How do people learn when investing more pays off?
People learned where spending more paid off, and a model of that learning explained their choices far better than the standard one.
Published: eLife, 2025 (co-first author)
Participants: 514 adults online, in an initial and a replication study, both preregistered
Design: A treasure-hunt game in which extra tickets raised the odds in some environments and not in others
Methods: Reinforcement-learning models fitted to every choice by expectation–maximization; model comparison with integrated BIC; parameter and model recovery; mixed-effects probit regression; canonical correlation analysis
The question
Most accounts of decision-making treat control as all or nothing: either your actions shape the outcome or they don’t. In everyday life, how much control you have often depends on how much effort, time or money you put in. We asked whether people learn this elasticity of control, and whether misjudging it leads them to invest too much or too little.
What we did
Participants played a treasure-hunt game across a series of planets. On each trip they could buy up to three tickets, each one more attempt to board a vehicle to the treasure. On some planets extra tickets helped, on others one ticket was enough, and on others nothing helped. We fitted competing learning models to every choice each person made, compared them with the integrated Bayesian Information Criterion, confirmed that the models and their parameters could be recovered from simulated data, and repeated the whole study in a new preregistered sample.
What we found
People bought more extra tickets only where extra tickets helped (mixed-effects probit regression; p = .01, replication p = .004). The elastic-control model reproduced their choices and the standard model, which learns how much control there is but not whether investing more adds to it, did not: where nothing helped, participants still bought a ticket on 47% of trips, close to the elastic model’s 49%, while the standard model predicted 63%. Model comparison favored the elastic model by a wide margin in both studies (log Bayes factors of at least 270 and 148).
Across people, the fitted parameters, led by the prior belief about elasticity, were linked to self-reported symptoms, mainly an impaired sense of agency (canonical correlation, ρ = .33, p = .004), a first result that needs further testing.
What it shows
The approach carries over to product and business questions: write competing explanations down as models, fit them to every decision rather than to averages, compare them on a principled criterion, check that the estimates can be trusted, and replicate before acting. The construct carries over too: whether people believe that putting in more will pay off shapes how much they put in, whether that is effort in a game, practice in an app or money on an upgrade.
Read the paper: The resource elasticity of control (eLife, 2025).
