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The more likely it is to be X, the more likely it is to be Not X?

This post is by Phil Price.

A paper by Wood, Douglas, and Sutton looks at “Beliefs in Contradictory Conspiracy Theories.”  Unfortunately the  subjects were 140 undergraduate psychology students, so one wonders how general the results are.  I found this sort of arresting:

In Study 1 (n=137), the more participants believed that Princess Diana faked her own death, the more they believed she was murdered.  In Study 2 (n=102), the more participants believed that Osama Bin Laden was already dead when U.S. Special Forces raided his compound in Pakistan, the more they believed he is still alive.

As the article says, “conspiracy advocates’ distrust of official narratives may be so strong that many alternative theories are simultaneously endorsed in spite of any contradictions between them.”  But I think the authors overstate things when they say “One would think that there ought to be a negative correlation between beliefs in contradictory accounts of events — the more one believes in a particular theory, the less likely rival theories will seem.”  Well, one might think that, but actually a positive correlation makes sense to me.  I can see how, if you really think that a lot of what the government says is a lie, you would think “well, I don’t know exactly which part of the Bin Laden account is a lie but they are probably lying about something; maybe he was already dead, or maybe he’s still alive now, but I don’t know which.”  The authors realize this is what is going on, they just make too much of how surprising it should be.


  1. Steve Sailer says:

    JFK conspiracy theorizing was quite respectable in the 1970s and 1980s, all the way up until the serious press’s backlash against Oliver Stone’s “JFK” that set in around the time that movie was up for a lot of Oscars. You can see this inability to choose a single conspiracy theory in “JFK,” which on first viewing seemed like an overwhelming feat of bravado filmmaking. But on second viewing you start to notice that it propounds two totally contradictory conspiracy theories: Col. Fletcher Prouty’s theory that this was a vast and meticulously planned coup by almost the entire military-industrial complex and DA Jim Garrison’s theory that Kennedy was assassinated by a few French Quarter eccentric homosexuals.

    • Andrew says:

      About one month into grad school I was talking with a friend and offhandedly referred to the Warren Commission as a “whitewash.” I can’t recall how it came up in conversation, but in any case my friend stopped the conversation and said, Whoa, what do you know about the Kennedy assassination? He started going on about Oswald, Tippett, etc., and I interjected and said, Hey, how did you know so much about this—was your dad on the Warren Commission? To which he responded, Yeah, he was.

      My question had of course been rhetorical, but my friend’s dad really was on the Warren Commission. Well, he was a counsel for the commission, but the counsel were the people who did all the work. You don’t think Gerald Ford read all those documents, do you???

      Anyway, my friend gave me a couple of his dad’s books, and I’m convinced that Oswald acted alone.

      The deeper message, I suppose, is that you can make all sorts of connections if you go to Harvard. And this was just grad school! I can only imagine what it was like for the undergrads. In contrast, I probably could’ve met all sorts of future captains of industry at MIT but we were all quietly doing our problem sets so we ever actually ended up speaking.

  2. John Mashey says:

    Clearly, some people have taken the Queen’s sage advice to new extremes:

    “Alice laughed: “There’s no use trying,” she said; “one can’t believe impossible things.”
    “I daresay you haven’t had much practice,” said the Queen. “When I was younger, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”
    Alice in Wonderland.

  3. Roger says:

    IOW, the authors claim to have found a surprising result, when they really just have an artifact of their poor questionnaire. Yes, of course it is reasonable to believe in the possibility of distinct scenarios.

  4. MAYO says:

    Gelman’s explanation is correct. One of the big problems is that people (not the subjects) understandably confuse likelihood with probability.

  5. derek says:

    The surveyors seem surprised by the conclusions that should come naturally with their survey design. If “belief that” was an all or nothing affair, then Belief A would crowd Belief B out 100%. But they designed the survey to account for fractional belief. As soon as they did that, they should have been ready for beliefs A and B to partially crowd out C. Of course A and B are contradictory to each other, but the point is they are each highly contradictory to C. The surveyors might as well have complained that there was any residual belief in C at all. They could have said “In Study 1 (n=137), participants believed that Princess Diana was murdered, but also that she died in an accident.”

  6. Martin Barrett says:

    “Princess Diana faked her own death” and “Princess Diana was murdered” are CONTRARY statements, not CONTRADICTORY. They do not jointly exhaust the space of possibilities under consideration, and neither may play the role of X to the other’s not-X.

    There is thus no apparent reason why an increase in degree of belief in one should not be accompanied by an increase in degree of belief in the other; neither does this seem surprising.

  7. Joseph says:

    I wonder if they didn’t make a mistake looking at correlation coefficients. To see what I mean suppose you have two conspiracy theories that are mutually contradictory. Label them C_1 and C_2. Then suppose you have a 100 people that break down as follows:

    89 believe neither C_1 or C_2
    1 believes C_1
    9 believe C_2
    1 believes C_1 and C_2

    Then P(C_1) = .02 (only two people believe it) and P(C_1 | C_2) = .1

    Since P(C_1)<P(C_1|C_2) you will get a positive correlation coefficient even though there is only one person out of 100 that holds the irrational view that both C_1 and C_2 are true.

    In fact, the correlation coefficient looks to be .19 in this case if I did the calculation right.

    So correlation could be a misleading measure of the extent of irrationality if you're not careful and might really through a monkey wrench in some their proposed explanations for why this happens.

  8. Matt Weber says:

    @Joseph: Whenever anyone reports a small number of correlation coefficients and doesn’t show the corresponding scatterplot, get worried. Anyone worthy of a psychology Ph.D. could code up an R script to produce a table of scatterplots to go with Table 1.

    The measure they use is pretty weird — it combines an agree/disagree rating with ratings of the extent to which each theory is plausible, worth considering, convincing, and coherent. Right off, the agree/disagree rating isn’t binary, i.e. subjects will presumably infer that they’re not being asked to give an up-or-down vote on a statement’s truth. And the other ratings are even more easily applied to statements you might not think were true. It’s very easy to imagine someone saying “I think Osama was already dead, but I think the idea that he’s still alive is plausible, coherent, and worth considering, and I could be convinced.” If we replaced “Osama is [dead|alive]” with a more anodyne point of political disagreement (“marijuana [is|is not] a gateway drug”), we’d think that person sounded very reasonable and open-minded.

  9. Blaise F Egan says:

    Karen Douglas gave a talk on this subject that I attended. It’s on the British Humanist Association Youtube channel.

  10. Peter K says:

    Your article here led me to read the study, as I’m fascinated by all the varying opinions of conspiracies and conspiracist thinking. By the end of the day, I’d written an article at my blog that I’m hoping will open the eyes of my readers to how even science (albeit not of the very highest order) can be a biased spin-factory when the topic is conspiracy.

    I state in my article that, “Academia Disregard Conspiracy Theories Except as the Subject of Research to Marginalize their Proponents!” That one had my smiling when I re-read it. My spoiler-alert summary is that I feel the conclusion of this study was “designed primarily to paint people with uncommon theories as unintelligent and to further shift the interest away from examination of the theories themselves.”

    Thanks for bringing it to my attention.