Abstract
The so-called ‘conjunction effect’, in which participants incorrectly assert that an instance from the conjunction of two sets is more probable than an instance from one of the two conjoining sets alone, has been a source of debate as to whether it is a genuine fallacy of individual thinking or not. We argue that reasoning about individuals follows a different process than reasoning about sets. 35 participants took part in 3 tasks: a) one involving blocks of different sizes and colours designed to evoke set-based reasoning, b) one where a particular block was ‘individuated’ by stating that it represented a particular person, and c) the original Tversky and Kahneman (Psychological Review 90(4):293–315, 1983) ‘Linda’ problem. As predicted, set-based reasoning was significantly more prevalent for the blocks task than for the other two tasks. Participants’ reasons for their choices suggest that some individuals correctly use set-based logic in one task and a social reasoning process for the other tasks.
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Appendix 1. Instructions to Participants for Each of the Three Tasks Used in the Experiment
Appendix 1. Instructions to Participants for Each of the Three Tasks Used in the Experiment
Note that in the materials below, ‘X’ is used as a variable, and would be substituted in practice with whatever response the participant had previously made.
Part (i): Blocks Task
The participant is shown the box of 16 blocks, and asked: ‘Please describe what you see.’ The experimenter takes care to make sure that they explicitly note that there are four colours and four sizes of blocks, prompting them gently if need be.
The experimenter summarises by saying that ‘There are Red, Blue, Green, and Yellow Blocks in each of four different sizes—let’s call them Very Small, Small, Medium and Large’.
The box of blocks is then removed from view by covering them (the blocks will remain hidden for the rest of the session), then the participant is asked the following questions. ‘Suppose I draw a block from the box at random, and that I can just as easily pick one of any size and of any colour.
Is the block most likely to be Red, Large, or Red and Large? (Participant makes a choice). Why? (Their verbal response is noted).
The participant is told, You chose X as the most likely option. Which is the next most likely option? (Participant makes a choice). Why? (Their verbal response is noted)’.
Part (ii): Individuated Blocks Task
(Blocks remain hidden from view throughout). The participant is instructed: ‘Consider the box of bocks again. Imagine that each one symbolises a particular individual. Imagine that one of the individuals involved is called Susan. Imagine also that the real person, Susan, is keen on nature, on preserving the natural environment, and on outdoor pursuits like hill walking and mountain climbing. Is the block that represents Susan most likely to be Green, Large, or Green and Large? (Participant makes a choice). Why? (Their verbal response is noted).
The participant is then told, You chose X as the most likely option. Which is the next most likely option? (Participant makes a choice). Why? (Their verbal response is noted).
Part (iii): Linda Problem
The participant is presented with following information: ‘Linda is 31 years old, 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.’ They are then asked: ‘Is Linda most likely to be a feminist, a bank teller, or a feminist bank teller?’ (Participant makes a choice). Why? (Their verbal response is noted).
They are then told: You chose X as the most likely option. Which is the next most likely option? (Participant makes a choice). Why? (Their verbal response is noted).
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Davies, J.B., Anderson, A. & Little, D. Social Cognition and the So-Called Conjunction Fallacy. Curr Psychol 30, 245–257 (2011). https://doi.org/10.1007/s12144-011-9111-4
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DOI: https://doi.org/10.1007/s12144-011-9111-4