The question

Dual process theories posit that human psychology is governed by a fast and implicit ‘system 1’ and a slow and deliberative ‘system 2’ (ref. 1). System 1 performs well in simple, familiar contexts and in choices between a few options — a scenario that has been extensively studied using binary choice tasks2,3,4. However, determining the best outcome is rarely a simple matter of selecting the better of two clearly defined or well learned options. Rather, decision makers must determine the best outcomes by surveying a range of economic factors, including the different possibilities, associated costs, available resources, future consequences and immediate constraints. These combinatorial considerations generate substantial computational complexity — defined as the computational resources required to solve a problem — and demand slow and effortful deliberation performed by system 2 thinking. We devised a combinatorial optimization task, the ‘knapsack task’, that used computational complexity to modulate trial difficulty, and used it to investigate how monkeys deliberate.

The discovery

On each trial, a touchscreen computer in front of the animals displayed multiple items that represented different sized juice rewards. For example, one item might be associated with 0.2 ml and another with 0.45 ml. Crucially, the monkeys were taught ahead of time the reward size associated with each item. The animals were tasked with selecting subsets of items, and they were rewarded with the sum of the selected subset if and only if that sum was less than or equal to 0.8 ml of juice. If the monkeys selected too few items, the sum would be less than 0.8 ml and so they were rewarded with less juice than possible, whereas if too many items were selected the sum would exceed 0.8 ml, and no reward would be received. Thus, the animals were incentivized to optimize: to identify the best subsets that satisfied a constraint. Each trial lasted 5 s, regardless of the animals’ behaviour, and did not include perceptual ambiguities, substantial sensorimotor challenges or probabilistic uncertainties. Accordingly, the differences in the performances and response times reflected differences in internal value deliberations.

We discovered that computational complexity affected the animals’ performance and computational strategies. As the problems became more complex, the animals’ performance dropped (Fig. 1a,b). The solutions submitted by the animals approximated those generated by efficient computer algorithms designed specifically to solve the optimization problem. Critically, the animals exhibited temporally extended deliberations that revealed the complexity of their computational strategies: the deliberation times matched the number of operations prescribed by the algorithms the animals approximated (Fig. 1c). These results demonstrated that computational complexity is a normative scale of cognitive difficulty. Moreover, they revealed that the monkeys used combinatorial reasoning strategies and performed serial cognitive operations in complex economic decisions, both hallmarks of system 2 deliberation1.

Fig. 1: Computational complexity drives extended deliberation.
figure 1

a, Box and whisker plots of the performance of monkey G on the knapsack task, showing that performance decreases as computational complexity (measured by the clustering parameter k) increases. b, As in a, for monkey B and thresholding parameter t. Note that k and t are different measures of complexity, but both influence the monkey’s performance similarly. c, Deliberation times for two monkeys, separated into trials with a limited (magenta) or exhaustive (pink) search. © 2023, Hong, T. & Stauffer, W. R., CCBY 4.0.

Full size image

The implications

Combinatorial optimization problems evoke sophisticated, deliberative reasoning because of their inherent complexity. Our data, together with recent work done in humans5, highlight that combinatorial optimization problems and computational complexity are ideal tools for understanding the psychological and neural bases of deliberative thinking.

A limitation of our current study is the lack of direct observation of the combinatorial search processes. The search process was inferred from the deliberation times and the submitted solutions. In the next iteration of the task, we will use head-fixed monkeys and record eye-tracking data to reveal overt search strategies.

We aim to understand the neural mechanisms that guide deliberation. How do neurons estimate complexity? What is the neural signature for the decision to deliberate? How do neurons and neuronal populations implement the algorithms that enable deliberative thinking? We will use single-neuron recordings and functional MRI (fMRI) while monkeys are engaged in the knapsack task to answer these and other questions. Ultimately, we hope to characterize the neural mechanisms that characterize and differentiate system 1 and 2 thinking. Results from this work will contribute neurophysiological evidence to enlighten centuries of discussions about dual process theories of the mind, the structure of thoughts, and the neurobiological bases of intuition, reasoning and insight.

Tao Hong & William R. Stauffer

University of Pittsburgh, Pittsburgh, PA, USA.

Expert opinion

“Here, for the first time, a simple yet powerful experimental paradigm is presented with which to study computationally complex decision making in nonhuman animals, namely monkeys. The authors thereby provide an animal model for one of the least understood aspects of human behavior — decision making under computational complexity.” Peter Bossaerts, University of Cambridge, Cambridge, UK.

Behind the paper

How brains solve optimization problems has been on my mind for a long time. The problems designed to test principles of computability, such as the knapsack problem, are fascinating. So too is the fact that humans and other animals can solve optimization problems. I am determined to know how we do this. Since my other main interest is economic behaviour, the 'knapsack task' was destined to be about value-based optimization. With the algorithms now in hand, I hope that this paradigm will help us reveal the neural implementation of value-based deliberation and even the neural basis of insight generation.

Lightning struck twice to enable this project. The first strike was winning the NIH New Innovator award (DP2), which provided the funds and the confidence to do the study. The second was when Tao joined my lab, because the only thing better than doing fascinating research is doing it with an amazing colleague in a collaboration that becomes greater than the sum of its parts. W.R.S.

From the editor

“This study stood out to us for the close correspondence between algorithms consistent with combinatorial reasoning and the monkeys’ choice behavior, opening possibilities for exploring the neural basis of complex value-based decision making in animals.” Luis A. Mejia, Senior Editor, Nature Neuroscience.