Cheon, Taksu; Takahashi, Taiki Interference and inequality in quantum decision theory. (English) Zbl 1241.81010 Phys. Lett., A 375, No. 2, 100-104 (2010). Summary: The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data indicating the breakdown of classical explanations are critically examined with quantum theory using the full set of quantum phases. Cited in 11 Documents MSC: 81P13 Contextuality in quantum theory 62C12 Empirical decision procedures; empirical Bayes procedures Keywords:contextual probability; sure-thing principle; quantum phase PDFBibTeX XMLCite \textit{T. Cheon} and \textit{T. Takahashi}, Phys. Lett., A 375, No. 2, 100--104 (2010; Zbl 1241.81010) Full Text: DOI arXiv References: [1] Aerts, D.; Aerts, S., Found. Sci., 1, 8597 (1994) [2] Pothos, E. M.; Busemeyer, J. R., Proc. R. Soc. B, 276, 2171 (2009) [3] Khrennikov, A. Yu.; Haven, E., J. Math. Psychol., 53, 378 (2009) [4] Shafir, E.; Tversky, A., Cogn. Psychol., 24, 449 (1992) [5] Tversky, A.; Shafir, E., Psychol. Sci., 3, 30509 (1992) [6] von Neumann, J.; Morgenstern, O., Theory of Games and Economic Behavior (1947), Princeton Univ. Press · Zbl 1241.91002 [7] Savage, L. J., The Foundation of Statistics (1954), Wiley: Wiley New York [8] Lüders, G., Ann. Phys. (Leipzig), 8, 322 (1951) [9] von Neumann, J., Mathematical Foundations of Quantum Mechanics (1955), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ [10] Gisin, N., Phys. Rev. Lett., 52, 1657 (1984) [11] Croson, R., Organ. Behav. Hum. Decis. Process., 180, 118 (1999) [12] Li, S.; Taplin, J., Chin. J. Psychol., 44, 25 (2002) [13] Matthew, M.; Busemeyer, J. R.; Wang, Z. A., Quantum game theory explanation of disjunction effects, (Sun, R.; Miyake, N., Proc. 28th Ann. Conf. Cogn. Sci. Soc. (2006)), 131 [14] Meyer, D. A., Phys. Rev. Lett., 82, 1052 (1999) [15] Eisert, J.; Wilkens, M.; Lewenstein, M., Phys. Rev. Lett., 83, 3077 (1999) [16] Cheon, T., Phys. Lett. A, 318, 327 (2003) [17] Cheon, T.; Tsutsui, I., Phys. Lett. A, 348, 147 (2006) [18] Cheon, T.; Iqbal, A., Phys. Soc. Jpn., 77, 024801 (2008) [19] Bell, J. S., Physics, 1, 195 (1964) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.