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Reasoning and choice in the Monty Hall Dilemma (MHD): implications for improving Bayesian reasoning.

Tubau E, Aguilar-Lleyda D, Johnson ED - Front Psychol (2015)

Bottom Line: The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize.Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning.Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities.

View Article: PubMed Central - PubMed

Affiliation: Departament de Psicologia Bàsica, Facultat de Psicologia, Universitat de Barcelona, Barcelona Spain ; Research Institute for Brain, Cognition and Behavior, University of Barcelona, Barcelona Spain.

ABSTRACT
The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning.

No MeSH data available.


Related in: MedlinePlus

Card shown by the informant (analogous to the host in the MHD) in six hypothetical repetitions of the game. Notice that among the three times that the informant shows the 7 (or the 8) he hides the ACE twice (adapted from Tubau, 2008).
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Figure 2: Card shown by the informant (analogous to the host in the MHD) in six hypothetical repetitions of the game. Notice that among the three times that the informant shows the 7 (or the 8) he hides the ACE twice (adapted from Tubau, 2008).

Mentions: For example, Krauss and Wang (2003; Experiment 3) compared the utility of an intervention based on a simplified representation of only three arrangements (similar to first three possibilities in Table 1) with a more complete representation of six arrangements (mental model representation from Johnson-Laird et al., 1999; similar to the diagram shown in Figure 2, but including the complete representation of each possibility instead of the frequency information). Results showed that the three-arrangements version promoted more correct responses. The benefit of the simplified representation was interpreted as a consequence of its higher resemblance to a natural frequency format (Krauss and Wang, 2003). However, it is not clear which words and numbers were included in the question requiring the probability judgment. As shown in other Bayesian problems, the match between the text of the problem and the text of the question has a significant effect on the responses (Girotto and Gonzalez, 2001; Ayal and Beyth-Marom, 2014). If the question was the same as in Kraus and Wang’s Experiment 2, then there would be a better match between the question (___ out of 3) and the simplified representation (three arrangements) than between the question and the complete version (six models). So, it could be the case that the more complete representation was less effective due to the additional steps needed to transform presented information into the form requested in the question.


Reasoning and choice in the Monty Hall Dilemma (MHD): implications for improving Bayesian reasoning.

Tubau E, Aguilar-Lleyda D, Johnson ED - Front Psychol (2015)

Card shown by the informant (analogous to the host in the MHD) in six hypothetical repetitions of the game. Notice that among the three times that the informant shows the 7 (or the 8) he hides the ACE twice (adapted from Tubau, 2008).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4379739&req=5

Figure 2: Card shown by the informant (analogous to the host in the MHD) in six hypothetical repetitions of the game. Notice that among the three times that the informant shows the 7 (or the 8) he hides the ACE twice (adapted from Tubau, 2008).
Mentions: For example, Krauss and Wang (2003; Experiment 3) compared the utility of an intervention based on a simplified representation of only three arrangements (similar to first three possibilities in Table 1) with a more complete representation of six arrangements (mental model representation from Johnson-Laird et al., 1999; similar to the diagram shown in Figure 2, but including the complete representation of each possibility instead of the frequency information). Results showed that the three-arrangements version promoted more correct responses. The benefit of the simplified representation was interpreted as a consequence of its higher resemblance to a natural frequency format (Krauss and Wang, 2003). However, it is not clear which words and numbers were included in the question requiring the probability judgment. As shown in other Bayesian problems, the match between the text of the problem and the text of the question has a significant effect on the responses (Girotto and Gonzalez, 2001; Ayal and Beyth-Marom, 2014). If the question was the same as in Kraus and Wang’s Experiment 2, then there would be a better match between the question (___ out of 3) and the simplified representation (three arrangements) than between the question and the complete version (six models). So, it could be the case that the more complete representation was less effective due to the additional steps needed to transform presented information into the form requested in the question.

Bottom Line: The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize.Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning.Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities.

View Article: PubMed Central - PubMed

Affiliation: Departament de Psicologia Bàsica, Facultat de Psicologia, Universitat de Barcelona, Barcelona Spain ; Research Institute for Brain, Cognition and Behavior, University of Barcelona, Barcelona Spain.

ABSTRACT
The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning.

No MeSH data available.


Related in: MedlinePlus