Correct Belief, Wrong Action and a Puzzling Gender Difference

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Abstract
We asked subjects to self-select into one of two contests, "coin" or "die." The winner in each of the contests is the person with most correct guesses of 20 coin flips or 20 rolls of a die, respectively. Most subjects reported that they believed that most people would go to the "coin" group. They were correct. Although the right action under this belief is to choose "die" most people chose to be with the majority. Both men and women tended to make this mistake, but women's propensity to err in this particular experiment was stronger. This is puzzling as our overall impression (based on preliminary experiments which were not documented scientifically) does not support the existence of gender differences in other strategic situations.