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Value [4][5] is typically modeled using a continuous representation (i.e., aReal number). A discrete representation of value has recently been postulated[6]. A quantized representation of probability in the brain was also positedand supported by experimental data [7]. Value and probability are inter-relatedvia Prospect Theory [4][5]. In this paper, we hypothesize that intertemporalchoices may also be quantized. For example, people may treat (or discount) 16days indifferently to 17 days. To test this, we analyzed an intertemporal taskby using 2 novel models: quantized hyperbolic discounting, and quantizedexponential discounting. Our work here is a re-examination of the behavioraldata previously collected for an fMRI study [8]. Both quantized hyperbolic andquantized exponential models were compared using AIC and BIC tests. We foundthat 13/20 participants were best fit to the quantized exponential model, whilethe 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, quantizedversions of these models are better fit to the experimental data than theircontinuous forms. We finally outline some potential applications of ourfindings.

A Quantized Representation of Intertemporal Choice in the Brain