the position that they endorse in their HIT approvals. We fitted a Bayesian linear regression model with the median conflict parameter as predictor and self-criticism (the median posterior probability of accepting criticism of a given position while endorsing it via a HIT approval) as the outcome variable. It was found that conflict detection credibly predicts self-criticism, b = 1.0, 95% HDI [.20, 1.77].Footnote ¹³

2.4.5. Gender distribution

A total of 787 participants were classified according to these 4 latent classes, but the analysis concentrated on the 769 participants who self-identified as either male or female. Past research with the CNI model and the PD models has shown that women tend to be more deontological than men and that there are no differences between women and men in their utilitarian tendencies (Conway and Gawronski, Reference Conway and Gawronski2013; Gawronski et al., Reference Gawronski, Armstrong, Conway, Friesdorf and Hütter2017). To investigate the distributions of gender within the latent classes, a Bayesian logistic regression model was fitted with self-reported gender as dependent variable (with ‘0’ = male; ‘1’ = female) and the latent classes as predictor. The median proportions of females within the latent classes matched previous results.Footnote ¹⁴ For the Altruism and DoubleEffect classes, an equal proportion of males and females remained within the 95% highest density interval.Footnote ¹⁵ To investigate differences in whether males and females resolve conflicts between Utilitarianism and Deontology in incongruent items, gender was used a predictor of the estimated Res parameter of the Conflict model. It was found that male participants had a higher posterior probability of resolving conflicts than female participants, ${\overset{\sim }{\Delta}}_{Male- Female}^{Res}$ = .05, 95% HDI [.03, .06].

2.4.6. Structural equation modeling

To test H ₁ (concern for the greater good), H ₂ (restricted concern for the greater good), and H ₃ (antisocial motivation), we finally used structural equation modeling with the R-package blavaan (Merkle and Rosseel, Reference Merkle and Rosseel2018) to analyze relationships between altruistic and egoistic covariates and the model parameters. We included the 4 latent classes to investigate which of the 3 motivations best characterize the behavior of participants classified by these latent classes.

Structural equation modeling (SEM) is a generalization of regression models. Some of its benefits are that direct and indirect effects of explanatory variables can be estimated and that conditional independence constraints from a causal model can be incorporated (Kline, Reference Kline2016; Shipley, Reference Shipley2016). Figure 8 illustrates the relationships between the covariates and the model parameters of the Conflict model across latent classes.

Figure 8 Multigroup SEM analysis of altruistic and egoistic covariates.

Note: Multi-group SEM analysis estimating how altruistic covariates (in green) and egoistic covariates (in red) affect the MPT parameters within each latent class (Altruism, Deontology, DoubleEffect, Utilitarianism). Only path coefficients with the 95% HDI not containing zero are shown. The SEM model included estimated variances and covariances which are not included in this graph due to lack of space. For convergence reasons, only empathy and primary psychopathy were permitted to affect the I (Inaction) parameter. Covariates: P = primary psychopathy; IWAH = identification with all of humanity; E = empathy; EgoM/EgoP/EgoR = moral, psychological, and rational egoism; GG = greater good scenarios. MPT Parameters: N_i/N_s = averaged norm-based response for intended means and side-effect; C_i/C_s = averaged consequence-based response for intended means and side-effect; I = general inaction bias; Con = conflict detection; Res = conflict resolution.

This multi-group structural equation model investigates whether relationships between altruistic and egoistic covariates and model parameters differ across the independently established latent classes. Each participant has individual-level parameter estimates (C, N, Con, Res, I) from the Conflict model, representing their response tendencies across different moral dilemmas. Using latent class membership as a grouping variable, the multi-group SEM estimates how altruistic and egoistic covariates predict these Conflict model parameters within each of the 4 classes (Altruism, Deontology, DoubleEffect, and Utilitarianism). This approach thus tests whether the covariates operate differently depending on the assigned latent class; a question that requires comparing patterns across classes rather than pooling them. The paths shown represent credible effects (95% HDI excluding zero) between covariates and parameters conditional on class membership.

As shown in Figure 8, moral egoism tended to be negatively associated with C and N parameters across 3 (Altruism, Deontology, and Utilitarianism) of the 4 latent classes. In the Deontology class, psychological egoism was also found to be negatively associated with the averaged C and N parameters. In the latent class of DoubleEffect class, psychological egoism was found to be negatively associated with C_side. In the Utilitarianism class, primary psychopathy was found to be negatively associated with the averaged C and N parameters. In the Deontology and Utilitarianism classes, primary psychopathy was negatively associated with the I parameter. Moreover, primary psychopathy tended to be positively associated with the Res parameter for Deontology and Utilitarianism.

Turning to the Altruistic covariates, in most cases it was found that there were no credible relationships with the model parameters, when controlling for the other variables. Exceptions were negative associations between empathy and the averaged C parameters for Deontology, a positive association between Empathy and the Con parameter for DoubleEffect, positive associations between GreaterGood (GG) and the Con parameter as well as between Empathy and inaction bias (I) in the class of Deontology. We discuss the import of these patterns for H ₁ to H ₃ below.

2.5.1. Model comparisons

We found (Table 9) that a model that permits violations of the invariance assumption for the C and N parameter (CNIS₁₄) outperforms a version of the CNI model without this feature (CNIS₆). Moreover, models that had the conflict architecture while accounting for invariance violations outperformed both latter models.

Based on participants’ performance on the Scorekeeping Task, it was possible to identify 4 latent classes. Of these, the class of deontologists was by far the largest (N = 426, 54.1%). Participants’ latent class memberships were then incorporated into a version of the Conflict model, such that separate group-level latent parameter means were estimated for each class. This class-informed version of the Conflict model outperformed models that did not incorporate latent class information (see Table 9).

2.5.2. Construct validity of the latent classes

The group-specific latent means of the best-fitting model had parameter estimates that conformed qualitatively to the interpretation of the latent classes (see Figure 7). Thus, participants adhering to Utilitarianism in the Scorekeeping Task were among those with the highest C parameters and lowest N parameters. Conversely, participants adhering to Deontology had the highest N parameters and were among those with the lowest C parameters. Furthermore, participants adhering to the Doctrine of Double Effect had the strongest effect of the manipulation of causal structure (intended means vs. foreseeable side-effect) corresponding to the pattern N_intend > N_side and C_intend < C_side. In contrast, participants adhering to Altruism were among the ones with the lowest estimates for both the C and N parameter and neither showed a preference for Utilitarianism nor Deontology in the Scorekeeping Task (Figure 4). However, these participants stood out in judging the altruistic behavior in the greater good scenarios to be morally obligatory, and they had the highest ratings of finding the self-interested actions morally wrong across greater good scenarios (Figure 5). Moreover, they were the only participants who had a higher posterior probability of sacrificing themselves over the other choices in a self-sacrifice version of the Switch Trolley dilemma (Appendix B). Since we chose to couple the causal structure manipulation to a difference in outcome certainty (whether the sacrifice ‘will occur’ or ‘is highly likely to occur’), we will consider the alternative hypothesis whether the resulting difference in expected values could account for the latent class of DoubleEffect in the General Discussion.

2.5.3. Primary psychopathy and CNI parameters

Studies that have reported positive associations between Utilitarianism and primary psychopathy (Bartels and Pizarro, Reference Bartels and Pizarro2011; Marshall et al., Reference Marshall, Watts and Lilienfeld2018) have relied on the conventional analysis of sacrificial dilemma. Compared to the CNI scenarios, this conventional analysis only investigates the ProGreater condition, in which norm-based and consequence-based responses are directly pitted against one another. The self-sacrifice scenario (Appendix B) replicates this effect that antisocial traits like primary psychopathy and rational egoism are associated with a higher probability of sacrificing an innocent person, whereas the prosocial traits like empathy and IWAH are positively associated with sacrificing oneself. For this condition only, the latent class of Utilitarianism also had the highest posterior probability of sacrificing an innocent person. However, the predictions for this particular incongruent condition are not diagnostic for the full predictions of Utilitarianism according to the Conflict model. Indeed, Figure 8 shows that the C parameters of the Conflict model are negatively associated with primary psychopathy and moral egoism in the latent class of Utilitarianism.

In addition, it was found that for 2 of the 4 latent classes there were credible effects of a negative association between primary psychopathy and the I parameter of the Conflict model. That is, across the CNI conditions, participants within these classes who are pronounced in subclinical psychopathy show a bias to selecting ‘action’ irrespectively of whether the benefits outweigh the costs, proscriptive or prescriptive norms are being tested, or whether the sacrifice is an intended means or merely a foreseeable side-effect. Possibly, the positive associations between the Res parameter, representing conflict resolution, and primary psychopathy within the latent classes of Deontology and Utilitarianism are also to be interpreted in this light. If a conflict is detected by members of these classes, participants more pronounced in primary psychopathy tend to find it easier to resolve it.

2.5.4. Underlying moral motivations

Using this traditional approach of only contrasting Utilitarian and Deontological responses in the ProGreater condition, Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015) found positive, bivariate correlations of utilitarian responses with primary psychopathy, rational egoism, psychological egoism, and negative associations with empathy and IWAH. On this basis, Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015) conclude that acceptance of instrumental harm in sacrificial dilemma may be an expression of a calculating, selfish mindset prone to transgress conventional standards of morality (H ₃ ) rather than an impartial concern with the greater good (H ₁ ).

As a third alternative, the discussion between Kahane et al. (Reference Kahane, Everett, Earp, Farias and Savulescu2015) and Conway et al. (Reference Conway, Goldstein-Greenwood, Polacek and Greene2018a) introduces the possibility that acceptance of instrumental harm reflects a moral disposition to minimize harm in the interest of the greater good, but one that is more restricted in scope (H ₂ ). According to H ₂ , participants may be morally motivated to select the outcomes that lead to the least suffering, but will not necessarily act against their own interest to make altruistic sacrifices that promote the greater good for strangers in distant countries.

Of the 3 hypotheses, H ₂ (Restricted Concern for the Greater Good) is best supported by our results based on structural equation analysis of partial correlations with the Conflict model parameters. It was thus found that moral egoism and primary psychopathy are negatively correlated with the C and N for participants adhering to Utilitarianism (against H ₃ : antisocial motivation). Similarly, it was found that both moral and psychological egoism were negatively correlated with both the C and N parameters for participants adhering to Deontology, which made up the largest group of participants. Furthermore, while participants adhering to Altruism have the highest probability of sacrificing themselves in the self-sacrifice dilemma (Appendix B), tend to find the altruistic behavior in the greater good scenarios obligatory, and have the highest scores on the greater good items, participants adhering to Utilitarianism did not exhibit this pattern (against H ₁ ).

Finally, empathic concern was negatively correlated with the averaged C_intend and C_side Footnote ¹⁶ in the latent class of Deontology. This latter negative association could be interpreted in light of H ₃ (antisocial motivation). Yet, in view of the negative associations between the C parameters and both moral egoism and primary psychopathy, another interpretation more favorable to H ₂ (restricted concern for the greater good) presents itself. To be able to sacrifice innocent people to achieve the overall best outcomes, reduced empathy may be needed, for as Choe and Min (Reference Choe and Min2011, p. 587) point out: ‘Once people feel themselves to be in the victim’s shoes, they are not able to sacrifice an innocent person no matter how great a profit is obtained’. We may thus conclude that the C parameters of the Conflict model do not measure a reduced aversion toward taking the lives of innocent people due to psychopathic traits (Bartels and Pizarro, Reference Bartels and Pizarro2011) or egoistic tendencies. But they are still a measure of approval of instrumental harm in conditions where the benefits are greater than the costs of the sacrifice. As such, the C parameters may be decreased by emphatic concern with the victim.

3.1.1. Participants

As per our preregistration, we aimed for 500 participants in each of the 2 between-participants conditions (explained below) after applying the following exclusion criteria: not having English as native language, completing the task in more than 2 standard deviations below or above the mean completion time, failing to answer at least one of 2 simple SAT comprehension questions correctly in a warm-up phase, and answering ‘not seriously at all’ to the question ‘How seriously do you take your participation’ at the beginning of the study. A total of 1,253 people completed the experiment over the Internet on Mechanical Turk via CloudResearch. The data analysis is based on a final sample of 1,013 participants, with 498 participants randomly assigned to the Anchor 25% condition and 515 participants in the Anchor 10% condition, in accordance with our preregistration. Applying the exclusion criteria had a minimal effect on the demographic variables. Mean age was 40.8 years, ranging from 18 to 94. 33.7 % of the participants self-identified as male, 64.7% self-identified as female, 21 participants indicated that they were non-binary and 1 participant preferred not to reveal their gender. 70.4% indicated that the highest level of education that they had completed was an undergraduate degree or higher.

3.1.2. Design

The experiment has a mixed design with the 4 CNI conditions (ProGreater, ProSmaller, PreGreater, and PreSmaller) and causal structure (intended means vs. foreseeable side-effect) varied within participants. Type of skip instruction is varied (Anchor 10% vs. Anchor 25%) as a between-participants factor.

3.1.3. Materials and procedures

The same stimulus materials were used as in Experiment 1. But unlike in Experiment 1, the 2 causal structures were displayed to the participants within one experimental session. Moreover, Experiment 2 neither included the Scorekeeping Task nor the covariates.

The crossing of the 4 CNI conditions with the two causal structures gives rise to eight versions of each dilemma. To obtain three independent replications of each CNI condition within each causal structure (i.e., three different dilemma scenarios instantiating each cell), 24 trials were presented to each participant. 12 of these trials were presented in one block with intended means and 12 were presented in one block with foreseeable side-effect contents. The order of the two blocks and the order of trials within a given block was random. The pairing of scenario (from 12 possible background scenarios that each implement the eight variations) to the randomly selected variation shown on a given trial was constrained by the following conditions: (1) participants did not see a given scenario (e.g., Vaccine) paired with the same CNI condition (e.g., ProGreater) across the two causal structures; (2) participants did not see scenarios in the same order across the 2 blocks; and (3) the last scenario in Block 1 was not the same as the first scenario shown in Block 2.

For each item, participants were presented with the three response options: action, inaction, and skip. The left-right location of the action and inaction response options on the screen varied randomly from trial to trial and the location of the skip response button was fixed to the right-most position across trials (to highlight its different role from that of the action and inaction responses).

After each moral judgment, participants were asked whether they agree or disagree with the statement ‘I feel torn between action and inaction’ on a 7-point Likert scale from 1 (‘completely disagree’) to 7 (‘completely agree’), following Conway et al. (Reference Conway, Weiss, Burgmer and Mussweiler2018b).

For the Anchor 10% condition, the instruction for the skip option was as follows:

For the Anchor 25% condition the instruction for use of the skip option was as follows:

Between blocks, participants were first informed that they had reached 50% of the study and instructed that they should consider the moral scenarios of Block 2 with a fresh mind, since they may differ in important ways from the previous scenarios. The instructions concerning the skip option were then shown once more. At the end of the study, participants were asked demographic questions concerning their age, level of education, primary language, and which gender they identify with.

3.2.1. Model comparison

Next, we investigated in a model-selection contest whether the Conflict model could be simplified to the CNIS-Conflict_simp model depicted in Figure 9 (H ₈ ), in which the Res parameter, representing conflict resolution, is removed (Table 13). Based on pilot studies, we predicted that the Conflict model without this simplification would perform better in terms of the fit versus parsimony trade-off, as quantified by the WAIC and LOOIC information criteria (Vehtari et al., Reference Vehtari, Gelman and Gabry2017). Going beyond the preregistration, we also sought to test whether the CNIS-Conflict_14a outperformed the CNIS model from Skovgaard-Olsen and Klauer (Reference Skovgaard-Olsen and Klauer2024), with 14 parameters for the intended means and side-effect conditions.

Table 13 Model comparison

Note: LOOIC = leave-one-out cross-validation information criterion. WAIC = Watanabe-Akaike information criterion. ‘elpd’ = expected log predictive density is a measure of the expected out-of-sample predictive accuracy. The test statistics T₁ and T₂ represent Bayesian p values and are based on the posterior predictive model checks in Klauer (Reference Klauer2010). Imposing the same constraint on the CNIS model as for the Conflict model on the C parameters, ( ${\mathrm{C}}_{\mathrm{intend}}^{\mathrm{Pro}>}$ = ${\mathrm{C}}_{\mathrm{intend}}^{\mathrm{Pre}>}$ and ${\mathrm{C}}_{\mathrm{intend}}^{\mathrm{Pre}<}$ = ${\mathsf{C}}_{\mathrm{side}}^{\mathrm{Pre}<}$ ), also did not make the former competitive with the latter: LOOIC_{10%, CNIS12} = 10363.59, LOOIC_{25%, CNIS12} = 12811.40.

Across both conditions, the information criteria clearly preferred CNIS-Conflict_14a over CNIS-Conflict_simp and the 14-parameter and 6-parameter versions of the CNIS model. A visual illustration of the substantial improvement in predictive performance of the Conflict model compared to the CNIS models is presented in Appendix B.

4.1.1. Participants

We aimed for ca. 300 participants in each of the 2 between-participants conditions (explained below) after applying the following exclusion criteria: not having English as native language, completing the entire task in more than 2 standard deviations below or above the mean completion time, finishing individual trials in zero seconds or more than 5 standard deviations of the response time of individual trials, failing to answer at least one of 2 simple SAT comprehension questions correctly in a warm-up phase, and answering ‘not seriously at all’ to the question ‘How seriously do you take your participation’ at the beginning of the study, and not showing non-respondence by responding to feeling-torn and confidence ratings in the same way in more than 80% of all trials across conditions.

A total of 813 people completed the experiment over the Internet on Mechanical Turk via CloudResearch. The data analysis is based on a final sample of 605 participants, with 308 participants in the 3 options condition and 297 participants in the 2 options condition. Applying the exclusion criteria had a minimal effect on the demographic variables. Mean age was 43.69 years, ranging from 18 to 87.Footnote ¹⁹ 37.56% of the participants self-identified as male, 60.29% self-identified as female, 9 participants indicated that they were non-binary and 4 participant preferred not to reveal their gender. 74.47% indicated that the highest level of education that they had completed was an undergraduate degree or higher.

4.1.2. Design

The experiment has a mixed design with the CNI conditions (ProGreater, ProSmaller, PreGreater, and PreSmaller) and causal structure (intended means vs. foreseeable side-effect) varied within participants. Response format is varied (2 response options [action, inaction] vs. 3 response options [action, inaction, skip]) as a between-participants factor.

4.1.3. Materials and procedures

The experiment followed the procedure of Experiment 2 with 3 exceptions. One was that response time was recorded for each individual trial as the interval from participants’ click on a continue button (after having read the scenario), which revealed the response options, to the response. The second change was that after each scenario response, participants were asked to rate both how torn they felt and how confident they were in their response on a 7-point Likert scale on a second page in this fixed order. The third exception was that participants in the 3-responses condition were instructed that they could ‘skip’ a decision whenever they were undecided about whether the described action was morally acceptable or not, with no further guidelines about the frequency of its use.

4.2.1. Three-responses format

To analyze the data, Bayesian linear regression models were used. First, we repeated the analysis from Experiment 2 showing that skip responses were predicted by feeling-torn ratings on individual trials, ${b}_{Skip}^{FeelingTorn}$ = .51, 95% HDI [.39, .63], and higher rates of skip responses were found for incongruent trials, ${b}_{Skip}^{Incongruent}$ = 1.17, 95% HDI [.41, 1.95]. Yet, the 95% HDI for their interaction did not exclude zero.

Second, we analyzed the 3 response options to investigate how skip responses differed from action/inaction responses in terms of (log) reaction times. It was found that there was a simple effect of inaction, ${b}_{Inaction}$ = −.08, 95% HDI [−.12, −.03], which was qualified by credible interactions between the type of trial and the dilemma response, ${b}_{Inaction}^{Incongruent}$ = .14, 95% HDI [.07, .20], ${b}_{Skip}^{Incongruent}$ = .23, 95% HDI [.01, .44]. Thus, the main pattern is captured by the contrasts illustrated in Figure 11.

Figure 11 Response times.

Note: The figure shows the log reaction times as a function of the dilemma judgment and trial type. For each condition, the number of measurements within the condition is displayed.

For both inaction and skip responses, credible contrasts were found such that the response was quicker in congruent than incongruent trials, ${\overset{\sim }{\Delta }}_{Congruent- Incongruent}^{Inaction}$ = −.17, 95% HDI [−.20, −.12], ${\overset{\sim }{\Delta }}_{Congruent- Incongruent}^{Skip}$ = −.26, 95% HDI [−.47, −.05]. Overall, the skip responses in the congruent condition were the quickest but skip responses in both the congruent and incongruent conditions also had the widest 95% HDI and so credible contrasts with action and inaction responses were not found. Taken together, skip responses were more frequent and required more time in incongruent than congruent trials.

4.2.2. Conviction scale: Validating the psychological interpretation of skip responses

Next, a comparison was made between the different dilemma judgments and both feeling-torn and confidence ratings to assess whether the effects reflect differences in experienced conflict. Since feeling-torn and confidence ratings were negatively correlated (r = −.73), we treated them as complementary indicators of a single underlying conviction dimension by reverse coding the feeling-torn ratings and taking the average of these with the confidence ratings. Higher conviction values indicate greater decisional certainty.

We first analyzed the 3-response format to validate that skip responses appropriately reflect low conviction, particularly on incongruent trials in which participants experience moral conflict. Differences between response types were analyzed using ordinal regression models. One model analyzed each outcome on the conviction scale separately, and a second analyzed binned categories (FeelingTorn: conviction < 4; Neutral: conviction = 4; Confidence: conviction > 4). Since the binned categories are simpler to interpret, we focus on those here while plotting results of both models (Figure 12).

Figure 12 Conviction scale, 3-responses format.

Note: This figure shows participants’ dilemma judgments (Action, Inaction, Skip) as a function of their conviction levels, separately for congruent and incongruent trials. Conviction was measured by combining feeling-torn and confidence ratings into a single scale: since these measures were negatively correlated (r = −.73), we reverse-coded feeling-torn ratings and averaged them with confidence ratings to create a unified conviction measure. The visualization displays both: (a) the probability distribution of specific conviction values for each judgment type (shown as colored histograms with the height representing probability), and (b) aggregated probabilities for 3 conviction categories (shown as dots with error bars representing 95% Bayesian credible intervals): FeelingTorn (conviction < 4), Neutral (conviction = 4), and Confidence (conviction > 4). Higher conviction values indicate greater certainty in one’s judgment.

For the binned conviction outcomes, simple effects of skip relative to action, ${b}_{Skip}$ = −3.07, 95% HDI [−3.67, −2.46] and trial type, ${b}_{Incongruent}$ = −2.54, 95% HDI [−2.75, −2.34], were found which were qualified by credible interactions between the type of trial and the dilemma response, ${b}_{Inaction}^{Incongruent}$ = .35, 95% HDI [.08, .61], ${b}_{Skip}^{Incongruent}$ = 1.26, 95% HDI [.59, 1.92]. Figure 12 illustrates these interactions.

To further investigate how conviction differed across response types, we examined posterior contrasts comparing the relative strength of confidence and feeling torn within each condition. In incongruent trials, credible contrasts were found such that there was a higher posterior probability that participants’ confidence outweighed how torn they felt than vice versa when selecting action or inaction, ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Incongruent, Action}$ = .12, 95% HDI [.03, .22], ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Incongruent, Inaction}$ = .27, 95% HDI [.18, .36]. In contrast, when selecting skip responses, there was a higher posterior probability that participants felt more torn than confident than vice versa, ${\overset{\sim }{\Delta }}_{FeelingTorn- Confidence}^{Incongruent, Skip}$ = .63, 95% HDI [.52, .73]. For congruent trials, credible contrasts were found such that there was a higher posterior probability that participants’ confidence outweighed how torn they felt than vice versa when selecting action or inaction, ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Congruent, Action}$ = .88, 95% HDI [.85, .90], ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Congruent, Inaction}$ = .87, 95% HDI [.84, .90]. In contrast, no credible differences were found in posterior probabilities for differences in relative strength of confidence and feeling-torn for skip responses with congruent trials. Taken together, skip responses were not only more frequent and slower in incongruent trials but also reflected a substantially lower confidence and stronger experienced conflict. This confirms that the skip option works as intended: as a low-conviction response that participants select when experiencing moral conflict.

4.2.3. Effects of response formats on conviction for action and inaction judgments

Having ensured that our conviction measure worked as expected in the 3-responses format, we next probed whether the skip option affected the conviction levels associated with definitive action or inaction judgments. To address this question, we compared conviction levels between the 2-responses format (where participants could only choose action or inaction) and the 3-responses format (where skip was also available) for just action or inaction responses. This allows a direct comparison of how the presence versus absence of a skip option affects action and inaction judgments. Credible differences were not found for reaction times. Since feeling-torn and confidence ratings were negatively correlated (r = −.71), a conviction scale was again created as above. On this scale, differences between the 2- and 3-responses formats were analyzed using an ordinal regression model (Figure 13).

Figure 13 Conviction. Response options.

Note: This figure compares Action and Inaction judgments as a function of conviction levels across 2 types of response formats: a 2-responses format (left panels: Action vs. Inaction only) and a 3-responses format (right panels: Action, Inaction, or Skip). Only Action and Inaction responses are shown to directly compare the formats. Conviction was measured by reverse-coding feeling-torn ratings and averaging them with confidence ratings (r = −.71). The visualization shows: (a) probability distributions of specific conviction values for each judgment type (colored histograms) and (b) aggregated probabilities for 3 conviction categories (dots with 95% Bayesian credible intervals): FeelingTorn (conviction < 4), Neutral (conviction = 4), and Confidence (conviction > 4).

For incongruent items, differences between the 2- and 3-responses formats emerge in that (1) for action selections, there is no credible difference in the posterior probabilities of the binned feeling-torn and confidence categories for the 2-responses format, ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Incongruent, Two}$ = .001, 95% HDI [−.09, .09], whereas a credible difference was found for the 3-responses format, ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Incongruent, Three}$ = .12, 95% HDI [.03, .22], (2) for inaction selections, a credible difference was found for both the 2- and 3-responses formats, but the difference was larger for 3 response options, ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Incongruent, Two}$ = .17, 95% HDI [.08, .26], ${\overset{\sim }{\Delta }}_{Confidence- FeelingTorn}^{Incongruent, Three}$ = .27, 95% HDI [.18, .37]. Taken together, the presence of the skip option led to increased decisional certainty in action and inaction responses relative to the 2-responses format.

4.2.4. Comparing the CNI model with the Conflict model

The Conflict model differs from the CNI model in representing the latent processes giving rise to the dilemma responses in congruent and incongruent items as qualitatively different. On the former octopus model, 8 latent processes are activated when participants are presented with incongruent items. Figure 14 illustrates the structural differences between these models using path diagrams. In these diagrams, each ‘path’ represents a latent cognitive process that can generate the observed response. The numbered arrows indicate the probability that each path is activated based on median model estimates.

Figure 14 Probability of path activations based on median MPT estimates.

Note: The figure compares the cognitive process paths of 2 models for moral dilemma judgments. The CNI model (top) assumes the same 4 processes operate for all trials. The Conflict model (bottom) assumes different processes for congruent trials (where norms and consequences align) versus incongruent trials (where they conflict). Each node labels a path in the model. A ‘path’ refers to a latent process that outputs the observed response following stimulus presentation; internally, this process may be determined by a sequence of steps. In this figure, each path is represented by a single arrow from a latent-process node to the response node, with numbers indicating the probability that this path is activated. Probabilities are calculated based on the median estimates of the model parameters of the CNI model (top row) and the Conflict model (second row), aggregating over both the intended means and side-effect conditions. ‘I’ = activation of the inaction-bias path. ‘A’ = activation of the action-bias path. ‘NRes’ = activation of the path of resolving a detected conflict in a norm-based way. ‘CRes’ = activation of the path of resolving a detected conflict in the consequence-based way. ‘SRes’ = activation of the path of skipping a detected conflict.

The CNI model (Figure 14, top) proposes that all dilemma judgments result from activations of the consequence-based response, the norm-based response, or a response bias toward action or inaction. The Conflict model (Figure 14, bottom) proposes that incongruent items (where norms and consequences conflict) activate additional conflict-resolution processes not present in congruent items: (a) C_Res: Resolving conflict by prioritizing consequences, (b) N_Res: Resolving conflict by prioritizing norms, (c) S_Res: Resolving conflict by skipping.

To compare the 2- and 3-responses formats, the proportion of C/N activation, conditional on action/inaction responses was computed. The complement of this proportion is the activation of the A or I path representing response biases, and so the proportion of C/N activation indicates the percentage of morally interpretable action/inaction responses.

It was found that there was a credible difference, such that a higher proportion of CN-activation was found for the Conflict model ( $\overset{\sim }{x}=.70$ ) than the CNI model ( $\overset{\sim }{x} = .62$ ), ${\overset{\sim }{\;\Delta }}_{CNI- CNISC}^{C/N\; activation}$ = −.08, 95% HDI [−.13, −.03]. That is, fewer action/inaction responses were attributed to response biases based on the Conflict model than the CNI model.

Since the CNI and Conflict models were fitted to different parts of the data (the 2- vs. the 3-responses format), they cannot be directly compared on information criteria like WAIC or LOOIC. Instead, their ability to fit their respective data sets can be compared by the T₁ and T₂ posterior model checks proposed in Klauer (Reference Klauer2010). T₁ measures whether the models succeed in capturing the mean observed frequencies of dilemma judgments. T₂ measures whether the models capture the variability (variances and covariances) among the observed response frequencies. A small (Bayesian) p value for each indicates that the model fails to capture an aspect of the data, because this aspect of the actual observations is unlikely to be predicted by the model. It was found that p_T1 = p_T2 = 0 for the CNI model fitted to the 2-responses format and that p_T1 = .52 and p_T2 = .02 for the Conflict model fitted to the 3-responses format. Figure 15 illustrates the posterior predictive performance of each model.

Figure 15 Posterior predictive performance of the 2 models.

Note: Observed response frequencies (blue bars) and posterior predictive frequencies (red points) for 2 models: CNI₅ (left) and CNIS-Conflict_14a (right). Columns correspond to the 4 CNI scenarios: Pre $<$ , Pre $>$ , Pro $>$ , Pro $<$ , where $>$ indicates that the benefit of the sacrifice is greater than the costs. Columns within panels show response type (action, inaction, skip), and panels are split by causal structure (Intended means vs. Foreseeable side-effect).

As Figure 15 shows, the Conflict model is better able to fit the 3-responses format than the CNI model is able to fit the 2-responses format. In this comparison, the CNI model was evaluated under favorable conditions: it was tested in its original 2-responses format and allowed to estimate separate C and N parameters for the intended-means and foreseeable side-effect cases. Nevertheless, the invariance assumption that fixes C and N across the 4 CNI conditions (ProGreater, ProSmaller, PreGreater, PreSmaller) still produces substantial misfits in the mean action and inaction response frequencies, indicating that one source of its problems lies in this invariance constraint.

5.5.1. Expected value vs. causal structure

Often the intended means versus foreseeable side-effect distinction is manipulated in terms of indirect harm versus direct use of personal force (Greene et al., Reference Greene, Sommerville, Nystrom, Darley and Cohen2001). In this case, the effects of instrumentality and personal force cannot be analyzed separately (Fahrenwaldt et al., Reference Fahrenwaldt, Olsen, Rahal and Fiedler2025). We manipulated the distinction differently such that the direct form of harm does not take the form of direct use of personal force. However, because our manipulation coupled causal structure and outcome certainty (whether the sacrifice ‘will occur’ or ‘is highly likely to occur’), an alternative hypothesis merits consideration. Perhaps the latent class of DoubleEffect is positioned between Deontology and Utilitarianism due to differences in expected values rather than causal structure.

Research on verbal probability expressions (Renooij and Witteman, Reference Renooji and Witteman1999; see their Figure 1) indicates that ‘highly likely’ corresponds to approximately 90–95% probability. Under this interpretation, the expected values would be: intended means EV = +4, foreseeable side-effect EV = +4.05 to +4.10, doing nothing EV = −5. For participants solely focused on maximizing expected values, the small difference of 0.05–0.10 between the intended means and foreseeable side-effect conditions would not justify different moral judgments. The Utilitarian latent class accepts the sacrifice in both conditions, and the Deontology latent class rejects it in both conditions; neither pattern is explained by this small, expected value difference. These 2 classes already make up most of our participants. Could it then be that the behavior of the smaller DoubleEffect class (who switch their judgments between conditions) is accounted for by this expected value difference? If so, we would have to assume that the large difference in expected values in the intended means condition between accepting the sacrifice (+4) and doing nothing (−5) is insufficient to motivate acceptance but that adding 0.05–0.10 crosses a critical threshold in the side-effects condition. Such a non-linear response to expected values would be surprising.

We find it more plausible that deontological considerations relating to the difference in causal structure and concerns about agent responsibility account for this pattern. In the intended means condition, a deontological prohibition against using the death of the victim instrumentally to achieve a goal discourages the sacrifice. In the side-effects condition, attention is drawn to the fact that there are causal factors affecting the victim’s fate outside the agent’s control which reduce their responsibility. We manipulated the 2 dimensions of causal structure and outcome certainty together because classic intended means cases (active euthanasia, terror bombing) involve certain harm, while classic side-effect cases (passive euthanasia, tactical bombing with collateral damage) involve probable but uncertain harm. The conceptual coupling between causal structure and outcome uncertainty is reflected in how the Doctrine of Double Effect is applied in philosophical discussions and real-world moral dilemmas. We conjecture that it is this conceptual coupling rather than small differences in expected values that drives the responses of the DoubleEffect latent class. But future research could examine the expected value hypothesis by systematically varying the ratio of lives saved and sacrificed and their probabilities to determine the importance of this factor.