Influence of display on resistance to change, facing the cognitive illusion induced by the “Monty Hall Dilemma”

Abstract

Under some conditions, reasoning can induce systematical biases in judgment known as cognitive illusions. Similar to optical illusions, cognitive illusions are likely to generate non-optimal behaviours. One of the most investigated cognitive illusions is the Monty Hall dilemma. In its standard version, a subject must make a choice between three cups with one of them hiding a reward. Once the subject has made a random choice, the researcher removes one of the remaining cups under which there is no reward and offers the subject a chance to change his first choice. Despite the cognitive illusion that the odds of winning are the same as sticking to their first choice, the subject is well advised to change this first choice since the odds of winning are now 2/3 by changing his choice as opposed to 1/3 by keeping his first choice. The purpose of this research is to investigate the effect of another display of the dilemma, by using three cards : a first one red on both sides, a second one white on both sides, and a third one red on either side and white on the other. Firstly, we compared the cognitive illusion brought about by Monty Hall dilemma in its standard version to that with three cards. We then asked the subject what the chances were that a card, put on the table and presenting a red side, would be red on both sides. Here again, the chances are not 1/2 but 2/3. Secondly, so as to increase the cognitive illusion effect, two cards only have been used : the card red on both sides and the card red on either side, insofar as the card white on both sides would never show a red side and had therefore to be excluded. We then asked the subject what the chances were that a card laid down on a table and showing a red side, would be red on both sides. Here again, the chances were not 1/2 but 2/3. Thirdly, we experimented to what extent a card whose apparent side is red could happen to have a white match on its other side. Here, by definition, the chances are not 1/2 but 1/ 3. Results tend to show that the illusion is so strong that the paradox remains, whatever the equipment used.