Time-varying decision boundaries: insights from optimality analysis

Gaurav Malhotra*, David Leslie, Casimir Ludwig, Bogacz Rafal

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

40 Citations (Scopus)
330 Downloads (Pure)


The most widely used account of decision-making proposes that people choose between alternatives by accumulating evidence in favor of each alternative until this evidence reaches a decision boundary. It is frequently assumed that this decision boundary stays constant during a decision, depending on the evidence collected but not on time. Recent experimental and theoretical work has challenged this assumption, showing that constant decision boundaries are, in some circumstances, sub-optimal. We introduce a theoretical model that facilitates identification of the optimal decision boundaries under a wide range of conditions. Time-varying optimal decision boundaries for our model are a result only of uncertainty over the difficulty of each trial and do not require decision deadlines or costs associated with collecting evidence, as assumed by previous authors. Furthermore, the shape of optimal decision boundaries depends on the difficulties of different decisions. When some trials are very difficult, optimal boundaries decrease with time, but for tasks that only include a mixture of easy and medium difficulty trials, the optimal boundaries increase or stay constant. We also show how this simple model can be extended to more complex decision-making tasks such as when people have unequal priors or when they can choose to opt out of decisions. The theoretical model presented here provides an important framework to understand how, why, and whether decision boundaries should change over time in experiments on decision-making.

Original languageEnglish
Pages (from-to)971-996
Number of pages26
JournalPsychonomic Bulletin and Review
Issue number3
Early online date20 Jul 2017
Publication statusPublished - 1 Jun 2018

Bibliographical note

Gold open access, funded by RCUK.

Structured keywords

  • Cognitive Science
  • Visual Perception


  • Decision-making
  • Decreasing bounds
  • Optimal decisions
  • Reward rate


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