Belief Miner: A Methodology for Discovering Causal Beliefs and Causal Illusions from General Populations

Having formed a null contingency about a certain phenomenon can lead people to discount a true causal relationship of a scientifically acknowledged cause for the same outcome. As Matute et al. (Matute et al., 2015) write: “The availability of more than one potential cause can result in a competition between both causes so that if one is considered to be a strong candidate, the other will be seen as a weak one.” This was verified via several experiments where it was found that participants who had established a prior belief about the effectiveness of an unproven bogus medicine – a causal illusion – weakened the belief in the effectiveness of a proven medicine. In contrast, participants who did not have a chance to develop the illusion had sustained trust in the proven medicine (Vadillo et al., 2013).

Experiments have shown that the strength of a causal illusion can be effectively controlled by the frequency at which the cause is present, even when its effectiveness to drive the outcome remains the same. This has important implications on a person’s belief in a proven medicine. The more frequently the competing (alternative) medicine has been administered and a confirmatory (yet specious) outcome has been experienced, either now or in the past, the smaller the belief in the proven medicine (Yarritu et al., 2015).

An effective way to convince people that they have fallen victim to the null contingency is to ask them not to take the treatment when they hope for an outcome to occur (Blanco et al., 2012). But this proves difficult when the cost of the treatment is low and the outcome is ubiquitous and persuasive. In fact, the ubiquity of both treatment and outcome are perfect conditions for a causal illusion to emerge (Vadillo et al., 2011; Yarritu et al., 2014). It fosters trust in the belief that there must be a causal relationship between the two since there are many opportunities for coincidences (Blanco et al., 2013).

While the examples given so far are relatively benign, there are more serious scenarios where these cognitive mechanisms can be harmful (Freckelton, 2012). A person with a natural medicine mindset, when receiving, say, a cancer diagnosis might resort to acupuncture, herbal treatments, fruit juice therapy, and spiritual consultations instead of seeking more conventional evidence-based interventions, such as surgery or radiation, and chemotherapy. This is what has been reported to have happened to Steve Jobs, the founder of Apple Computer and an exceptionally tech-savvy and forward-thinking individual (Cartwright, 2011). It vividly shows that gaining immunity from null contingencies is hard.

Causal illusion has been of interest to researchers for a long time. It can reveal many cognitive and behavioral practices, as described in Section 2.1. To study different research questions, researchers typically tweak the trial matrices (Table 2) to create desired scenarios and then conduct control experiments based on that.

These experiments typically involve hypothetical scenarios set in the medical domain. Participants are asked to impersonate doctors who are assigned a set of fictitious computer-modeled patients (i.e., the total number of trials). In some scenarios, the participants take on an active role in prescribing medical treatments for some illnesses, while in others they simply observe the patients follow a certain treatment regime. As the experiment proceeds, participants see records of patients who either have or have not taken a certain medicine and then have or have not recovered from the disease (based on the trial matrices). At the end of the experiment, the participants are asked whether the treatment was effective or not (for example see (Matute et al., 2015)).

The experiments are meticulously designed to expose the triggers and impacts of causal illusions. They are highly controlled laboratory studies and focus on very simple and elementary causal relationships. Our crowd-based belief miner takes these studies out of the research laboratory into the wild where an abundance of data awaits, reflecting complex causal chains with many links and paths. There are also many unexpected cause and outcome variables that might be discovered when the crowd-sourced data are studied in depth. It is a tool by which complex cognitive conflicts can be efficiently extracted and exposed for real-life phenomena of possibly high complexity. While this approach cannot directly replicate the usage of trial matrices shown in Table 2, it can produce the conclusions that are typically derived from the experiments that use trial matrices. Furthermore, it is easy to set up for practitioners.

Another interesting aspect of our methodology is that it asks participants to engage in a critical assessment of their beliefs, by ways of reviewing the small causal network they construct. As we have already hinted at in the introduction, we found evidence of the implications of a theory proposed by Walsh and Sloman (Walsh and Sloman, 2004), who experimented with the concept of contradiction as a way to get people to revise their beliefs in a causal illusion. They suggest that a person might reduce their belief in the effectiveness of a certain treatment upon discovering that some elements of it have an outcome that is opposite of what they expected.

Bigham et al. (Bigham et al., 2015) identified three broad areas for collective intelligence and HCI. They are 1) directed crowdsourcing, where a single person or a group guides a large set of people to accomplish a task (e.g., labeling a large dataset (Kairam and Heer, 2016; Chang et al., 2017), CommunityCrit (Mahyar et al., 2018)); 2) collaborative crowdsourcing, where a group of people works together to accomplish a task (e.g., Wikipedia, Project Sidewalk (Saha et al., 2019), ConceptScape (Liu et al., 2018)); and 3) finally, passive crowdsourcing, where people do not coordinate and are not consciously aware of participating in a crowdsourced system, however, one can still mine their behavior to infer collective intelligence (e.g., mining search history).

In this paper, we mainly focus on directed crowdsourcing (referred to as crowdsourcing from here on) since we provided explicit direction to our crowd workers. In a crowdsourcing experiment, a crowd worker typically completes a small part of the overall task (i.e., micro-tasks) (Chung et al., 2019; Kittur et al., 2008, 2011). These micro-tasks are eventually aggregated for inferring collective intelligence. In our case, a micro-task refers to creating a causal network between a small number of attributes.

Over the years, several methods and tools have been proposed for measuring and increasing the efficacy of the design of the micro-tasks based crowdsourcing (Kittur et al., 2013, 2012; Rzeszotarski and Kittur, 2012; Bernstein et al., 2010; Kittur et al., 2011; Noronha et al., 2011). Of particular interest is Quality Control in crowdsourcing (Kittur et al., 2013), which ensures the validity of the collected response from crowd workers. This is important since crowd workers tend to spend minimum effort and sometimes try to game the systems (Kittur et al., 2013). The currently established methods for quality controls typically fall into two broad categories: task design and post-hoc analysis (Kittur et al., 2013). Examples for task design include fault-tolerant subtasks (Bernstein et al., 2010; Kittur et al., 2011; Noronha et al., 2011; Krishna et al., 2016), attention check (Agley et al., 2022), peer review filters (Dow et al., 2012; Kittur et al., 2011; Bernstein et al., 2010; Horton and Chilton, 2010), intelligent task assignment (Kim et al., 2018) and optimizing instructions (Kittur et al., 2008; Downs et al., 2010; Lasecki et al., 2015; Qiu et al., 2020). Examples for post-hoc analysis include comparison with gold standards (Downs et al., 2010; Callison-Burch, 2009; Berenberg and Bagrow, 2018), validation study (Saha et al., 2019), agreement between crowd workers (Callison-Burch, 2009; Ipeirotis et al., 2010), and behavior analysis (Rzeszotarski and Kittur, 2012; Robert and Romero, 2015; Gadiraju et al., 2015; Chiang et al., 2021; Yin et al., 2018).

Our work can be seen as a post-hoc analysis model for causal crowdsourcing. We use causal relations collected from experts (i.e., gold standards), a popular post-hoc method, to find illusions in the crowd-generated causal networks. Although relevant work in causal crowdsourcing (Berenberg and Bagrow, 2018) employed comparison with gold standards on a smaller scale, our work both scales up the approach and adds a nuanced dimension to the post-hoc analysis model tailored for causal crowdsourcing. This makes our contribution one of the first to delve into such depth and granularity in this domain. Finally, we believe our findings will guide future task designs for causal crowdsourcing. Appropriate task designs can make people self-aware and help them avoid falling victim to causal illusions. We lay down this future direction in our discussion (Section 11).

While causality is a core concept across several scientific domains, designing crowdsourced experiments for collecting causal relations is a relatively new research area. Caselli et al. contributed to this area by focusing on annotating causal relations in narrative texts, specifically news data, through crowdsourcing experiments (Caselli and Inel, 2018). Their work analyzed parameters affecting annotation quality and compared crowdsourced and expert annotations, emphasizing the generation of structured data based on narrative strategies. The most relevant work in this space, however, is Iterative Pathway Refinement (Berenberg and Bagrow, 2018), a network search strategy where workers modify a short linear pathway between attributes. The authors showed that their method is more efficient than a single line-based micro task, provides better contexts to crowd workers, and the union of the pathways can create a large network. Yen et al. (Yen et al., 2021) extended this line of work by proposing CausalIDEA, an interactive interface where users can create small networks as well as provide textual explanations for creating specific causal relations. The causal diagrams and textual narratives add a new dimension to understanding causal beliefs. The authors investigated how a user’s causal perception is affected by seeing the causal networks created by others. Furthermore, Yen et al. introduced CrowdIDEA (Yen et al., 2023), a tool that integrates crowd intelligence and data analytics to support causal reasoning, featuring a three-panel setup: enabling access to crowd’s causal beliefs, data analytics, and the ability to draw causal diagrams. Their study also demonstrated that seeing the crowd’s causal beliefs significantly improved the accuracy of causal relationships in the final diagrams of the participants and reduced reliance on data analytics, showcasing the tool’s potential to enhance causal reasoning processes.

These prior works provide evidence that people can identify causal relations between pairs of events and collaboratively create causal networks that are information-rich. While inspiring, they consider causal crowdsourcing from an algorithmic or data science perspective, focusing either on creating large networks or training datasets for Causal ML (Kusner et al., 2017). In contrast, we consider causal crowdsourcing as a tool to surface how causal illusions persist in a domain, which prior works have largely overlooked (Berenberg and Bagrow, 2018; Yen et al., 2021).

While we do not focus on data science or machine learning, our work has implications for Causal ML. For example, failing to detect causal illusions and erroneous causal relations can introduce biases into datasets, leading to skewed decision-making based on inferred causal relations (Wang and Mueller, 2015; Hoque and Mueller, 2022; Ghai and Mueller, 2023). Broader ML literature has also demonstrated that ML models trained with datasets containing spurious relations or errors may perform poorly and yield incorrect inferences  (Yapo and Weiss, 2018; Rastogi et al., 2022; Panch et al., 2019; Kusner et al., 2017).

In summary, the absence of mechanisms to detect causal illusions is a significant obstacle to the practical application of causal crowdsourcing in different domains, including social science and policy-making (domain of this work), causal ML, finances, and health. We aim to bridge this gap.

We offer two angles of evaluation or analysis of the collected causal belief data: 1) an aggregated quantitative and qualitative overview of the causal beliefs; and 2) causal illusion detection. The metrics required are defined below:

In this section, we provide the initial design goals for the interface. Some part of the interface loosely follows the methodology proposed in prior works (Berenberg and Bagrow, 2018; Yen et al., 2021): people create small causal networks to demonstrate their beliefs, and then the small networks are aggregated into a large causal network. However, we non-trivially enhanced the methodology to meet the following design goals:

Before collecting causal beliefs, the set of single/multi-word attributes relevant to the domain must be identified. Experiments with techniques purposed to automatically extract attributes specific to “climate change” (our demonstration domain) from relevant text documents were only mildly successful. To identify the relevant attributes for our domain (climate change), we manually extracted them from reputable climate-related sources ¹¹1 https://www.climaterealityproject.org/blog/key-terms-you-need-understand-climate-change https://www.climaterealityproject.org/blog/10-indicators-that-show-climate-change https://opr.ca.gov/facts/common-denier-arguments.html. We also determined specific words to represent upward and downward trends, ensuring natural comprehension, such as “fewer (human activities)”, “less (methane)”, and “decreasing (solar radiation)”. This process yielded a table of 17 attributes with trend terms (34 attributes in total, combining trends with attributes). We then validated these attributes via an informal discussion session with three climate science experts from our university. All experts hold PhDs in relevant fields and have been conducting climate science research for at least ten years. All agreed that the attributes are of importance to any climate science expert, and understanding people’s perceptions about them is crucial.

In addition to extracting the attributes, we also use Word2Vec (Mikolov et al., 2013), a neural word embedding model trained on the English Wikipedia corpus containing many climate-related documents, to compute attribute coordinates based on semantic distances. We used these coordinates to lay out the variables in the 2D space of the initial interface (Section 5.3). The Word Mover Distance (WMD) was employed for multi-word attributes, calculating the minimum distance words need to travel between documents. We also explored other text embedding models, including BERT (Devlin et al., 2018), RoBERTa (Liu et al., 2019), and GloVe (Pennington et al., 2014). After a discussion with the research team, we found Word2Vec’s embeddings to be the most suitable option.

We note that we did not utilize the Word2Vec coordinates in our final and redesigned interface because we adopted a different layout approach (Section 8.1).

The collection interface is a web-based interface implemented using Python as the back-end language and D3 for visualization (Bostock et al., 2011). We used MongoDB as a database for our collected results. The input to the interface is a dataset containing nodes of a causal network ($V$) where the edge list ($E$) is unknown. Thus, this interface is our tool to infer $E$ from the crowd. The detail of the input dataset is provided in Section 5.2. We describe the visual component of the several interface modules in the following sections. The modules are independent and can be implemented according to the intended sequential workflow. Snapshots of each module are provided as supplemental material. We further describe our workflow specific to the experimental setup later in Section 6.

We assigned credibility scores to the causal links based on the methodology proposed in Section 4. Five experts, including two authors of this paper, participated in this stage. The other three experts are climate science experts from our university. They hold PhDs in relevant fields and have been conducting climate science research for at least ten years. Experts independently created their version of the causal networks using the 34 attributes. We provided them with climate change-related literature that is publicly accessible and is more likely to be used by the general population ²²2 https://climate.nasa.gov/
https://www.epa.gov/
https://www.noaa.gov/
https://www.climatecentral.org/ . Figure 3 shows the causal networks created by the experts. The ground truth establishment procedure yielded a dataset of all possible causal links and their credibility scores.Based on our proposed evaluation metrics in Section 4, we conduct an extensive analysis of the causal belief data collected during the experiment. The results are presented next.

For the outcome variable “increasing temperature” (synonymous with “more intense heat waves” in climate science (Organization, [n. d.])), we identified two competing causes: the simple bogus cause “increasing solar radiation” and the true cause “more fossil fuel burning.” The trial matrices for both outcome variables, as shown in Table 3, can be constructed following a similar approach as in Table 2.

The left trial matrix represents the classic bogus cause of “increasing solar radiation.” We have added the parentheses to the former since this is a truly imaginary cause as the solar radiation is not really increasing. It indicates that regardless of whether solar radiation increases or not, there will be more intense heat waves. The second column for the opposite outcome, “less intense heat waves,” is set to false for both conditions since this outcome is not observed in real life or simulations. The trial matrix on the right represents the true cause of “more fossil fuel burning.” It is scientifically established that “more fossil fuel burning” causes “more intense heat waves,” while “less fossil fuel burning” eliminates the outcome. The second column, “less intense heat waves,” reflects the inverse relationship, as expected in a genuine causal relationship.

It is important to note that our crowd-sourced tool does not provide values for each cell in these trial matrices. Our focus is not on conducting formal experiments with complete matrices, but rather on designing experiments to assess the degree of causal illusion in a general population. We compare the magnitudes of the upper left cells in the trial matrices for the bogus and true causes to gauge the level of causal illusion. Most principled work on causal illusions also largely focuses on these types of results. Additionally, we identify critical links in the causal chain and assess potential knowledge gaps, which are discussed in Section 7.4.2.

The low ANC scores in Section 7.2 indicate a lack of credibility among the crowd-created networks. We explore this further by analyzing the concept of Causal Illusion.

The redesigned interface utilized a similar web-based technology as our initial interface. We excluded the attribute “renewable energy” from our input dataset, as it had a low number of votes in the formative study. The interface also has modules similar to the initial interface. We describe major changes to the modules below.

In the final study, in contrast to the formative study, we implemented a rigorous quality control process to ensure data integrity. First, we noticed from the formative study that while we designed the crediblilty score to measure causal beliefs and illusions, it can also be used to filter out potential fraudulent or random causal relations. For example, an excessive number (3 or more out of 5) of non-credible links (credibility score = 0) could indicate randomly created relations or fraudulent behaviors. We flagged such relations and crowd workers in the final study. Then, the research team manually reviewed each case. During the review, we examined patterns of inconsistencies, repeated responses, and indications of random or careless selection. Based on the manual review, we identified and excluded workers who produced unreliable or fraudulent data. We provide two examples of such data in Figure 9-A and B. Note that the lack of credibility (a score of 0) does not necessarily mean fraudulent behavior. We accepted submission as long as the overall network exhibited a pattern of understanding and relevance, even if some links had a credibility score of 0 (Figure 9-C). We interpreted these results as beliefs stemming from potentially flawed understanding, which are of potential interest to us, and accepted the results. Thus, the combined networks had links with credibility scores spanning from 0 to 3.

We conducted the study in phases, 10 participants at a time, allowing us to calculate node exploration in the aggregated network and perform quality control at each phase. All 31 workers whose results were rejected due to incomplete or fraudulent data were from AMT. Thus, we decided to conduct the rest of the study on Prolific, as it is known for its more stringent participant vetting process and higher-quality data. We ensured all participants finished the study exactly once. Therefore, every participant from AMT and Prolific constructed their own network from the ground up without building upon one another’s work. This led us to have 101 valid workers. We present various aspects of the crowd workers’ demographics in Figure 10. Geographically, we only collected results from the United States.

We employed the “Six Americas Super Short SurveY (SASSY)” Group Scoring Tool to segment our participants into different groups based on their responses to climate change (Chryst et al., [n. d.]). We present the results in Figure 11. The majority of workers (36) were “Alarmed” and expressed high concern about climate change. There were also significant numbers of workers in the “Dismissive” group (25) who held dismissive or denying attitudes. Other categories included “Concerned” (11), “Cautious” (10), “Doubtful” (16), and “Disengaged” (3). The group scoring tool also allowed us to compare the groups to national averages (Figure 11). Compared to national averages from December 2022, we observed some variations in the distribution of attitudes toward climate change. Nevertheless, all groups were present in our participant pool, reflecting a range of perspectives and attitudes toward climate change.

We conducted the study in phases (10 participants at a time). After each phase, we analyzed the combined network created by the crowd and compared it with the previous phases. We also checked how many nodes/attributes have been explored in the combined network. We stopped the study once the network was saturated, displaying minimal changes from previous phases. We present the final node exploration status in Appendix B.2. Additionally, we considered the representation of the participants in terms of the SASSY groups. We wanted representatives from each group.

Similar to the formative study, we mention the most noteworthy aspect of the most popular causal links below.

• •

  Similar to the formative study, the most voted causal relations in the final study reflected widely acknowledged scientific facts. The top relation (24 votes, average confidence (AC) = 3.5, credibility score (CS) = 3) was “increasing temperature $\rightarrow$ melting sea ice”. Other top relations attributed the “more trapped heat” to “increasing CO2” (21 votes, 3.5 AC, 3 CS) and “increasing temperature” to “more trapped heat (18 votes, 3.3 AC, 3 CS).

• •

  There was evidence of recognizing underlying factors of climate change, such as linking “more human activities” to “decreasing forests” (6 votes, 3.7 AC, 2 CS) and “increasing CO2” (4 votes, 3.5 AC, 2 CS) and considering “increasing CO2” as an effect of “decreasing forests” (10 votes, 3.7 AC, 3 CS) and “increasing emissions” (8 votes, 3.5 AC, 3.5 CS) (Forests, 2022; Climate.gov, [n. d.]).

• •

  There was also evidence of physical understanding; many marked that “increasing wildfire” leads to “decreasing forests” (16 votes, 3.5 AC, 3 CS) and “increasing emissions” (6 votes, 3.7 AC, 3 CS) and “increasing CO2” (6 votes, 3.5 AC, 2 CS), and, in turn, “increasing wildfires” is caused by “increasing temperature” (12 votes, 3.2 AC, 2 CS) and “more intense heatwaves” (7 votes, 4.14, 2 CS).

• •

  Among the causal links that received at least 10 votes, all were highly credible links (CS=3) except for 2 links: “increasing temperature” $\rightarrow$ “increasing wildfires” and “more trapped heat” $\rightarrow$ “melting sea ice” (CS=2). Interestingly, these links also received the lowest AC scores (3.2 and 2.8, respectively) compared to others, exhibiting a parallel trend to the formative study findings. While these links are partially correct, they lack crucial mediators. It is important to acknowledge that wildfires are primarily caused by dry weather resulting from drought, which is a consequence of rising temperatures. Similarly, the consistent trapping of heat contributes to increasing temperatures, which leads to the melting of sea ice (Drought.gov, 2022; Life, [n. d.]).

In Figure 14 we present the Discrepancy Network along with various levels of discrepancies. Similar to the formative study, the ratio of misinformed links consistently stays higher (47 out of 92 visible links). In contrast to the formative study, the results of the current study reveal a multitude of cases where the crowd demonstrated a significant degree of obliviousness, with 26 out of 92 visible links exhibiting this phenomenon. We present the statistics of various values of different discrepancy/illusion scores in Table 5.

In Figure 15, we present some noticeable cases within the discrepancy network. The crowd selected increasing solar radiation as a cause for more intense heatwaves, this misconception is consistent among the participants of both studies (Figure 15-A). The crowd also seemed to think that expanding forest causes increasing wildfires (Figure 15-B), whereas, the relationship between expanding forests and increased wildfires is more nuanced. Factors such as climate conditions, human activities, and forest management practices play significant roles in determining wildfire risk (Nps.gov, 2022; Drought.gov, 2022).

Several intriguing instances of obliviousness were observed within the crowd as depicted in Figure 15-X, Y, Z. Notably, the crowd exhibited a preference for attributing emissions to increasing wildfires, which is indeed a valid relationship. However, there was a comparative disregard for the influence of fossil fuel burning and coal burning on emissions. Additionally, a certain level of unawareness was evident regarding the interplay between variables such as drought, precipitation, and temperature-related factors like trapped heat and heatwaves. This highlights the need to prioritize the dissemination of accurate information concerning the impact of rising temperatures on drought conditions.

Figure 17 presents crowd workers’ agreement on the usability and learning statements. The results reflect an overall positive outlook toward the usability of our system. For the knowledge-related statements, the majority of workers felt neutral to positive towards the statement “I became more aware of the relationships that govern climate change” and disagreed with the statement “My views on climate change have been altered”. We think this happened because they might not have felt comfortable agreeing to such a strong statement.

The two studies show that Belief Miner is data-driven and agnostic to the method used to collect the data. Regardless of the collection mechanism, Belief Miner can extract causal illusions given a set of causal networks collected from the crowd and ground truth collected from experts. Thus, we were able to apply the same method in both studies, even though the underlying protocol and interfaces were different.

We found a wide range of causal beliefs and illusions in the studies. Some findings from the studies align while others do not. For example, in both studies, participants with causal illusions assigned lower confidence scores to their networks. However, we could not replicate some results from the formative study in the final study. For example, we did not find the causal illusion reported in Figure 7 from the formative study in the final study. Several factors could contribute to this phenomenon: the redesigned interface, the participants’ pool, or the changes in the general knowledge about climate change within the timeframe of the studies (Fall 2021 to Spring 2023).