The known unknowns: neural representation of second-order uncertainty, and ambiguity

Dominik R Bach, Oliver Hulme, William D Penny, Raymond J Dolan

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)


Predictions provided by action-outcome probabilities entail a degree of (first-order) uncertainty. However, these probabilities themselves can be imprecise and embody second-order uncertainty. Tracking second-order uncertainty is important for optimal decision making and reinforcement learning. Previous functional magnetic resonance imaging investigations of second-order uncertainty in humans have drawn on an economic concept of ambiguity, where action-outcome associations in a gamble are either known (unambiguous) or completely unknown (ambiguous). Here, we relaxed the constraints associated with a purely categorical concept of ambiguity and varied the second-order uncertainty of gambles continuously, quantified as entropy over second-order probabilities. We show that second-order uncertainty influences decisions in a pessimistic way by biasing second-order probabilities, and that second-order uncertainty is negatively correlated with posterior cingulate cortex activity. The category of ambiguous (compared with nonambiguous) gambles also biased choice in a similar direction, but was associated with distinct activation of a posterior parietal cortical area; an activation that we show reflects a different computational mechanism. Our findings indicate that behavioral and neural responses to second-order uncertainty are distinct from those associated with ambiguity and may call for a reappraisal of previous data.

Original languageEnglish
Pages (from-to)4811-4820
Number of pages10
JournalThe Journal of Neuroscience
Issue number13
Publication statusPublished - 30 Mar 2011


  • Adult
  • Brain
  • Brain Mapping
  • Choice Behavior
  • Decision Making
  • Female
  • Gambling
  • Humans
  • Magnetic Resonance Imaging
  • Male
  • Photic Stimulation
  • Uncertainty
  • Young Adult
  • Comparative Study

Cite this