Reasoning: Analysis of the effects of context on the rate of conjunctive responses in the probabilistic truth table task
By: Christos Theodoropoulos
Tags: Reasoning, Psychology, Cognitive Science, Cognition, Decision Making

Discussion & Elaboration

Overall, the results of the experiment declared that the responses to conditional statements of the form “If A then C” can be affected by small changes in the context of the task and the way of the material is presented [1]. More concretely, when the problem was framed as the throw of a die the conjunctive interpretations were increased. Generally, people estimate probabilities based on their experience and what they can retrieve. In the case of the dice, most of the participants had experience with probability problems related with dice during their education. So, they tend to use as availability heuristic that in the problems with representation of a die the entire set of possibilities (the six sides of the die) should be taken into account. On the other hand, framing the context as a deck of cards, conditional responses were increased. The positioning of the different logical cases didn’t affect significantly the responses of the participants in a straight-forward manner, but it played an important role in the shifting towards the conditional interpretation mainly. It would be a good idea to ask participants for feedback about any possible shift after the completion of the trials. This step would give insightful information about the reasons, which made the participants change their interpretation.

As Jubin and Barrouillet mentioned, “the findings of the experiment supports the hypothesis that the responses to the probabilistic truth table do not entirely depend on the interpretation of the conditional, but also on the second step identified by Pfeifer [2] on inferring the probability” [1]. In other words, “a same interpretation can lead to different responses” [1]. It is not clear how participants understand the question in order to give a final response. There is a possibility that actually some of them interpret the problem as finding a conditional probability, however, their final response corresponds to conjunctive probability. As the results of the experiment shown, changes on the context and the positioning of the logical cases, without indeed changing the conditional sentence, affected the way participants decoded the question and inferred the probability.

Actually, the conditional and conjunctive probability have the same numerator but the denominator of the fraction is different. Based on A and C facts, the numerator is A and C logical cases, where the denominator is A case for the conditional probability and all cases, A and ¬A, for the conjunctive probability. The findings of the study presented that the activation of knowledge of previous probabilistic problems related to dice affected the final response of some participants [1]. This evidence challenges the reliability, robustness and added value of the probabilistic truth table task as a method to understand the interpretation of conditional probabilistic statements.

Clearly, the difference between conditional and conjunctive probability is ¬A cases. Studies with traditional truth tables, before the emergence of the new paradigm psychology of reasoning, mentioned that the predominance of conditional responses is a result based on the participants’ (majority) decision that the ¬A cases are irrelevant for assessing thetruth value of the conditional [1]. With that in mind, the probabilistic truth table task is not more informative than the traditional approach, for the way of interpreting and understanding probabilities [1]. Additional feedback from conjunctive responders and participants that shift towards conditional responses through the experiment trials may give insightful information.

Except for the hard evidences that context and way of positioning affected the responses of the participants, interpreting the responses observed in the task from a psychological perspective is challenging. The predominance of conditional responses does not necessarily mean that the participants approached the problem from a pure probabilistic view [1].One of the most popular theory of reasoning, mental model theory (Johnson-Laird), is able to provide an end-to-end explanation of the experiment results. This theory suggests that people do not access the probabilities directly, they create appropriate mental simulations in order to infer probabilities based on the provided premises. This means that the ability of answering correctly probabilities problems relies on the capability of constructing highly representative mental models based on the given facts. Previous studies [3], [4], [5], [6] gave credits to that fundamental theory of reasoning.

In the current study, the findings can be explained on the basis of two steps of creating mental models. The vast majority of the participants gave consistent responses, either conditional or conjunctive). So, the initial mental model, which they construct, was that for capturing (A & C) logical cases (numerator of the probability fraction). The more difficult part of the process was the second stage, the construction of the additional models in order to define the basis of the probability. More precisely, the second stage was about creating representation in order to exclude the ¬A cases from the basis. This happens by creating two mental models for (¬A & C) and (¬A& ¬C) cases [1]. With that in mind, conjunctive responders may be unable to create the models of the second stage in order to remove the unwanted cases for calculating the conditional probability. “Mental models, it is argued, offer economical forms of representation that appear psychological plausible. Johnson-Laird [8] proposed that models are built in accordance with the principle of truth and wrote: ‘Individuals minimizethe loadon working memory by tending to construct mental models that represent explicitly only what is true and not what is false.’ This incompleteness is a source of error in dealing whit reasoning tasks.” [7]

This inability of producing the mental models of the second stage can be also supported by the dual process theories. Based on this wave of thought, there are two different cognitive systems. “System 1” is automatic, effortless, is related to heuristic fast processing and leads to intuitive cognition, while “System 2” is related to analytic processing and leads to analytical and rational cognition [9]. So, the easier part of creating the initial model for (A & C) cases could be a result of heuristic System 1 (thinking fast). On the other hand, the more complex second step requires the effective, rule-based and analytical System 2 (thinking slow). Conjunctive responders probably did not use the System 2 and stopped after the automatic heuristic process [4], [5], [6]. This could be also a result of the belief-bias effect, especially when the context was related to the sides of a die. Prior beliefs and experience could influence the reasoning of the participants. On the other hand, conditional responders may use the System 2 in order to use their working memory and analytical capabilities and exclude the ¬A cases [4], [5], [6]. Dual processing approach can also explain the shift towards conditional responses. As the System 1 precedes the System 2, some conjunctive responders used their analytical system throughout the experiments trials in order to realize that they should give conditional responses [1].

Conclusion

The probabilistic truth table task seeks to examine the interpretative procedure of the conditional statement “If A then C”. However, this study and the extended discussion based on the results, point out that a cognitive processing step is involved. The desired outcome that the meaning of conditional is probabilistic in nature (new paradigm of psychology) is not fundamentally proved [1]. Approaches based on Mental Model Theory and Dual Processing Theories could give rational and well-defined explanations for the findings of the experiment procedure. Based on those facts, the validity of the probabilistic task in studying conditional reasoning should be questioned [1].