Psychophysical Neuroeconomics of Decision Making: Nonlinear Time Perception Commonly Explains Anomalies in Temporal and Probability Discounting

Abstract

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.

The Q-Exponential Decay of Subjective Probability for Future Reward: A Psychophysical Time Approach

“…Our present results suggest that, in psychological time, future is increasingly more risky. Future studies in neuroeconomics and neurofinance [3,14] should examine neural basis of this psychological tendency. Furthermore, recent advances in high throughput genomic data in neurobiology by Changeux's group can help us to analyze brain's organization by utilizing Tsallis' statistics [19].…”

“…After plotting the group data of their subjective time and probabilities, we utilized nonlinear curve fitting (with R statistical language) for fitting mathematical models for dynamics of subjective probability and subjective time. The goodness-of-fit (tradeoff between overfitting and poor fitting) was parameterized with AIC (Akaike Information Criterion = 2 × (the number of free parameters) − 2 ln( ℎ )), following our previous studies [6,13,14]. Note that AIC punishes an increase in the number of free parameters in the models for exploring parsimonious explanations for observed data [18].…”

“…Our previous studies revealed that the q-exponential time discount model fitted best among the three discount models (i.e., exponential, simple hyperbolic, and q-exponential) [4,7,8]. It is to be noted that the q-exponential time-discount model is derived from exponential discounting with logarithmic psychophysical time [2][3][4]13,14]. Several authors speculated that temporal discounting in intertemporal choice occurs due to an increase in uncertainty associated with delay, because future is risky.…”

Pharmacological and Expectancy Effects of a Low Amount of Alcohol Drinking on Outcome Valuation and Risk Perception in Males and Females

“…To examine participants’ risk perception, we assessed the subjective perception of the likelihood of uncertain gain (Lh gain ) and loss (Lh loss ) (± 100,000 yen (hypothetical), approximately equal to $1,000, on a 180 mm scale) at seven probabilities of 0.05, 0.1, 0.3, 0.5, 0.7, 0.9, and 0.95. Additionally, to further assess risk perception by utilizing the nonlinear time perception theory of decision under risk [ 20 ], we asked participants for their subjective perception of the waiting time for both uncertain gain (WT gain ) and loss (WT loss ) with seven probabilities (0.05, 0.1, 0.3, 0.5, 0.7, 0.9, and 0.95), as described in previous studies [ 8 , 21 ] (e.g., “For how long do you feel you should wait until you win 100,000 yen with probability of 50% in repeated gambles?” for the gain task; “For how long do you feel you should wait until you lose 100,000 yen with probability of 50% in repeated gambles?” for the loss task). Participants were asked to draw a line on a 180 mm scale to indicate the subjective waiting time or subjective likelihood (minimum of 0 mm and maximum of 180 mm) until receiving reward ( Fig 1B ).…”

“…In neuroeconomics study, the risky decisions are characterized by two behavioral and psychological parameters: underestimating the risk perception of negative consequences and sensitivity to punishment (often in addition to overestimating the likelihood of positive consequences and/or high sensitivity to reward) [ 7 ]. Previous studies have also demonstrated a gain-loss asymmetry in risk perception by utilizing the psychophysical measurement of risk perception and the subjective valuation of gain (reward) and loss (punishment) [ 8 , 9 ]. The subjective theory of value is a theory of value that advances the idea that the value is not determined by any inherent property but instead the value is determined by individual places on the achievement of his desired ends [ 10 ].…”