ABSTRACT
Value [4][5] is typically modeled using a continuous representation (i.e., a Real number). A discrete representation of value has recently been postulated [6]. A quantized representation of probability in the brain was also posited and supported by experimental data [7]. Value and probability are inter-related via Prospect Theory [4][5]. In this paper, we hypothesize that intertemporal choices may also be quantized. For example, people may treat (or discount) 16 days indifferently to 17 days. To test this, we analyzed an intertemporal task by using 2 novel models: quantized hyperbolic discounting, and quantized exponential discounting. Our work here is a re-examination of the behavioral data previously collected for an fMRI study [8]. Both quantized hyperbolic and quantized exponential models were compared using AIC and BIC tests. We found that 13/20 participants were best fit to the quantized exponential model, while the remaining 7/20 were best fit to the quantized hyperbolic model. Overall, 15/20 participants were best fit to models with a 5-bit precision (i.e., 25 = 32 steps). In conclusion, regardless of hyperbolic or exponential, quantized versions of these models are better fit to the experimental data than their continuous forms. We finally outline some potential applications of our findings.
ABSTRACT
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information encoding process whereby a continuous quantity is systematically divided into a finite number of possible categories. Rounding is a simple example of quantization. We apply this information theoretic concept to develop a novel quantized (i.e., discrete) probability distortion function. We develop three conjunction probability gambling tasks to look for evidence of quantized probability representations in the brain. We hypothesize that certain ranges of probability will be lumped together in the same indifferent category if a quantized representation exists. For example, two distinct probabilities such as 0.57 and 0.585 may be treated indifferently. Our extensive data analysis has found strong evidence to support such a quantized representation: 59/76 participants (i.e., 78%) demonstrated a best fit to 4-bit quantized models instead of continuous models. This observation is the major development and novelty of the present work. The brain is very likely to be employing a quantized representation of probability. This discovery demonstrates a major precision limitation of the brain's representational and decision-making ability.
