Seminar:" Quantum Decision Theory (QDT) In Social Science"
Speaker: Dr. Sudip Patra
The anomalies which have been found between the standard utility maximization theory and the real life data, have been classified under various categories, such as, failure of the sure thing principle (which is a central premise of the expected utility theory, EUT), presence of disjunction effects in decision making, presence of order effects in decision making, and overall the failure of the basic law of total probability in decision making under the contexts of ambiguity and uncertainty. Again the failure of EUT to predict such behaviors also indicates the failure of classical probability theory/ classical Boolian logic theory in predicting human behavior in such contexts. The reason being that the standard EUT upon which the decion theory/ the standard Neoclassical paradigm is based is again based on the classical set theory of probability. Kolgomorov (1933) provided the modern foundation of the measure theory of probability, which is deeply embedded in the Boolian logic theory. Again the later developments in the line of Bayesian probability updating theory/ Bayesian learning theory is also deeply embedded in the classical probability theory only. For example the law of total probability which is central to the Bayesian paradigm is basically derived from the set theory of probability. Given this backdrop QDT has emerged as a strong alternative for decision making theory in general. Again the reason for QDT‘s success in explaining the paradoxes (as mentioned above) is based on the fact that QDT is essentially a non-classical logic based theory. The probability measure in QDT is based on the Hilbert space formulation, which is in general an infinite dimensional complex space (in social sciences however we can workwith the finite dimensional real subspace of the total Hilbert space), and the measurement of probability is based on the projector measure (either standard projection operators as used in Quantum Mechanics or more general POVM operators which are more suitable for specific scenarios in decision making contexts, for example un-sharp measurements) which collapses (as in the standard Copenhagen version of QM) the general superposed mental state/ belief state of the agents into Eigen subspaces of the Hilbert space, which then becomes the final state of belief. Hence QDT helps us in one, measure the probability of choosing a specific decision state, and two, helps updating the belief state of the decision maker accordingly. There are alternative mathematical formulations available for such measurements(please refer to, Quantum Social Science, 2013). The striking success of QDT is evident from the significantly better match of the predictions with the real data points, in various scenarios, from prisoners dilemma experiments to asset pricing theory to general probability updating. In probability updating too QDT can avoid some central problems which Bayesian probability updating face, namely, the zero prior updating problem, hence this theory can be used in special scenarios where agents do update their posteriors to high values given that prior probabilities are near zero/ non informative, which is impossible in Bayesian paradigm (Haven and Khrennikov, 2013).
About the Speaker:
Dr. Sudip Patra is Ph. D. from Glasgow University, UK and currently working as Assistant Professor at Jindal Global University, Haryana.