A Quantized Representation of Probability in the Brain

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.