A Quantized Representation of Intertemporal Choice in the Brain

Value (Kahneman and Tversky, 1979), (Tversky Kahneman, 1992) is typically modeled using a continuous representation (i.e., a Real number). A discrete representation of value has recently been postulated (Woodford, 2020). A quantized representation of probability in the brain was also posited and supported by experimental data (Tee and Taylor, 2019). Value and probability are inter-related via Prospect Theory (Kahneman and Tversky, 1979), (Tversky Kahneman, 1992). In this article, 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 (Cox and Kable, 2014). 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., $2^{5}= 32$ 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.