Why are some people just so obstinate? — Bayes Theorem & The Backfire Effect

What do Flat-earth­ers, Anti-vaxxers, 9/11-con­spir­acists, Jesus-mythi­cists and Obama cit­i­zen­ship deniers have in com­mon?

Well, sub­con­scious­ly at least, they all dis­play a con­tempt for Bayes’ the­o­rem, and arguably they strong­ly man­i­fest the ‘Backfire effect.’ Welcome to anoth­er instal­ment of Cognitive Bias Wednesday, today look­ing at the ‘back­fire effect,’ with a pre­lude on Bayes’ the­o­rem.

statsWhy is it that even when pre­sent­ed with all the data and infor­ma­tion, some peo­ple refuse to mod­i­fy their beliefs? That even with all the weight of evi­dence that the world is round, or that vac­cines don’t cause autism, that they refuse to budge in their beliefs, and even seem to become more set in their ways. While some of this behav­iour is cer­tain­ly con­scious, at least some is also the prod­uct of a cog­ni­tive bias oper­at­ing behind the scenes: the ‘back­fire effect.’ This is also why most of the argu­ments that occur on the inter­net are rel­a­tive­ly fruit­less. However, before we get to the cog­ni­tive bias, it is worth hav­ing a brief jour­ney through a neat cog­ni­tive fea­ture, the the­o­ry of Bayesian infer­ence.

bayes-theorem-equationThomas Bayes was a 18th cen­tu­ry Presbyterian min­is­ter, philoso­pher, and sta­tis­ti­cian; and while he pub­lished works in both the­ol­o­gy and math­e­mat­ics, he is best known for his con­tri­bu­tion to sta­tis­tics, posthu­mous­ly. His work on what would even­tu­al­ly become known as Bayesian prob­a­bil­i­ty the­o­rem was only pub­lished after his death, and the impact of it would be com­plete­ly unknown to him. While Bayesian mod­el­ling and sta­tis­tics are applic­a­ble in a wide spec­trum of fields and prob­lems, from mem­o­ry the­o­ry and list length effects that my pre­vi­ous lab worked on (MaLL), 1 through to Richard Carrier’s appli­ca­tion to his­to­ri­og­ra­phy, 2 and many more (just don’t get me start­ed on the null hypoth­e­sis sig­nif­i­cance test­ing debate). 3 The key fac­tor for this inves­ti­ga­tion is in the Bayesian log­ic applied to the belief-revi­sion loop. In lay terms Bayesian sta­tis­tics can be used to pre­dict how much some­one will believe in a propo­si­tion when pre­sent­ed with a cer­tain evi­dence set.

lutececointossTake for exam­ple the good old coin toss test, sup­pose you have a coin with one side heads and the oth­er tails. Logic and the laws of prob­a­bil­i­ty would indi­cate that it should be a 50/50 chance of being heads. But what hap­pens if you flip a coin 5 times and get 5 heads in a row, well sta­tis­ti­cal­ly speak­ing it is still a 50–50 chance, even though the prob­a­bil­i­ty of get­ting a long con­sec­u­tive run trends with 2(n-1). What about if you get 92 heads in a row, 4 or 122 heads, 5 do the odds change then? Probability and sta­tis­tics give us a clear no, it is still 50–50 no mat­ter how big n is. However, if you ask gam­blers at a casi­no, or for that mat­ter most peo­ple on the street, you will get a star­tling response. Many respon­dents will say that as it is a 50–50 prob­a­bil­i­ty the chance of the next coin toss being tails increas­es to even out the over­all trend. Why? Well it is a bit of a faulty belief-revi­sion loop, and this trend is able to be pre­dict­ed by Bayes’ Theorem. Using Bayesian infer­ence and apply­ing it to epis­te­mol­o­gy we can pre­dict the mod­i­fi­ca­tion of the belief loop and see that degrees of belief in the out­come of a coin toss will rise and fall depend­ing on the results, even though the sta­tis­tics remains the same. Furthermore, these mod­i­fi­ca­tions are over­whelm­ing­ly con­ser­v­a­tive in most peo­ple, and this should give us pause for thought when we find evi­dence that chal­lenges our beliefs.

But what does this have to do with the back­fire effect? I hear you ask. Well the back­fire effect is essen­tial­ly where the Bayesian infer­ence mod­el of the belief-revi­sion loop fails, and fails bad­ly. Normally when peo­ple are pre­sent­ed with infor­ma­tion that chal­lenges their beliefs and pre­sup­po­si­tions they engage in the Bayesian belief revi­sion loop as above, and slow­ly change (even if slow­er than you would think). However, when test­ing how peo­ple respond to cor­rec­tion of mis­in­for­ma­tion Nyhan and Reifler found that, in some cas­es, rather than mod­i­fy­ing their beliefs to accom­mo­date or fit with the infor­ma­tion that they have received, they instead clung to their beliefs more strong­ly than before. 6  Essentially in their tests the pres­ence of cor­rect­ing mate­r­i­al for polit­i­cal mis­con­cep­tions served to strength­en the mis­con­cep­tion, rather than mod­i­fy it. They dubbed this the ‘Backfire Effect.’

Now this isn’t dis­played by every­one in the pop­u­lace, although I would argue that it works with­in our sub­con­scious all the time. Some ear­ly research shows that the back­fire effect com­mon­ly rais­es its head when the mat­ters are of emo­tive salience. So even though some of the more amus­ing inci­dences of the back­fire effect that are com­mon­ly high­light­ed involve peo­ple shar­ing satir­i­cal news sto­ries from The Onion or Backburner as if they were real news arti­cles, oth­ers are less benign. Indeed, for almost every amus­ing inci­dence of peo­ple not check­ing their Bayesian revi­sion loops and falling prey to the back­fire effect, there are just as many where peo­ple are strong­ly rein­forced in their faulty beliefs on items that mat­ter. One of the notable items recent­ly has been the issue of vac­ci­na­tion, where I have seen sev­er­al acquain­tances strong­ly hold to the proven faulty and fraud­u­lent research that ‘linked’ vac­cines with autism. Here the over­whelm­ing body of evi­dence finds no link between the two, and yet they stren­u­ous­ly hold to the link.

arguing-internetSo what can be done about it? Well this blog post is one use­ful step. Being aware of the back­fire effect should help us eval­u­ate our own belief sys­tems when we are chal­lenged with con­tra­dic­to­ry evi­dence. After all we are just as sus­cep­ti­ble to the back­fire effect as any oth­er human being. So we should be eval­u­at­ing our­selves and our own argu­ments and beliefs, and see­ing where our Bayesian infer­ence leads us, with the humil­i­ty that comes from the knowl­edge of our own cog­ni­tive bias­es, and the fact that we might be wrong. However, it should also help us to sym­pa­thise with those who we think are dis­play­ing the back­fire effect, and hope­ful­ly help us to con­tex­tu­alise and relate in such a way that defus­es some of the bar­ri­ers that trig­ger the back­fire effect.

Please weigh in on the com­ments as to what you thought about my expla­na­tion of Bayesian infer­ence and the back­fire effect. Also let me know what oth­er cog­ni­tive bias­es you would like to see cov­ered.


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  1. Dennis, Simon, Michael D. Lee, and Angela Kinnell. “Bayesian Analysis of Recognition Memory: The Case of the List-Length Effect.” Journal of Memory & Language 59, no. 3 (2008): 361–76.
  2. Carrier, Richard. Proving History: Bayes’s Theorem and the Quest for the Historical Jesus. First Edition edi­tion. Amherst, N.Y: Prometheus Books, 2012.
  3. Lee, Michael D., and Eric-Jan Wagenmakers. “Bayesian Statistical Inference in Psychology: Comment on Trafimow (2003).” Psychological Review 112, no. 3 (July 2005): 662–68; dis­cus­sion 669–74. doi:10.1037/0033–295X.112.3.662.
  4. Rosencrantz and Guildenstern Are Dead: Act 1
  5. Lutece Twins, Bioshock: Infinite
  6. Nyhan, Brendan, and Jason Reifler. “When Corrections Fail: The Persistence of Political Misperceptions.” Political Behavior 32, no. 2 (March 30, 2010): 303–30. doi:10.1007/s11109-010‑9112-2.