How (Ir)rational Is it to Believe in Contradictory Conspiracy Theories?

There is evidence that not only believing in one conspiracy theory (CT) makes a person more probable to believe in others, however unrelated their content is, but that people can even believe in contradictory CTs about a single event. After piloting locally relevant conspiracy theories on a convenient Serbian speaking sample (N = 152), we sought to replicate this finding on a larger sample (N = 252), but introduced several changes. We differentiated necessarily and probably mutually exclusive CTs, and interviewed the participants who answered contradictory to understand the reasoning behind it. The participants were more prone to endorse probably than necessarily exclusive items (we registered positive correlations in former and no correlation or negative correlation in later). Two strategies enabled them to overcome the contradiction: (a) distilling the crucial content and downplaying other information and (b) treating the contradictory scenarios as possible versions of events. Taken together, these results indicate that participants are not as irrational as sometimes portrayed.

The aim of the present study was (a) to explore if endorsement of different CTs is positively correlated and correlated to conspiracy mentality (b) to specifically analyze the correlation between contradictory CTs, and compare the ones necessarily exclusive and probably exclusive, (c) to register and categorize the cognitive strategies respondents use when endorsing contradictory statements.
We expected that endorsement of different specific CTs would correlate positively (H1) and that it would be correlated with general proneness to conspiratorial thinking (H2). Furthermore, we expected that endorsement of contradictory CTs would correlate positively (H3), although the participants would be more prone to simultaneously endorse pairs of probably exclusive than pairs of necessarily exclusive CTs (H4).

Method Participants and Procedure
To pre-select familiar CTs, we conducted an online pilot survey (number of participants N = 152, 65 males) with 32 items containing potentially widespread CTs. We constructed the scale drawing from previous published international works (Goertzel, 1994;Swami et al., 2010;Brotherton et al., 2013;Dagnall, Drinkwater, Parker, Denovan, & Parton, 2015), and scarce regional ones (Blanuša, 2009(Blanuša, , 2011, as well from the traditional media, social networks, forums and blogs. For the final version, we selected items with the average familiarity of at least three on a five-point scale. After the pilot study that allowed us to construct a culturally sensitive instrument for assessing belief in CTs, we conducted the main study on a different sample. The participants were 252 high school and university students (82 males, M Age = 19.77, SD = 1.58). We chose this particular age group (late adolescents and emerging adults), as they are still in process of forming a coherent worldview, so we reasoned they might be more prone to endorsing contradictory narratives. They completed a pen and pencil survey under a self-generated code name.
Upon analyzing the data, we formed a subsample of participants who endorsed contradictory CTs by answering with either 3 -Agree or 4 -Strongly agree on a four-point Likert scale (N = 122). Out of those, we randomly polled 26 participants and conducted semi-structured interviews with them i . Interviews were recorded and transcribed verbatim for further analysis. The sampling for this qualitative phase of the study was ceased when the theoretical saturation was reached.

Instruments
Belief in Specific CTs. We designed a 16-items questionnaire covering various CTs chosen in the pilot stage (i.e. "1969 moon landing of US astronauts was staged"; "Pharmaceutical companies deliberately keep the cure for HIV away from the public"). Items were evaluated using a Likert scale with a 4-point response format (1 = Completely disagree, 4 = Completely agree). We excluded the midpoint of the Likert type scale used to measure the endorsement of CTs, thereby forcing the respondents to decide whether it is more likely to be true or not. We reasoned that having a midpoint might have artificially inflated the correlations in the initial study, as they might have partially stemmed not from endorsing the CTs but from being indecisive. Internal consistency (Cronbach's Alpha = .78) allowed us to compute a single score.

Exploring Belief in Contradictory Conspiracy Theories 96
Contradictory CTs. On top of chosen 16, we added nine mutually contradictory items, out of which some were necessarily exclusive (i.e. "Slobodan Milošević was killed in the Hague" and "Slobodan Milošević did not actually die in the Hague, but faked his own death") and some probably exclusive (i.e. "HIV virus is deliberately produced in the USA" and "HIV virus is deliberately produced in Europe"). To avoid circularity in later correlational analysis, these items were not included in the total score of Belief in Specific CTs. Locally specific contradictory CTs were construed around three events: the death of Slobodan Milošević in the Hague, the assassination of Željko Ražnatović Arkan and the true identity of Josip Broz Tito. Slobodan Milošević (1941Milošević ( -2006  To measure proneness to conspiratorial thinking, we adapted five-item Conspiracy mentality questionnaire Semi-structured interview consisted of several parts. The first part aimed at warming up the participants and leading them to think through their answers on the questionnaire ("Do you remember your answer to the item '1969 moon landing of US astronauts was staged?'" and "Why did you answer like that?"). Next part consisted of the same questions as the previous one, but this time concerning a pair of mutually exclusive items that the participant endorsed. Following that, we pointed to the fact that this is a case of contradictory claims and asked the participant to give us the reason behind endorsing both ("One might say that this representation of the event and the previous one can't go together, that they contradict each other. How do you understand this? Can you explain how both can be true?"). This procedure has been repeated with all pairs of contradictory items endorsed by the participant.

Results
We will start with a detailed description of CM and specific CT endorsement in the sample, and then proceed to test the hypotheses about their interrelatedness, as well as the endorsement of contradictory CTs of different types. Finally, we will qualitatively analyze the strategies respondents reported to have used when they endorsed contradictory narratives and illustrate them with typical citations by the participants. The instruments, database and interview transcripts are available at https://osf.io/zxq2x/.

Lukić, Žeželj, & Stanković 97
The reliability of Belief in Specific CTs questionnaire was α = .78, and the reliability of CMQ on our sample was α = .67, slightly lower than in the original study (reliability of different versions of the questionnaire ranged from α = .72 to α = .84, Bruder et al., 2013). The exploratory factor analysis yielded with one factor explaining 44% of the variance. Taken together, this allowed us to calculate a summary score. The average endorsement, standard deviation and the percentage of endorsement for all CTs used in present research are detailed in Table 1.  (Horn, 1965) and inspection of the scree plot (Cattell, 1966;Buja & Eyuboglu, 1992). Based on the mentioned criteria, one factor emerged with parallel criteria average higher than the 95 th percentile, explaining 24% of total variance, with item loadings varying from .32 ("Hidden messages in commercials") to .62 ("Vaccines cause diseases"). To test the assumption that items from Belief in Specific CTs questionnaire and Conspiracy mentality questionnaire will form two separate factors, we compared a single-factor model and a two-factor model in confirmatory factor analysis. We found that two-factor model (χ 2 /df = 1.98, GFI = .88, RMSEA = .06, CFI = .79), although not optimal on all parameters, fitted the data better than single-factor model (χ 2 /df = 2.25, GFI = .82, RMSEA = .07, CFI = .73).
Full correlation matrix of specific CTs and CMQ items is detailed in Table 2. Specific CTs and CMQ items were either positively related or unrelated. Similarly, all pairs of contradictory items were mostly related to other CTs and items from CMQ, forming an expected pattern. Also in line with initial expectations, we registered a substantial correlation between average specific CT endorsement and CM (r = .49, p < .001).
Endorsing contradictory CTs. Almost half of our participants (48.4%) endorsed at least one pair of mutually exclusive CTs. Participants endorsed more pairs of probably exclusive CTs than pairs of necessarily exclusive CTs (Table 3).
Unlike Wood et al. (2012), we found both positive and negative correlations between mutually exclusive CTs depending on the type of relation between them. Namely, probably exclusive CTs were positively correlatedspecifically "HIV was produced in Africa", "HIV was produced in Europe", "HIV was produced in the USA" (r USA-EUR = .58, p < .001; r USA-AFR = .28, p < .001; r EUR-AFR = .17, p < .001) and "Josip Broz Tito was a Russian spy" and "Josip Broz Tito was an American spy" (r = .23, p < .001). On the other hand, one pair of necessarily exclusive CTs was negatively correlated -"Željko Ražnatović Arkan was killed" and "Željko Ražnatović Arkan is still alive" (r = -.27, p < .001), whilst the other pair was unrelated -"Slobodan Milošević was killed in the Hague" and "Slobodan Milošević did not actually die in the Hague" (r = .06, p = .346) ii .
There were positive correlations between the number of endorsed pairs of mutually exclusive CTs and the score on Belief in Specific CTs questionnaire (τ = .31, p < .001; ρ = .37, p < .001) iii , as well as between the number of endorsed pairs of mutually exclusive CTs and the score on CMQ (τ = .20, p < .001; ρ = .24, p < .001).

Type of answers
Probably exclusive CTs Necessarily exclusive CTs

Origin of HIV Tito Arkan Milošević
Contradictory answers 108 (42%) 6 (2%) 23 (9%) 6 (2%) Non-contradictory answers 144 (58%) 246 (98%) 229 (91%) 246 (98%) Content analysis of the interview transcripts revealed two types of reasoning behind endorsing mutually exclusive items, upon we excluded cases of answering in a random or inattentive manner iv . All explanations given by the participants were unproblematically recognized as indicating one of the following strategies behind endorsing contradictory CTs: a) Distilling crucial content. Emphasizing the shared aspect of contradictory items that is considered crucial and disregarding the aspect that is different because it is considered to be of secondary relevance. For example, the participants are more focused on the fact that HIV was man-made than on the actual geographical origin of the virus: "It is irrelevant. I don't know if it was produced in the USA or Europe, but I believe it was created deliberately, with a specific aim." "I truly believe it is fabricated intentionally! I wouldn't bet on a particular place of origin. What is important to me is that it is created by someone, and not the details, if it was in Africa or Europe..." It seems that the respondents are able to circumvent the contradiction by reinterpreting the claims and extracting the shared aspect of the content that is relevant to them -in this case, it is the thesis of a secret plot to create HIV virus. The concrete location is considered to be information of secondary importance and the one they are unsure of. Some participants even represent Europe and the USA as a single political area with shared interests ("Europe, America... it's the Western civilization"), which further makes the difference in geographical origin of the virus irrelevant when endorsing the claims.
This first explanatory strategy was typical for probably exclusive CT items -75% of the answers in this category were explained this way (and none of the necessarily exclusive CT items).
b) Evoking possible scenarios. Treating contradictory items as possible scenarios -different explanations that make sense, sound credible or could be accurate under certain conditions. Since participants are not sure which one of the alternative explanations is true, they endorse both as equally plausible: "Well, I don't know, either he was killed, or he staged his own death... For me, these are both possible options." "Well, it is possible that he is alive, but, in case he is dead, it certainly had something to do with the state." We could not assume that the respondents in this situation believe in any of the two options expressed by the contradictory claims, but they certainly suspect the official story about the event. So, they are not sure if someone was killed or faked his own death, but they are sure "there is something suspicious about it". And that is Exploring Belief in Contradictory Conspiracy Theories 102 why they endorse both claims as potentially true, although they do not know which of them actually happened.
Therefore, they also evade contradiction since they endorse claims as "either A or B is true", not as "both A and B are true".
This second explanatory strategy was typical or necessarily exclusive CT items -all of the answers in this category were explained this way (and only 25% of the probably exclusive CT items).

Conclusions and Implications
First, our results strongly corroborate the idea of CTs of very different content being related and forming a unified belief system. Most of the endorsements of specific CTs were moderately positively correlated and they form one principal component. We found a moderate positive correlation between belief in specific CTs and proneness to conspiratorial thinking, which goes in line with the results of previous research. Along with the results of confirmatory factor analysis that favor the two independent factors model, we argue that belief in specific CTs and conspiracy mentality, although correlated are not fully overlapping constructs. Namely, CMs content is generic and independent of cultural or historical content; due to abstractness of its items it can be more acceptable to general public in comparison to specific CTs -some of the CMQ items were even criticized to be factual, instead of conspiratorial (Swami et al., 2017).
Second, in their seminal study, Wood et al. (2012), reported only positive correlations between endorsements of contradictory CTs and did not differentiate between probably exclusive and necessarily exclusive CTs in a single design. In the present research, however, participants were sensitive to the type of mutual exclusiveness and the percentage of the endorsement of necessarily and probably exclusive items as well as their correlation support this conclusion. Around half of our participants endorsed at least one pair of contradictory CTs and, as predicted, participants endorsed pairs of probably exclusive items more than they endorsed pairs of necessarily exclusive ones. In addition, we registered positive correlations between CTs which were probably exclusive and no correlation or even negative correlation between those that we proposed as necessarily exclusive. This finding illustrates that it is important to further explore the logical relations between the beliefs and the way the participants organize them in coherent belief systems.
Third, through the interviews, we sought to understand the reasoning behind the endorsement of contradictory items. Analysis of the interview data indicates that in case of the agreement with contradictory CTs, the respondents actually interpret the claims so as to avoid contradictions. They construct a higher order interpretation of the events in which suspicion towards the "official story" is central and mutually exclusive CTs are seen as probable alternative explanations -only one of which might be true. This is consistent with the finding of Harambam and Aupers (2015) that people who believe in conspiracy theories perceive themselves as "skeptics".
The qualitative analysis thus highlighted several problems with the questionnaire as a way to assess beliefs in CTs and the typical interpretations of questionnaire data. Namely, one concrete CT can be an elaborate system of beliefs which we simplify and narrow down to one sentence in a questionnaire. That forces the respondents to compromise when assessing their truthfulness. They reinterpret the statement in the way it fits their belief system and the information available to them, ignoring some pieces and cherry-picking other pieces of the CTs content in the process. Lukić,Žeželj,& Stanković 103 In addition, a participant's agreement with a statement sometimes does not indicate the endorsement of its content, but the endorsement of any explanation that is alternative to the official one. The respondents assume that they have only a limited knowledge about certain events so they are not in a position to give definitive answers -as one of them said: "I can't really claim something like that (regarding what happened in the case of Arkan's murder), because I am not an important person". They actually respond to the items by assessing the probability of the given scenario -"There is a possibility that they did (landed on the Moon in 1969), but I can't say 'yes' or 'no'". Since the respondents reported having assessed probability for an explanation to be true (it may have happened like that), this allowed for different (even contradictory) representations of events to be simultaneously probable, therefore contradictory beliefs to coexist without being irrational. Our findings can fit the three-level model recently put forward by Wood (2017), in which general conspiracy ideation leads to conspiracy suspicions about specific event, which in turn can breed different specific conspiracy beliefs. If the conspiracy beliefs can share a common assumption, however vague (e.g. "climate change/death of an important person is a hoax"), it is possible for them to simultaneously exist.
Taking all this into account, one should be careful before drawing a conclusion that the respondents who endorsed a CT really "believe" in it. Thus, participants' answers on response scales should be interpreted more carefully. Additionally, more elaborate response scales could be developed that would allow e.g. separate assessment of the likelihood of an event or the credibility of the explanation etc., so the respondents' relation towards the items becomes clearer. The knowledge about an event, i.e. the quantity and quality of the information available to a participant should also be assessed and its relationship with believing in CTs clarified.
On the other hand, even when they believe in a certain CT, their explanations indicate that this belief is in most cases really superficial -without any greater engagement in form of researching and considering facts that could support or discredit their belief. This is not surprising, since this research, as all the previous ones, has been conducted on the general population. Studying persons who are particularly committed to and involved with CTs could provide a better-grounded basis for drawing conclusions about reasoning behind beliefs in CTs, including those contradictory ones.
This research goes to show that people who endorse CTs are not as irrational as sometimes portrayed. Adequately understanding proneness to conspiracy beliefs is especially relevant in a contemporary context, characterized by complexity and ambiguity of social events and the abundance of information sources together with the lack of acknowledged epistemic authorities. Discussed methodological challenges indicate that conspiratorial worldview should be studied more thoroughly, preferably in the multi-method framework and with more sensitivity to its content and the participants' responding strategies.

Notes
i) The participants who endorsed probably exclusive CTs and the ones who endorsed necessarily exclusive CTs were evenly represented in the interview sample. Since the participants have completed the survey under self-generated code names for anonymity reasons, these code names were then used to search for the participants for the interview phase. Participants, of course, had the option to refuse being interviewed by not approaching the researcher when their code name had been listed. ii) We also used Kendall's τ (τ = .04, p = .458) and Spearman's ρ (ρ = .05, p = .459) as a measure of correlation between these two variables because of low mean of endorsement on item "Slobodan Milošević did not actually die in the Hague". iii) We used Kendall's τ and Spearman's ρ as a measure of correlation between these two variables because of the extreme violation of the normal distribution in the number of endorsed pairs of exclusive CTs.
Exploring Belief in Contradictory Conspiracy Theories 104 iv) When confronted with their answers on the CTs questionnaire, part of the participants readily declared that they gave answers in a random or careless manner. Around 30% of all answers (eight respondents in total) examined were classified as such. We treated those answers as invalid, i.e. not as indicators of endorsing contradictory CTs by the participants, since the participants have not read or have not elaborated the content of the items.

Funding
The research was supported by Serbian Ministry of Education, Science and Technological Development; project No 179018.