So everyone probably is familiar with the “conjunction fallacy.” It figures in Tversky & Kahneman’s famous “Linda problem”:
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
Which is more probable?
1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.
According to T&K (1983), about 85% of people select 2. This is a mistake, in their view because “Linda is a bank teller” subsumes all the cases in which she is a bank teller and thus logically includes both the cases in which she is a “bank teller active in the feminist movement” and all the cases in which she is a “bank teller not active in the feminist movement.” On this reading, belonging to class 2 cannot logically be more probable than belong to class 1.
Nevertheless, people make the mistake because 2 is more concrete and conveys a picture that is more vivid than 1. Those who over-rely on heuristic, “System 1” information processing are thus likely to seize on it as the “right answer.” Individuals who score higher in conscious, effortful, “System 2” processing tend to be more likely to supply the correct answer (Toplak, West & Stanovich 2011).
What happens, though, when the individual actor featured in the problem behaves in a manner that evinces bad character, and the more vivid “choice 2” includes information that he possesses certain political outlooks? People tend to attribute bad character to those who disagree with them politically. So will the likelihood of their picking choice 2 be higher if the actor’s political outlooks differ from their own?
We wanted to figure this out. So in our variant of the “Linda problem,” we informed our subjects, approximately 1200 ordinary people, that
Richard is 31 years old. On his way to work one day, he accidentally backed his car into a parked van. Because pedestrians were watching, he got out of his car. He pretended to write down his insurance information. He then tucked the blank note into the van’s window before getting back into his car and driving away.
Later the same day, Richard found a wallet on the sidewalk. Nobody was looking, so he took all of the money out of the wallet. He then threw the wallet in a trash can.
We then assigned them to one of three conditions:
“Which of these two possibilities do you think is more likely?
1. ex-felon condition
Which of these two possibilities do you think is more likely?
(a) Richard is self-employed ____
(b) Richard is self-employed and a convicted felon ___
2. procontrol.
Which of these two possibilities do you think is more likely?
(a) Richard is self-employed ____
(b) Richard is self-employed and a very strong supporter of strict gun control laws? ___
3. anticontrol
Which of these two possibilities do you think is more likely?
(a) Richard is self-employed ____
(b) Richard is self-employed and a very strong opponent of strict gun control laws? ___
The motivation to test this proposition originated in a cool article by Will Gervais (et al. 2011), who found that when “Richard” is described as an atheist, people are more likely to display the “conjunction fallacy” than when he is described as an “atheist” or as a “rapist”; we adapted the “Richard” vignette from their study.
What did we find?
Well, first of all, the probability of the conjunction fallacy was highest, regardless of political outlooks, when Richard was described as a convicted felon. Moreover, this bias grew in magnitude as subjects became more right-leaning in their politics.
But when Richard was described as either a "strong opponent"or a "strong supporter" of gun control laws, left-leaning subjects were slightly more likely to display a bias congenial to their political outlooks. Right-leaning ones displayed no meaningful bias in their appraisals.
So there you go. Make of this what you will!
References
Gervais, W.M., Shariff, A.F. & Norenzayan, A. Do you believe in atheists? Distrust is central to anti-atheist prejudice. Journal of Personality and Social Psychology 101, 1189 (2011).
Toplak, M., West, R. & Stanovich, K. The Cognitive Reflection Test as a predictor of performance on heuristics-and-biases tasks. Memory & Cognition 39, 1275-1289 (2011).
Tversky, A. & Kahneman, D. Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review 90, 293-315 (1983).