Heuristics and optimal solutions to the breadth:depth dilemma

Rubén Moreno-Bote, Jorge Ramírez-Ruiz, Jan Drugowitsch, Benjamin Y. Hayden

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In multialternative risky choice, we are often faced with the opportunity to allocate our limited information-gathering capacity between several options before receiving feedback. In such cases, we face a natural trade-off between breadth—spreading our capacity across many options—and depth—gaining more information about a smaller number of options. Despite its broad relevance to daily life, including in many naturalistic foraging situations, the optimal strategy in the breadth–depth trade-off has not been delineated. Here, we formalize the breadth–depth dilemma through a finite-sample capacity model. We find that, if capacity is small (∼10 samples), it is optimal to draw one sample per alternative, favoring breadth. However, for larger capacities, a sharp transition is observed, and it becomes best to deeply sample a very small fraction of alternatives, which roughly decreases with the square root of capacity. Thus, ignoring most options, even when capacity is large enough to shallowly sample all of them, is a signature of optimal behavior. Our results also provide a rich casuistic for metareasoning in multialternative decisions with bounded capacity using close-to-optimal heuristics.

Original languageEnglish (US)
Pages (from-to)19799-19808
Number of pages10
JournalProceedings of the National Academy of Sciences of the United States of America
Volume117
Issue number33
DOIs
StatePublished - Aug 2020

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS. This work is supported by the HHMI (Grant 55008742), Ministry of Economic Affairs and Digital Transformation (Spain) (Grant BFU2017-85936-P), and Catalan Institution for Research and Advanced Studies–Academia (2016) to R.M.-B.; by NIH (Grant DA037229) to B.Y.H.; and by a scholar award from the James S. McDonnell Foundation (Grant 220020462) to J.D.

Funding Information:
This work is supported by the HHMI (Grant 55008742), Ministry of Economic Affairs and Digital Transformation (Spain) (Grant BFU2017-85936-P), and Catalan Institution for Research and Advanced Studies?Academia (2016) to R.M.-B.; by NIH (Grant DA037229) to B.Y.H.; and by a scholar award from the James S. McDonnell Foundation (Grant 220020462) to J.D.

Publisher Copyright:
© 2020 National Academy of Sciences. All rights reserved.

Keywords

  • Decision making | Risky choice | Bounded rationality | Breadth–depth dilemma | Metareasoning

PubMed: MeSH publication types

  • Journal Article
  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

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