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1958, p. 9): "The revolution in heuristic problem solving will force man to consider his role in a world in which his intellectual power and speed are outstripped by the intelligence of machines. Fortunately, the new revolution will at the same time give him a deeper understanding of the structure and working of his own mind." It is interesting to note the significance attached by these authors to quantum mechanics in the same paper in these words: "In dealing with the ill-structured problems of management we have not had the mathematical tools we have needed—we have not had judgment mechanics' to match quantum mechanics" (p. 6). The expectations of Simon and Newell, expressed half a century ago, regarding the necessity of understanding of our own mind and a mechanics of the decision-making process are not yet fulfilled. However, we are now gaining momentum in the direction of understanding the human decision processes even through quantum mechanics. Thus, the objective of this paper is to introduce these concepts and review the recent progress to stimulate more exploratory research on applications of quantum mechanics concepts in decision making.
Kahneman, Tversky, and Shafir have made notable contributions in the area of judgment under uncertainty and the influence of heuristics and biases on the cognitive system (Tversky and Kahneman 1974, Tversky and Shafir 1992, Shafir and Tversky 1992). The significance of the work is attested to by the fact that Kahneman was awarded the Nobel Prize in 2002. Results of several experiments related to the judgment under uncertainty, as noted by Tversky and Shafir (Tversky and Shafir 1992, Shafir and Tversky 1992), in the area of human psychology could not be explained by the classical statistics. The disjunction effect experimentally observed by Tversky and Shafir (1992) is a typical example of the intricacies of the human mind that could not be understood by the classical decision theory. For example, in an experiment of Tversky and Shafir (1992), a participant is offered to play a gamble (by tossing a coin) with a 50% chance of winning $200 and a 50% chance of losing $100. After the first play, the participant is offered to play the second identical game with or without the knowledge of the outcome of the first gamble. It has been observed that a majority of participants are ready to accept the second gamble after knowing that they have won the first one, and a majority of participants are also ready to accept the second gamble after knowing that they have lost the first one, but only a small fraction of participants are ready to accept the second gamble if they do not know the outcome of the first gamble. The question arises: if they prefer to accept the second gamble in case they win or lose the first gamble, then according to the sure-thing principle of Savage (1954), they should prefer to accept the second gamble even when they do not know the
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