How Humans Solve Complex Problems: The Case of the Knapsack Problem

Life presents us with problems of varying complexity. Yet, complexity is not accounted for in theories of human decision-making. Here we study instances of the knapsack problem, a discrete optimisation problem commonly encountered at all levels of cognition, from attention gating to intellectual discovery. Complexity of this problem is well understood from the perspective of a mechanical device like a computer. We show experimentally that human performance too decreased with complexity as defined in computer science. Defying traditional economic principles, participants spent effort way beyond the point where marginal gain was positive, and economic performance increased with instance difficulty. Human attempts at solving the instances exhibited commonalities with algorithms developed for computers, although biological resource constraints-limited working and episodic memories-had noticeable impact. Consistent with the very nature of the knapsack problem, only a minority of participants found the solution-often quickly-but the ones who did appeared not to realise. Substantial heterogeneity emerged, suggesting why prizes and patents, schemes that incentivise intellectual discovery but discourage information sharing, have been found to be less effective than mechanisms that reveal private information, such as markets.