________________
outcome of the first gamble. However, the experiment contradicts such logical expectations. Why? We could not yet get the answer of this "why" from the conventional (classical) theories. Such a violation of the sure-thing principle of Savage (1954) has also been observed by Tversky and Shafir (1992) in another experiment related to buying an attractive vacation package.
The successful studies to explain some of these paradoxes by incorporating mathematical equations related with quantum mechanics into the psychology (Aerts 2009, Busemeyer et al. 2006, Pothos and Busemeyer 2009, Khrennikov 2009, Yukalov and Sornette 2009a) clearly reveal that some aspects of the human behavior, which could not yet be explained by the classical decision theory, can be explained by quantum mechanical equations. The investigations of Bordley (1998) and Bordley and Kadane (1999) also suggest the importance of quantum mechanical notions and equations in explaining some aspects of human decision making. It may be noted that classical mechanics and quantum mechanics differ ideologically as well as mathematically; and for macrosystems the approximate form of mathematical equations of quantum mechanics agrees with the equations of classical mechanics.
If the decision-making processes of the human mind follow the probabilistic behavior of quantum mechanics, then one can expect the applicability of the same in other areas, which are directly affected by human decision making. Thus, it is not surprising that researchers in economics and finance have explored application of quantum mechanics (Baaquie 2004, Bordley 2005, Kondratenko 2005, Baaquie 2009a). The application of quantum mechanics to economics and finance can be seen in various areas, such as a price dynamics model (Choustova 2007), stock price (Schaden 2003, Bagarello 2009), interest rate (Baaquie 2009b), incorporation of private information (Ishio and Haven 2009, Haven 2008), etc. As an example of the value of quantum mechanics in the field of economics, one can refer to the study conducted by Segal and Segal (1998). In this study they consider quantum effects to explain extreme irregularities in the evolution of prices in financial markets. In the concluding paragraph of this study, Segal and Segal (1998, p. 4075) write: "The quantum extension of Black-Scholes-Merton theory provides a rational, scientifically economical, and testable model toward the explanation of market phenomena that show greater extreme deviations than would be expected in classical theory 0000"
In Appendix-A in the e-companion, we have described some facts related to the historical development of quantum mechanics. At the beginning of the twentieth
104
