Social Behavior and Personality: Cross-cultural comparison of responses to the Monty Hall dilemma

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.

Although the MHD and RRD are similar in structure and sequence, nonetheless, they are drastically different. The rational solution in the MHD is to switch in the final stage, while in the RRD the rational solution is to stick with one's initial guess (Granberg, 1996). In either case, following the rational solution yields a 2/ 3 chance of winning.

The four countries (Brazil, China, Sweden, U.S.) were chosen on the basis of the author's available contacts. However, everyone can agree that the variance among these cultures is very substantial. The research was considered exploratory so no directional predictions were made. Some of the comparisons are of obvious interest. For instance, it is known that students in China do much better on a variety of mathematics tests than students in the U.S., even when intelligence is carefully controlled (Geary et al., 1997). However, it is not known whether such differences extend to problems involving conditional probability.

METHOD

The U.S. data were gathered in undergraduate sociology and social psychology classes at the University of Missouri with 83 men and 107 women subjects. The Swedish data were collected as part of a survey of first year students in the departments of political science, journalism, and public administration at Goteborg University. This Swedish sample was comprised of 160 men and 186 women. The respondents in China were 136 students at East China Normal University and 63 students at Fudan University. The Chinese subjects were all first year students, averaging 18 years of age; these 99 men and 100 women were majoring in a variety of academic disciplines. The Brazilian sample was slightly older, averaging 21 years of age, and was evenly divided among social science, commerce, philosophy, and psychology majors. This sample of 200 consisted of half men and half women students.

In each country about half of the students were randomly assigned to answer a form containing the MHD; the other half were given a form containing the RRD. Overall, 472 subjects in four countries answered the MHD version and 463 subjects answered the RRD version. The wording for the MHD was as follows:

"Suppose you are a contestant on a game show. The host, who is known to be completely honest, has placed a new car behind one of three doors and a goat behind each of the other doors. `First you point to a door,' the host says. `Then I'll open one of the other doors and show that it has a goat. After I've shown you the goat, you make your final choice, and you win whatever is behind that door.' You begin by pointing to a door, say door number 2. The host then shows you that door 1 has a goat. What would your final choice be? Would you stick with door 2 or switch to door 3?" The wording for the RRD version was as follows:

"Suppose you are a contestant on a game show. The host, who is known to be completely honest, has placed a new car behind each of two of three doors and a goat behind the other door. `First you point to a door,' the host says. `Then I'll open one of the other doors and show that it has a car. That door will no longer be available to you. After I've shown you that door with a car, you make your final choice, and you win whatever is behind that door.' You begin by pointing to a door, say door number 2. The host then shows you that door 1 has a car. What would your final choice be? Would you stick with door 2 or switch to door 3?"

RESULTS

Continued from page 1.

The main results are summarized in Table 1. In each country people responded similarly to the MHD by showing a strong tendency toward the nonoptimal answer of sticking with their initial selection. The percentage of subjects who checked "stick" in the MHD overall was 83%, and ranged between only 79% for China and 87% for Brazil. The U.S. and Sweden were intermediate with 84% and 83%, respectively, checking that they would stick. These four percentages are not significantly different from one another (x^sup 2^ = 2.18, df = 3, p > .OS); however, in each country, the observed split departed significantly from a 50-50 distribution (p

Similar results were found for the RRD. On this problem, for which the optimal solution is to stick, the percentage sticking was 84% overall, 78% for Brazil, 81% for China, 85% for the U.S., and 87% for Sweden. Once again, the four countries were not significantly different from each other (ZZ = 4.44, df =3, p > .OS), but the subjects within each country showed a significant departure from a chance distribution of 50-50 (p

Within each country, the responses to the MHD were not significantly different from those for the RRD. The largest difference occurred in the case of Brazilian subjects, 87% of whom chose to stick in the MHD, compared to 78% in the RRD. This difference is in the opposite direction from rationality, but the difference of 9 percentage points is not statistically significant (p > .OS). Thus, to paraphrase Granberg and Brown (1995), people within each of these four rather different cultures showed a strong tendency to stick when they should stick but also tended to stick when they should have switched.

Combining across cultures and across the type of problem, women were more likely to indicate "stick" (86%) than were men (81%). Thus, the main effect of gender implies a slight and marginally significant tendency for women, more than men, to stick more in two-stage decisions (x^sup Z^ = 3.91, dfl, p

DISCUSSION

The gender effect which we observed was no more than a slight difference, and it is not easy to replicate. The safest statement to make is that if there is a difference, women may be ever so slightly more likely to stick with an initial judgment in a two-stage decision. However, the difference is so small that it does not warrant much attention.

Our main finding is of cross-cultural similarity in the tendency of people to respond erroneously to the MHD type of two-stage decision problem. Thus, it appears that there is something inherent in the MHD, as a cognitive illusion, which leads people in very different cultures to respond similarly. People misapprehend the true probabilities, perceiving the odds to be even, and then tend to stick with their original selection. They are probably seeking to avoid the greater negative affect associated with being wrong after switching away from the winning alternative (Granberg & Brown, 1995). Because the four cultures studied encompass very considerable variety, the temptation is to infer that the tendency to stick in the MHD reflects a universal human propensity; it may, however, be premature to go that far.

It can be argued also that while the wording was made as nearly the same as possible, the actual meaning of the problem posed may have been quite different. That is, people may have been responding similarly - but for different reasons. In retrospect, perhaps the problem should have concerned some valuable prize other than a new car. It is difficult to say exactly what meaning the problem had for the Chinese students, living in a country with fewer televisions and cars per capita and to whom the game show format may have been relatively unfamiliar. However, that would create more of an interpretive problem if the Chinese students had responded differently, but they did not. The game show format is highly familiar in the other countries, Brazil and Sweden, and, of course, the U.S. where the show "Let's Make a Deal," with Monty Hall as host, originated.

Another objection concerns what motivation or incentive the subjects had to do well, i.e., to solve the problem correctly. However, evidence from laboratory experiments using an MHD type of problem with real monetary incentives implies that the tendency to stick with a preliminary, revocable decision observed in the four cultures in the current study does not exaggerate what would be observed if real prizes were at stake (Granberg & Brown, 1995; Friedman, 1998; Granberg & Dorr, 1998). Also, the fact that people in each culture departed significantly from a 50-50 distribution of responses is a strong indication that these subjects were giving their best estimate of what they would actually do, and were not responding randomly.

People in any culture can, of course, learn to solve conditional probability problems successfully--even though they are not easy. Such problems often involve counterintuitive solutions and cannot be solved correctly merely by applying everyday common sense. This type of problem can be referred to as a biologicalsecondary task, and therefore, one would predict greater success for a given culture only if that type of problem were emphasized and practised in schools or elsewhere in that culture (Geary, 1995).

REFERENCES

Bar-Hillel, M., & Falk, R. (1982). Some teasers concerning conditional probabilities. Cognition, 11, 109-122.

Engel, E., & Venetoulias, A. (1991). Monty Hall's probability puzzle. Chance, 4(2), 6-9. Falk, R. (1992). A closer look at the probabilities of the notorious three prisoners. Cognition, 43, 197223.

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Gilovich, T., Medvec, V., & Chen, S. (1995). Commission, omission, and dissonance reduction: Coping with regret in the "Monty Hall" problem. Personality and Social Psychology Bulletin, 21, 182-190.

Granberg, D. (1996). To switch or not to switch. Pp. 169-196 in M. vos Savant (ed.) The power of logical thinking. New York: St. Martin's Press.

Granberg, D., & Brown, T. (1995). The Monty Hall dilemma. Personality and Social Psychology Bulletin, 21, 711-723.

Granberg, D., & Dorr, N. (1998). Further exploration of two stage decision making in the Monty Hall dilemma. American Journal of Psychology, 111, 561-579.

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Segall, M., Campbell, D., & Herskovits, M. (1966). The influence of culture on visual perception.

DONALD GRANBERG University of Missouri, MO, USA

Donald Granberg, Professor of Sociology, University of Missouri - Columbia, MO, USA.

The author thanks Liu Fan, David Geary, Mikael Gilljam, Chen Go-peng, Soren Holmberg, Suli Jia, Andrea Moraes, Renata Moraes, Anna Ronstrom, and Anders Widfeldt for their advice and assistance. Copies of the questionnaire in the Chinese, Portuguese, and Swedish versions are available upon request to the author.

Please address correspondence and reprint requests to: Donald Granberg, Department of Sociology, University of Missouri, Columbia, Missouri, USA, 65211. E-Mail: