Within the internet science community, there had been many efforts to improve collective decision-making by means of specific technologies [1
]. For example, understanding how people reason (and, eventually, commit mistakes) at individual level or in group is crucial to improve the design of online crowdsourcing systems and software [5
]. In this paper, we investigate a paradigmatic reasoning error, the conjunction fallacy.
Conjunction fallacy has been investigated since the famous paper of Tversky and Kahneman [7
] on extensional reasoning. In this paper they proposed a variety of scenarios in which they asked to rank the probability of different sentences. The most famous scenario is the Linda’s problem. Given a description of Linda (suggesting that she might be a feminist), people ranked the sentence She is a bank teller (P(A)) less likely than She is a bank teller and is active in the feminist movement (P(A&B)). However, from a normative point of view, probability theory dictates that P(A&B) ≤ P(A). The violation of this rule has been originally explained recurring to the concept of representativeness heuristic. People rate the probability of the various sentences on the bases of the degree to which an event (i) is similar in essential characteristic to its parent population, and (ii) reflects the salient features to the process by which it is generated. Therefore, when people have to rank the probability of the sentences related to Linda, using the representativeness heuristic means to employ the similarity between the description of Linda and the sentences to be ranked as a criterion of choice [8
]. This problem has stimulated a great deal of research [9
], including attempts to define more precisely the concept of heuristic and a variety of other explanations [13
]. For example, we can cite a paper of Tentori, Crupi, and Russo [18
] sustaining that inductive confirmation is the critical factor for the conjunction fallacy. According to them, the crucial factor is not the high perceived probability of the added conjunction (the fact that Linda is a feminist) but how much the added conjunct appears to be likely in light of the Linda’s description. On the contrary, Politzer and Noveck [17
], on the bases of the conversational rules of Grice, Cole, and Morgan [19
], supposed that the conjunction fallacy arises because of a misunderstanding of the conjunct option. Even if some findings are contrasting such hypotheses, conjunction fallacy is a firm phenomenon and it has been used under different conditions to test hypothetical scenarios and to explain real life task’s biases (e.g., clinical diagnosis, sport predictions). In sum, the representativeness account (despite caution and criticism) is the standard interpretation of conjunction fallacy [20
]. The explanation based on the representativeness heuristics (together with other biases that can be explained in terms of heuristic) has led to speculate the existence of two systems of reasoning. This idea is marked with the general label of dual- or two-system theories [21
The judgment based on representativeness heuristic is immediate and effortless. Many authors [21
] tend to contrast this rapid and automatic judgment with a deliberate and slower form of reasoning. In the literature there is a high number of different expression indicating these two forms of reasoning (see, for example [25
]). The different terminologies are often associated with slightly different theoretical point of views. Sloman [25
] speaks of the intuitive system (i.e., a basically associative system that operates on the bases of similarity and contiguity but it is also capable of representing causal structure) and the deliberative system (i.e., based on symbol manipulation, application of abstract rules). Within the dual-process framework, conjunction fallacy arises because there is an automatic and immediate similarity-based impression (e.g., the description of Linda is very similar to a feminist), whereas the deliberative system fails to inhibit this response (and suggesting a more formal analysis of the problem). This distinction has a central role in human sociality, including cooperation, honesty and altruism and other pro-social behaviors (see [28
] for a review).
The dual systems view can be seen closely associated to the famous distinction about two types of thinking found in Bruner [29
]. Bruner, in his famous essay, distinguished between two modes of thought: narrative and paradigmatic. In his opinion, narrative can be defined as the tendency of organizing experience into a form with a plot, structure, emphasizing intentionality and causal relations. On the contrary, the paradigmatic mode of thought is based on logic, mathematics, and abstract rules. In Bruner’s opinion, narrative is a tool for sense-making, creating self-identity and apprehend and interpret the world. Among the many examples that Bruner cite to support this idea, there are the famous experiments of Michotte in which simple elements (triangles or circles) in motion on a screen are described in intentional terms. Keren and Schul [30
] wrote: “despite the apparent similarity between Bruner’s mode of reasoning and the other two-systems under discussion, we suggest that they are different in essence. As we discussed above, a fundamental requirement of any two-systems framework is that the system could be isolated [31
] —namely, that each part could function without depending on the machinery of the other. Bruner’s modes of reasoning, according to our interpretation, are free of this requirement.” The point is that the two modes of thought in Bruner [29
] are different ways to interpret reality (and each modality has different criteria for establishing truth). In our view, each mode of thought involves both the deliberative and the intuitive system. When constructing a narrative, there is a prevalence of intuitions (based on personal experience, imagination, associative memory) but also rule-based deliberations are used (the controlled use of language, the application of norms and rules within the narrative).
Similarly, the paradigmatic thought involves mainly deliberations (in order to make verifications, to make formal analysis) of course, but intuitions may be used too (lot of rules in mathematics and science are associated to intuition, see [32
]). In this paper, we have investigated the influence of Bruner’s modes of thought on conjunction fallacy. We think that the mode of thought involved in answering the Linda’s problem is going to influence the strategy (narrative-based or paradigmatic-based) adopted by participants and thus the answer produced, in this paper, the expressions, “strategy of reasoning” and “mode of thought” are employed as synonyms to refer to the paradigmatic/narrative distinction. It is possible to speculate that a narrative-based strategy should favor the violation of the conjunction rule, since the conjunctive sentence is more coherent with the starting scenario. Indeed, the probabilistic bias naturally arise from the implications of the story presented in the text. Another important feature related to the narrative thought is the social dimension. In Bruner’s point of view, narrative is the primary mode of thought and it has a fundamental role in creating and negotiating meanings within a community. Without entering into the deep complexity of Bruner’s position, according to his findings, humans tend to organize experiences and collective memories mainly in the form of narratives. Narrative is a conventional form, transmitted culturally and constrained by individual’s level of mastery: unlike the constructions generated by logical and scientific procedures that can be weeded out by falsification, narrative constructions can only achieve “verisimilitude”. Narratives, then, are a version of reality whose acceptability is governed by convention and “narrative necessity” rather than by empirical verification and logical requisites [33
]. With regard to the group factor, as far as we know, only the study of Charness, Karni, and Levin [34
] tried to determine the influence of group reasoning (versus individual reasoning). Their results support the idea that when subjects are allowed to consult with each other, the conjunction fallacy decreases. Moreover, some experiments carried out on children demonstrated that children who use stories to solve cognitive or socio-cognitive problems are more flexible in social interactions and tend to find arrangements with partners in order to get possible solution of problems [35
]. In order to explore the variety of dimensions that may be involved in the Linda problem, we introduced two additional variables to the original study: group effect (individual/group discussion) and format of the answer (open-ended/multiple choice condition). So, to investigate how these different conditions (individual/group discussion and open/multiple choice answer format) affect performance, answers with an open response have also been classified depending on the explanation given in their scriptures.
Two extra dimensions are then introduced for the open format condition: narrative-based explanation and paradigmatic-based explanation. We also assessed words used in open ended answers using the Linguistic Inquiry and Word Count (LIWC) software. LIWC is a computerized text analysis program that outputs the percentage of words in a given text that fall into one or more of over 80 linguistic (e.g., first-person singular pronouns, conjunctions), psychological (e.g., anger, achievement), and topical (e.g., leisure, money) categories. It builds on previous research establishing strong links between linguistic patterns and personality or psychological state [37
]. We used a LIWC analysis in order to estimate whether the use of some specific word patterns found in open ended answers could help us in predicting the correctness of the answers, the belonging to the group condition and the mode of thought used [38
]. In particular, LIWC was employed in order to discriminate a classification of responses according to the dual process of thought [23
] and narrative/paradigmatic modes of thought [29
]. Indeed, in the dual-process of thought framework the usual approach involves an a-priori classification of the response options (e.g., sentence A is associated to deliberation whereas sentence A&B with intuition [18
]). However, employing an open-format question, the use of LIWC may help to discriminate narrative/paradigmatic modes of thought by using words classification in psychologically meaningful categories [38
5. Discussion and Conclusions
Results support the idea that conjunction fallacy may arise from the use of narrative thought, especially when people think in isolation. More specifically, the main effect related to the group factor showed a greater amount of wrong responses when participants responded individually compared to the group condition. This observation is in line with [34
] results that found a decrease of conjunction fallacy in group reasoning compared to individual reasoning. This can be explained in terms of a possible influence of paradigmatic minority on the result of the elaboration of the narrative majority in a group condition. In other words, there can be a tendency of small groups to reason in a paradigmatic, conventional way. Another option is that this effect is present because the paradigmatic mode of thought induces easier social negotiation processing.
Independently by the group factor, the narrative mode of thought was more associated to conjunction fallacy responses compared to open answers provided with the paradigmatic mode of thought. However, taking into account only the narrative responses, we observed that conjunction fallacy arises mostly when participants responded alone. On the contrary, when people take a decision in group, the majority of narrative-based responses were correct. So, the narrative mode of thought has its effectiveness increased (in terms of the normative criterion) if exposed to a group discussion. This finding is already known in literature: as found in [35
] and in [36
] the presence of individuals expressing both modes of thought (i.e., narrative/paradigmatic) in a collaborative group problem solving can substantially modify participants’ way to classify the task. In our study, we think that the presence of a paradigmatic approach of someone (the minority) within the group, modified the narrative majority’s mode of representing the task and its solution. Narrative participants could have then reorganized the task in consequence of the presence of a paradigmatic participant within their group. However, at the moment of writing their answer, individually as requested, they shifted back to their original narrative mode of thought. This interpretation goes against of the trivial equivalence narrative mode of thought matches with intuition and paradigmatic mode of thought matches with deliberation. This work can be seen as a first step in studying the relationship between Bruner’s modes of thought and the two systems accounts of reasoning. More research is needed to find out the actual relationship between those two distinctions.
The use of LIWC analyses allowed to identity a set of words or expressions associated to different kinds of predictions. First, responses characterized by use of numbers, conditional verbs, terms related to tentative, anxiety and feelings were associated to a paradigmatic modality of thought. On the contrary, it was possible to identify the use of a narrative strategy of reasoning with the use of third singular person in the answers, words referred to the act of seeing and words referred to positive emotions.
Some interesting results obtained with the LIWC analysis are related to the words that are used in wrong/right answers. Considering all the experimental conditions together (individual vs group; paradigmatic vs narrative), LIWC analysis showed that the use of words referred to socially oriented actions, the use of conditional verbs and words related to affections and time are associated with wrong answers. This can be explained by the willing of participants to create a narration of Linda’s life, instead of calculating the probability of the option provided. For example, the use of words expressing socially oriented actions may be related to the fact that Linda is described as a socially engaged person and participants wanted to restate those aspects in order to justify their answer. On the contrary, we found an intensive use of transitive verbs and words referred to the writer himself in association to right answers. This can be explained with the fact that transitive verbs are generally used for simple statements (e.g., facts, not hypothesis) in Italian, and that the use of “in my opinion” formula could be related to the willing of being honest and describing facts in a statement.
The main limitations of this work are the limited sample size (and thus a low statistical power) and the different size of each samples, as well as the possibility of the presence of other non-measured confounding variables (such as the working memory capacity of the participants, cultural differences, the IQ). Indeed, it is important to note that our results are also compatible with other explanations: for example, the higher proportion of correct answers of individuals participating in group discussion compared to the other condition could be explained in terms of diversity of ideas instigating individuals to think from different perspectives. With regard to the modelling attempts, we train the parameters of each model with the same datasets; in order to achieve an actual validation of such attempts, future research is required to test the models with other datasets.
Concluding, taking into account Bruner’s modes of thought in conjunctive reasoning can help to highlight how the narrative mode of thought is strongly associate to the violation of conjunction rule. This violation can be seen as a mistake by the normative criterion of probability theory, but it’s extremely likely within the narratives constructed by participants. Given the importance of dual-process theory of thought for prosocial behavior [28
], integrating Bruner’s perspective with the dual-process framework may give clues for the design of crowdsourcing technologies. Given the importance of dual-process theory of thought for prosocial behavior [28
], integrating Bruner’s perspective with the dual-process framework may give clues for the design of crowdsourcing technologies. In particular, both the size imposed to the operative sub-communities characterizing complex network devoted to crowdsourcing activities, as well as the narrative (i.e., the semantic and logical structures) adopted to present the issues should be designed considering also the factor under scrutiny in our research. In this way it should be possible to further improve the intervention effectiveness, and promote a specific cognitive approach (i.e., narrative versus paradigmatic) to the social interaction devoted to the crowdsourcing dynamics.