Cross-cultural comparison of responses to the Monty Hall dilemma

Social Behavior and Personality, 1999 by Granberg, Donald

Students in Brazil, China, Sweden, and the United States were compared as to how they responded to a two-stage conditional probability problem. In each culture, there was not only a significant tendency to stick with an itial decision when they should stick, but also to stick when they should switch. On this type of problem, the four cultures did not differ significantly.

This article reports data from a cross-cultural comparison of responses to a two-stage decision problem involving conditional probability. That problem is the "notorious" Monty Hall Dilemma (MHD). In the MHD, a subject makes a tentative guess as to which of three doors contains a valuable prize. Then the host reveals the contents behind one of the unchosen doors, showing it to be a loser. The host then gives the subject a choice of sticking with their initial guess or switching to the other remaining door. The dilemma or problem is whether one would stick or switch, given the events which have already transpired. Provided certain key assumptions are built into the instructions, the rational solution in the MHD is to switch. By switching one wins with a 2/3 probability, while sticking yields only a 1/3 chance of winning (Engel & Venetoulias, 1991; Falk, 1992; Friedman, 1998; Georges & Craine, 1995; Selvin, 1975; Shaughnessy & Dick, 1991).

To the U.S. subjects tested in the initial MHD studies, this solution seemed highly counterintuitive:; consequently, they showed a strong tendency to stick when they should have switched (Granberg & Brown, 1995; Granberg & Dorr, 1998). This raises a question that can be addressed only through cross-cultural comparisons. Is there something inherent in the intersection between human cognition and the MHD itself, which leads people generally to stick in this two-stage decision when they should switch? Or is there something specific to the socialization process in the U.S. which leads people reared in the U.S. to respond predominantly in an incorrect way to the MHD?

This way of framing the research question parallels that used by Segall, Campbell and Herskovits, (1966) in their research on the susceptibility of people in various cultures to optical illusions. They referred to the question as the "nativist-empiricist controversy," the former predicting similarities across cultures and the latter predicting differences, due to varying learning experiences. The MHD can be considered a cognitive illusion (Gilovich, 1991); that is, the odds appear to be 50:50, when, in fact, they are 2:1.

While the subjects in the initial U.S. studies showed a strong and significant tendency to stick in the MHD, there were, nonetheless, indications that the situation is at least somewhat fluid. Although a sizeable majority (80-90%) decided to stick in their first encounter with the MHD, the tendency was certainly not invariant - as some subjects did decide to switch (Granberg & Brown, 1995). A further indication of fluidity is provided by Gilovich, Medvec and Chen, (1995) who showed that a confident and assertive confederate can successfully influence a subject to switch (or stick) in the MHD. This fluidity implies that the way in which a cross-cultural comparison of responses to the MHD will turn out is by no means a foregone conclusion.

Part of the difficulty which some people have with problems involving conditional probability has to do with ambiguity in the way in which the question is stated (Bar-Hillel & Falk, 1982; Falk, 1992; Nickerson, 1996). Therefore, in devising the wording for the MHD, an effort was made to minimize ambiguity and to build into the wording certain key assumptions. For the 2/3 solution to obtain in the MHD, it is necessary to assume that the host knows both the location of the prize and the subject's initial guess, and uses that knowledge to show deliberately an incorrect, unchosen alternative after the subject has made her initial guess. It is further assumed that the host is committed to the procedure of opening an unchosen incorrect door, and to giving the contestant the choice of whether to stick or to switch. Without evidence to the contrary, it is reasonable to assume also that the three doors are initially equally likely to contain the prize, and that when the subject's initial guess is correct, the host chooses randomly which of the other two doors to open.

Insofar as it was possible, these crucial assumptions were built into the wording of the MHD problem used in this research. They were kept in mind also as the problem was translated into Chinese, Portuguese, and Swedish and then backtranslated into English prior to use in the cross-cultural phase of the study. The goal in this initial study was to have about 200 undergraduate students, divided about equally by gender, in each of four countries think about-and respond toan MHD-type of problem.

As a further comparison, within each country, about half of the subjects responded to the standard MHD, while the other half responded to an inverted form of the MHD called the "Russian Roulette Dilemma" or RRD. In the RRD, there is a valuable prize behind each of two doors, and there is only one losing door. The subject selects a door, and then the host opens and eliminates one of the other doors which had been a potential winner. The subject is then given the choice of sticking with her initial selection or switching to the other remaining door.