In one of my mulling and musing posts (And One More Thing) I claimed that conspiracy theorists should be deterred by outright contradictions if there are to preserve minimal rationality. Would one seriously believe that the U. S. government is concealing both the fact that bin Laden died before 9/11 and that he was not killed in 2011, but remains alive in hiding? It beggars the imagination to endorse both propositions when they are presented next to each other. If they are presented at different times and in different contexts, however, the force of one’s own forgetting and that of the survey taker, may ease the demands of coherence. Other popular and contradictory conspiracy theories revolve around Diana Spencer’s (un)death (she was killed by the Windsors, the Egyptians, and not at all) and astronautics (humans never landed on the moon and moon missions are ongoing; while the government is covering up both these facts).

Wood, Douglas & Sutton (2012) suggest that individuals prone to conspiracist ideation will not shrink from contradiction. In two studies, they find positive correlations between degrees of agreement with mutually exclusive ideas. Their first study is concerned with causes of Diana’s death and their second study is concerned with the life and death of bin Laden. That study also contains ratings of one’s belief in the idea that the Obama administration is covering up what happened during the raid. Results show that the more respondents agreed with the idea that a cover-up occurred, they more they agreed with [a] bin Laden was already dead, and [b] that he is still alive. When the cover-up variable was statistically controlled, the correlation between [a] and [b] dropped to zero.

Wood et al. suggest that the correlation between contradictory conspiracy ideas [a] and [b] should be negative even though it is to be expected that both correlations involving the direct measure of a general conspiracy [c] are positive. With the correlation between cover-up [c] and Laden alive [a] being .41 and the correlation between [c] and Laden already dead [b] being .51, the correlation between [a] and [b] cannot drop below -.58, although it can be as positive as .99.

If one demands a negative correlation between [a] and [b], as Wood et al. appear to do, it is not possible to obtain positive correlations between both conspiracy ideas and the cover-up narrative at the same time. If the correlation between [a] and [b] is -1, and if the correlation between [a] and [c] and between [b] and [c] are to be the same, then what one gets is 0. In other words, if people rationally realize that they can pick one and only one conspiracy theory, general conspiracist ideation must remain unrelated to the endorsement of any particular conspiracy theory.

Now consider a population in which most individuals are not conspiracy theorists. It is easy to show that in such a population a strong negative correlation between two sets of conspiracy ideas cannot be obtained, and that it is possible to get a positive correlation even though most of the conspiracy theorists only endorse one such theory – as minimal rationality demands.

To illustrate, imagine a village comprising 10 individuals. Eight of them do not believe in cover-ups, one believes in a corrupt government [c] and conspiracy [a], and one believes in a corrupt cover-up and conspiracy [b]. The correlations are .67 between [c] and [a] and between [c] and [b]. The correlation between [a] and [b] is -.11, which is the lowest possible value given the two correlations involving [c]. Now convert one villager to believing that the government is corrupt government and that both conspiracy theories are true. The correlations between [c] and [a] and between [c] and [b] rise to .76. More strikingly, the correlation between [a] and [b], the two contradictory conspiracy theories, is now +.37, and it cannot mathematically be lower than +.17 (although the partial correlation between [a] and [b], controlling for [c] is -.5. This result is obtained, although 2/3 of those who believe in any conspiracy theory, believe only in one. There is only a single person who is doubly irrational in the Wood sense.

I conclude from this that stronger evidence is needed to support the claim that most conspiracy theorists are not only irrational in believing the implausible, but that they suffer from a deeper irrationality of believing more than one contradictory irrationality at once. Math constrains how nutty we can get.

For relief from the contemplation of numbers, see here for a report on Neil Armstrong's conversion to the theory that NASA faked his moon landing.

Wood, M. J., Douglas, K. M., & Sutton, R. M. (2012). Dead and alive: Beliefs in contradictiory conspiracy theories. Social Psychological and Personality Science, 3, 767-773. doi: 10.1177/1948550611434786

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