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Ergodicity-breaking reveals time optimal decision making in humans

Author

Listed:
  • David Meder
  • Finn Rabe
  • Tobias Morville
  • Kristoffer H Madsen
  • Magnus T Koudahl
  • Ray J Dolan
  • Hartwig R Siebner
  • Oliver J Hulme

Abstract

Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To optimise wealth over time, agents should adapt their utility function according to the dynamical setting they face. Linear utility is optimal for additive dynamics, whereas logarithmic utility is optimal for multiplicative dynamics. Whether humans approximate time optimal behavior across different dynamics is unknown. Here we compare the effects of additive versus multiplicative gamble dynamics on risky choice. We show that utility functions are modulated by gamble dynamics in ways not explained by prevailing decision theories. Instead, as predicted by time optimality, risk aversion increases under multiplicative dynamics, distributing close to the values that maximise the time average growth of in-game wealth. We suggest that our findings motivate a need for explicitly grounding theories of decision-making on ergodic considerations.Author summary: How people take risks is central to our understanding of how they make decisions. Theories of decision making commonly assume that preferences for risk are like personality traits, being both idiosyncratic to individuals and stable over time. A new theory based on the thermodynamic concept of ergodicity predicts that risk preferences should be determined by the dynamical settings that people make decisions in. We show that a simple manipulation of the dynamics of a gambling game exerts a strong and systematic effect on people’s willingness to take risks. The level of risk taking and how this changed with different dynamics was quantitatively predicted from first principles within ergodic theory. We show that existing theories of decision making cannot adequately account for these changes in risk preference. This work is relevant across the behavioral sciences insofar as it challenges the validity of one of the most widespread assumptions in modern decision theory. ​

Suggested Citation

  • David Meder & Finn Rabe & Tobias Morville & Kristoffer H Madsen & Magnus T Koudahl & Ray J Dolan & Hartwig R Siebner & Oliver J Hulme, 2021. "Ergodicity-breaking reveals time optimal decision making in humans," PLOS Computational Biology, Public Library of Science, vol. 17(9), pages 1-25, September.
    • Handle: RePEc:plo:pcbi00:1009217
    DOI: 10.1371/journal.pcbi.1009217
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    References listed on IDEAS

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    1. Ole Peters & Murray Gell-Mann, 2014. "Evaluating gambles using dynamics," Papers 1405.0585, arXiv.org, revised Jun 2015.
    2. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    3. Ole Peters & Alexander Adamou, 2018. "The time interpretation of expected utility theory," Papers 1801.03680, arXiv.org, revised Feb 2021.
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