Mathematical principles of probability entail that for any future event, the probability that it will occur Is at least as great as the probability that both it and some other given event will occur. Consider, for example, the following statements that were shown to subjects in a 1998 study.
X The percentage of adolescent smokers In Texas will decrease at least 15% from current levels by September 1, 1999.
Y The cigarette tax in Texas will increase by $1.00 per pack in 1999.
Z The cigarette tax in Texas will increase by $1.00 per pack in 1999, and the percentage of adolescent smokers in Texas will decrease at least 15% from current levels by September 1, 1999.
Z("Kand X") could not have been more probable than X. Nevertheless, many of the subjects judged Zto be more probable than X. This mistaken form of reasoning, displayed with surprising frequency in various studies in addition to the 1998 study, is known as the "conjunction fallacy."
A number of researchers have offered alternative explanations for the seeming manifestations of the mistake, thus arguing that the fallacy is less widely committed than the various studies would indicate. Some have claimed that research subjects can take "probability" in a sense that does not conform to the mathematical principles of probability. Detailed descriptions of some such conceptions of "probability" have been developed under the names of "confirmation" and "support." Other researchers would claim, correctly, that subjects shown Z(" Kand X") and ^simultaneously will sometimes think of Xas involving the negation of Y—as a claim that the percentage of adolescent smokers in Texas will decrease, but without the $1.00 increase in the cigarette tax.
However, although the subjects in the 1998 study were to consider Xand Z simultaneously, the statements were presented in terms of bets rather than explicit requests for judgments of relative probability. Subjects were asked to choose between Zand X, with a chance of winning $50.00 if the chosen statement turned out to be true. Terms such as "most probable," "likely," etc., were thus avoided, and the interpretation of X\n conjunction with the negation of Kwas thereby eliminated. And with these alternative explanations eliminated, many of the subjects nonetheless bet on Zrather than X:
