In mathematical physics and psychology, “quantum decision theory” has been proposed to explain anomalies in human decision-making. One of such quantum models has been proposed to explain time inconsistency in human ...In mathematical physics and psychology, “quantum decision theory” has been proposed to explain anomalies in human decision-making. One of such quantum models has been proposed to explain time inconsistency in human decision over time. In this study, we conducted a behavioral experiment to examine which quantum decision models best account for human intertemporal choice. We observed that a q-exponential model developed in Tsallis’ thermodynamics (based on Takahashi’s (2005) nonlinear time perception theory) best fit human behavioral data for both gain and loss, among other quantum decision models.展开更多
Probability discounting is defined as the devaluation of outcomes as the probability of receiving or paying those decreases. A q-exponential probability discounting model based on Tsallis’ statistics has been propose...Probability discounting is defined as the devaluation of outcomes as the probability of receiving or paying those decreases. A q-exponential probability discounting model based on Tsallis’ statistics has been proposed in econophysics (Takahashi, 2007, Physica A). We examined (a) fitness of the models to behavioral data of probability discounting of both gain and loss;and (b) relationships between parameters in the q-exponential probability discounting model across gain and loss. Our results demonstrated that, for both gain and loss, the q-exponential model better fits the behavioral data than exponential and hyperbolic functions, and there is the sign effect in q-exponential probability discounting. Relationships between Kahneman-Tversky’s prospect theory in behavioral economics and the q-exponential probability discounting are high-lightened.展开更多
Anomalies in decision over time (e.g., “hyperbolic time discounting”) and under risk (e.g., Allais paradox and hyperbolic probability discounting) have been attracting attention in behavioral and neuroeconomics. We ...Anomalies in decision over time (e.g., “hyperbolic time discounting”) and under risk (e.g., Allais paradox and hyperbolic probability discounting) have been attracting attention in behavioral and neuroeconomics. We have proposed that psychophysical time commonly explains anomalies in both decisions (Takahashi, 2011, Physica A;Takahashi et al., 2012, J Behav Econ & Finance). By adopting the q-exponential time and probability discounting models, our psychophysical and behavioral economic experiment confirmed that nonlinear distortion of psychophysical time is a common cause of the anomalies in decision both over time and under risk (i.e., intertemporal choice and decision under risk). Implications for psychophysical neuroeconomics and econophysics are discussed.展开更多
Mathematical frameworks of quantum theory have recently been adopted in cognitive and behavioral sciences, to explain the violations of normative decision theory and anomalies in cognition. However, to date, no study ...Mathematical frameworks of quantum theory have recently been adopted in cognitive and behavioral sciences, to explain the violations of normative decision theory and anomalies in cognition. However, to date, no study has attempted to explore neural implementations of such “quantum-like” information processing in the brain. This study demonstrates that neural population coding of information with nonlinear neural response functions can account for such “quantum” information processing in decision-making and cognition. It is also shown that quantum decision theory is a special case of more general population vector cording theory. Future applications of the present theory in the rapidly evolving field of “psychophysical neuroeconomics” are also discussed.展开更多
Whether people tend to punish criminals in a socially-optimal manner (i.e., hyperbolic punishment) or not is unknown. By adopting mathematical models of probabilistic punishment behavior (i.e., exponential, hyperbolic...Whether people tend to punish criminals in a socially-optimal manner (i.e., hyperbolic punishment) or not is unknown. By adopting mathematical models of probabilistic punishment behavior (i.e., exponential, hyperbolic, and q-exponential probability discounting model based on Tsallis thermodynamics and neuroeconomics, Takahashi, 2007, Physica A;Takahashi et al., 2012, Applied Mathematics), we examined 1) fitness of the models to behavioral data of uncertain punishment, and 2) deviation from the socially optimal hyperbolic punishment function. Our results demonstrated that, the q-exponential punishment function best fits the behavioral data, and people overweigh the severity of punishment at small punishing probabilities and underweigh the severity of punishment at large punishing probabilities. In other words, people tend to punish crimes too severely and mildly with high and low arrest rate (e.g., homicide vs. excess of speed limit), respectively. Implications for neuroeconomics and neurolaw of crime and punishment (Takahashi, 2012, NeuroEndocrinology Letters) are discussed.展开更多
文摘In mathematical physics and psychology, “quantum decision theory” has been proposed to explain anomalies in human decision-making. One of such quantum models has been proposed to explain time inconsistency in human decision over time. In this study, we conducted a behavioral experiment to examine which quantum decision models best account for human intertemporal choice. We observed that a q-exponential model developed in Tsallis’ thermodynamics (based on Takahashi’s (2005) nonlinear time perception theory) best fit human behavioral data for both gain and loss, among other quantum decision models.
文摘Probability discounting is defined as the devaluation of outcomes as the probability of receiving or paying those decreases. A q-exponential probability discounting model based on Tsallis’ statistics has been proposed in econophysics (Takahashi, 2007, Physica A). We examined (a) fitness of the models to behavioral data of probability discounting of both gain and loss;and (b) relationships between parameters in the q-exponential probability discounting model across gain and loss. Our results demonstrated that, for both gain and loss, the q-exponential model better fits the behavioral data than exponential and hyperbolic functions, and there is the sign effect in q-exponential probability discounting. Relationships between Kahneman-Tversky’s prospect theory in behavioral economics and the q-exponential probability discounting are high-lightened.
文摘Anomalies in decision over time (e.g., “hyperbolic time discounting”) and under risk (e.g., Allais paradox and hyperbolic probability discounting) have been attracting attention in behavioral and neuroeconomics. We have proposed that psychophysical time commonly explains anomalies in both decisions (Takahashi, 2011, Physica A;Takahashi et al., 2012, J Behav Econ & Finance). By adopting the q-exponential time and probability discounting models, our psychophysical and behavioral economic experiment confirmed that nonlinear distortion of psychophysical time is a common cause of the anomalies in decision both over time and under risk (i.e., intertemporal choice and decision under risk). Implications for psychophysical neuroeconomics and econophysics are discussed.
文摘Mathematical frameworks of quantum theory have recently been adopted in cognitive and behavioral sciences, to explain the violations of normative decision theory and anomalies in cognition. However, to date, no study has attempted to explore neural implementations of such “quantum-like” information processing in the brain. This study demonstrates that neural population coding of information with nonlinear neural response functions can account for such “quantum” information processing in decision-making and cognition. It is also shown that quantum decision theory is a special case of more general population vector cording theory. Future applications of the present theory in the rapidly evolving field of “psychophysical neuroeconomics” are also discussed.
文摘Whether people tend to punish criminals in a socially-optimal manner (i.e., hyperbolic punishment) or not is unknown. By adopting mathematical models of probabilistic punishment behavior (i.e., exponential, hyperbolic, and q-exponential probability discounting model based on Tsallis thermodynamics and neuroeconomics, Takahashi, 2007, Physica A;Takahashi et al., 2012, Applied Mathematics), we examined 1) fitness of the models to behavioral data of uncertain punishment, and 2) deviation from the socially optimal hyperbolic punishment function. Our results demonstrated that, the q-exponential punishment function best fits the behavioral data, and people overweigh the severity of punishment at small punishing probabilities and underweigh the severity of punishment at large punishing probabilities. In other words, people tend to punish crimes too severely and mildly with high and low arrest rate (e.g., homicide vs. excess of speed limit), respectively. Implications for neuroeconomics and neurolaw of crime and punishment (Takahashi, 2012, NeuroEndocrinology Letters) are discussed.
