@Article{BarrettoGarcia2023,
  author          = {Barretto-Garc\'{i}a, Miguel and de Hollander, Gilles and Grueschow, Marcus and Polan\'{i}a, Rafael and Woodford, Michael and Ruff, Christian C.},
  journal         = {Nature human behaviour},
  title           = {Individual risk attitudes arise from noise in neurocognitive magnitude representations.},
  year            = {2023},
  issn            = {2397-3374},
  month           = sep,
  pages           = {1551--1567},
  volume          = {7},
  abstract        = {Humans are generally risk averse, preferring smaller certain over larger uncertain outcomes. Economic theories usually explain this by assuming concave utility functions. Here, we provide evidence that risk aversion can also arise from relative underestimation of larger monetary payoffs, a perceptual bias rooted in the noisy logarithmic coding of numerical magnitudes. We confirmed this with psychophysics and functional magnetic resonance imaging, by measuring behavioural and neural acuity of magnitude representations during a magnitude perception task and relating these measures to risk attitudes during separate risky financial decisions. Computational modelling indicated that participants use similar mental magnitude representations in both tasks, with correlated precision across perceptual and risky choices. Participants with more precise magnitude representations in parietal cortex showed less variable behaviour and less risk aversion. Our results highlight that at least some individual characteristics of economic behaviour can reflect capacity limitations in perceptual processing rather than processes that assign subjective values to monetary outcomes.},
  citation-subset = {IM},
  comment         = {Barretto-Garcia et al. (2023). Individual risk attitudes arise from noise in neurocognitive magnitude representations. Nature Human Behavior.

# Terminology: 
NPC: numerical parietal cortex 

# Prior research

* noisy logarithmic coding (NLC) model (Khaw et al., 2021): risky payoff precision is related to risk aversion 
	- Khaw, M.W., Li, Z., and Woodford, M. (2021). Cognitive imprecision and small-stakes risk aversion. The Review of Economic Studies 88.
* Neural decoding accuracy in IPS is related to task performance (Kersey and Cantlon, 2017; Lasne et al., 2019)
	- Lasne, G., Piazza, M., Dehaene, S., Kleinschmidt, A., and Eger, E. (2019). Discriminability of numerosity-evoked fMRI activity patterns in human intra-parietal cortex reflects behavioral numerical acuity. Cortex 114.


# Experiment

## Paradigm

* Numerosity comparison with coin clouds. The first set varied from 5 to 28 were drawn from a geometric sequence with steps of sqrt(2) (5, 7, 10, 14, 20, 18), while we varied the second set by multiplying each magnitude from the first set by a factor of 2^(h/4) where h is in discrete steps from -6 to 6 (.36 ... 2.8). Clouds were presented for 600 ms each, with a ISI of 6-9 s
* Risky choice between two coin clouds; the greater one has a 55% probability of winning, smaller one a 100% probability. We varied the distribution of monetary payoffs with the sure gamble varying from 5 to 28 drawn from a geometric sequence with steps of sqrt(2) similar to the perceptual magnitude task and the probabilistic lotteries varying by a factor of 2^(h/4) in steps of 0 to 8.
* Risky choice with arabic numerals

## Results

* Decoded numerosity in parietal cortex. This gave them a posterior distribution over posterior stimuli given the BOLD activation pattern, and thus also a measure of neuronal noise (see also Kersey and Cantlon, 2017; Lasne et al., 2019),

* The precision of these distributions 1/SD correlated with behavioral accuracy. Further, the larger the magnitudes, the less precise the representations

* In behavior, indifference point for magnitude task is at a ratio of 1; indifference point for risky choice is at ratio > 1, given that participant should choose the greater cloud only for a ratio > 1/(success probability). The authors take this as evidence for a common mechanism underlying magnitude estimation and risky choice, but it really just shows that people take into consideration the success probability in risky choice. 

* In risky choice, non-symbolic representations are more noisy.

* Risk aversion correlates with precision in number estimation


* behavioural precision, $\gamma_{perceptual}$, significantly mediated (\alpha \times \beta) the effect between neural precision and risk aversion, \pi, for both non-symbolic($p_MCMC$ =0.013) and symbolic (p_{MCMC} = 0.019) visual displays (Fig 7a,b).},
  completed       = {2023-09-25},
  country         = {England},
  doi             = {10.1038/s41562-023-01643-4},
  file            = {:/Users/endress/Articles/Individual_risk_attitudes_arise_from_noise_in_neur.pdf:PDF},
  groups          = {Moral learning by numbers},
  issn-linking    = {2397-3374},
  issue           = {9},
  keywords        = {Humans; Choice Behavior; Magnetic Resonance Imaging; Parietal Lobe; Attitude},
  nlm-id          = {101697750},
  owner           = {NLM},
  pii             = {10.1038/s41562-023-01643-4},
  pmc             = {3065064},
  pmid            = {37460762},
  pubmodel        = {Print-Electronic},
  pubstate        = {ppublish},
  revised         = {2023-09-27},
}

{"_id":"qoh38td6TNFP3cgLW","bibbaseid":"barrettogarcia-dehollander-grueschow-polania-woodford-ruff-individualriskattitudesarisefromnoiseinneurocognitivemagnituderepresentations-2023","author_short":["Barretto-García, M.","de Hollander, G.","Grueschow, M.","Polanía, R.","Woodford, M.","Ruff, C. C."],"bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Barretto-García"],"firstnames":["Miguel"],"suffixes":[]},{"propositions":["de"],"lastnames":["Hollander"],"firstnames":["Gilles"],"suffixes":[]},{"propositions":[],"lastnames":["Grueschow"],"firstnames":["Marcus"],"suffixes":[]},{"propositions":[],"lastnames":["Polanía"],"firstnames":["Rafael"],"suffixes":[]},{"propositions":[],"lastnames":["Woodford"],"firstnames":["Michael"],"suffixes":[]},{"propositions":[],"lastnames":["Ruff"],"firstnames":["Christian","C."],"suffixes":[]}],"journal":"Nature human behaviour","title":"Individual risk attitudes arise from noise in neurocognitive magnitude representations.","year":"2023","issn":"2397-3374","month":"September","pages":"1551–1567","volume":"7","abstract":"Humans are generally risk averse, preferring smaller certain over larger uncertain outcomes. Economic theories usually explain this by assuming concave utility functions. Here, we provide evidence that risk aversion can also arise from relative underestimation of larger monetary payoffs, a perceptual bias rooted in the noisy logarithmic coding of numerical magnitudes. We confirmed this with psychophysics and functional magnetic resonance imaging, by measuring behavioural and neural acuity of magnitude representations during a magnitude perception task and relating these measures to risk attitudes during separate risky financial decisions. Computational modelling indicated that participants use similar mental magnitude representations in both tasks, with correlated precision across perceptual and risky choices. Participants with more precise magnitude representations in parietal cortex showed less variable behaviour and less risk aversion. Our results highlight that at least some individual characteristics of economic behaviour can reflect capacity limitations in perceptual processing rather than processes that assign subjective values to monetary outcomes.","citation-subset":"IM","comment":"Barretto-Garcia et al. (2023). Individual risk attitudes arise from noise in neurocognitive magnitude representations. Nature Human Behavior. # Terminology: NPC: numerical parietal cortex # Prior research * noisy logarithmic coding (NLC) model (Khaw et al., 2021): risky payoff precision is related to risk aversion - Khaw, M.W., Li, Z., and Woodford, M. (2021). Cognitive imprecision and small-stakes risk aversion. The Review of Economic Studies 88. * Neural decoding accuracy in IPS is related to task performance (Kersey and Cantlon, 2017; Lasne et al., 2019) - Lasne, G., Piazza, M., Dehaene, S., Kleinschmidt, A., and Eger, E. (2019). Discriminability of numerosity-evoked fMRI activity patterns in human intra-parietal cortex reflects behavioral numerical acuity. Cortex 114. # Experiment ## Paradigm * Numerosity comparison with coin clouds. The first set varied from 5 to 28 were drawn from a geometric sequence with steps of sqrt(2) (5, 7, 10, 14, 20, 18), while we varied the second set by multiplying each magnitude from the first set by a factor of 2^(h/4) where h is in discrete steps from -6 to 6 (.36 ... 2.8). Clouds were presented for 600 ms each, with a ISI of 6-9 s * Risky choice between two coin clouds; the greater one has a 55% probability of winning, smaller one a 100% probability. We varied the distribution of monetary payoffs with the sure gamble varying from 5 to 28 drawn from a geometric sequence with steps of sqrt(2) similar to the perceptual magnitude task and the probabilistic lotteries varying by a factor of 2^(h/4) in steps of 0 to 8. * Risky choice with arabic numerals ## Results * Decoded numerosity in parietal cortex. This gave them a posterior distribution over posterior stimuli given the BOLD activation pattern, and thus also a measure of neuronal noise (see also Kersey and Cantlon, 2017; Lasne et al., 2019), * The precision of these distributions 1/SD correlated with behavioral accuracy. Further, the larger the magnitudes, the less precise the representations * In behavior, indifference point for magnitude task is at a ratio of 1; indifference point for risky choice is at ratio > 1, given that participant should choose the greater cloud only for a ratio > 1/(success probability). The authors take this as evidence for a common mechanism underlying magnitude estimation and risky choice, but it really just shows that people take into consideration the success probability in risky choice. * In risky choice, non-symbolic representations are more noisy. * Risk aversion correlates with precision in number estimation * behavioural precision, $γ_{perceptual}$, significantly mediated (α × β) the effect between neural precision and risk aversion, π, for both non-symbolic($p_MCMC$ =0.013) and symbolic (p_MCMC = 0.019) visual displays (Fig 7a,b).","completed":"2023-09-25","country":"England","doi":"10.1038/s41562-023-01643-4","file":":/Users/endress/Articles/Individual_risk_attitudes_arise_from_noise_in_neur.pdf:PDF","groups":"Moral learning by numbers","issn-linking":"2397-3374","issue":"9","keywords":"Humans; Choice Behavior; Magnetic Resonance Imaging; Parietal Lobe; Attitude","nlm-id":"101697750","owner":"NLM","pii":"10.1038/s41562-023-01643-4","pmc":"3065064","pmid":"37460762","pubmodel":"Print-Electronic","pubstate":"ppublish","revised":"2023-09-27","bibtex":"@Article{BarrettoGarcia2023,\n author = {Barretto-Garc\\'{i}a, Miguel and de Hollander, Gilles and Grueschow, Marcus and Polan\\'{i}a, Rafael and Woodford, Michael and Ruff, Christian C.},\n journal = {Nature human behaviour},\n title = {Individual risk attitudes arise from noise in neurocognitive magnitude representations.},\n year = {2023},\n issn = {2397-3374},\n month = sep,\n pages = {1551--1567},\n volume = {7},\n abstract = {Humans are generally risk averse, preferring smaller certain over larger uncertain outcomes. Economic theories usually explain this by assuming concave utility functions. Here, we provide evidence that risk aversion can also arise from relative underestimation of larger monetary payoffs, a perceptual bias rooted in the noisy logarithmic coding of numerical magnitudes. We confirmed this with psychophysics and functional magnetic resonance imaging, by measuring behavioural and neural acuity of magnitude representations during a magnitude perception task and relating these measures to risk attitudes during separate risky financial decisions. Computational modelling indicated that participants use similar mental magnitude representations in both tasks, with correlated precision across perceptual and risky choices. Participants with more precise magnitude representations in parietal cortex showed less variable behaviour and less risk aversion. Our results highlight that at least some individual characteristics of economic behaviour can reflect capacity limitations in perceptual processing rather than processes that assign subjective values to monetary outcomes.},\n citation-subset = {IM},\n comment = {Barretto-Garcia et al. (2023). Individual risk attitudes arise from noise in neurocognitive magnitude representations. Nature Human Behavior.\n\n# Terminology: \nNPC: numerical parietal cortex \n\n# Prior research\n\n* noisy logarithmic coding (NLC) model (Khaw et al., 2021): risky payoff precision is related to risk aversion \n\t- Khaw, M.W., Li, Z., and Woodford, M. (2021). Cognitive imprecision and small-stakes risk aversion. The Review of Economic Studies 88.\n* Neural decoding accuracy in IPS is related to task performance (Kersey and Cantlon, 2017; Lasne et al., 2019)\n\t- Lasne, G., Piazza, M., Dehaene, S., Kleinschmidt, A., and Eger, E. (2019). Discriminability of numerosity-evoked fMRI activity patterns in human intra-parietal cortex reflects behavioral numerical acuity. Cortex 114.\n\n\n# Experiment\n\n## Paradigm\n\n* Numerosity comparison with coin clouds. The first set varied from 5 to 28 were drawn from a geometric sequence with steps of sqrt(2) (5, 7, 10, 14, 20, 18), while we varied the second set by multiplying each magnitude from the first set by a factor of 2^(h/4) where h is in discrete steps from -6 to 6 (.36 ... 2.8). Clouds were presented for 600 ms each, with a ISI of 6-9 s\n* Risky choice between two coin clouds; the greater one has a 55% probability of winning, smaller one a 100% probability. We varied the distribution of monetary payoffs with the sure gamble varying from 5 to 28 drawn from a geometric sequence with steps of sqrt(2) similar to the perceptual magnitude task and the probabilistic lotteries varying by a factor of 2^(h/4) in steps of 0 to 8.\n* Risky choice with arabic numerals\n\n## Results\n\n* Decoded numerosity in parietal cortex. This gave them a posterior distribution over posterior stimuli given the BOLD activation pattern, and thus also a measure of neuronal noise (see also Kersey and Cantlon, 2017; Lasne et al., 2019),\n\n* The precision of these distributions 1/SD correlated with behavioral accuracy. Further, the larger the magnitudes, the less precise the representations\n\n* In behavior, indifference point for magnitude task is at a ratio of 1; indifference point for risky choice is at ratio > 1, given that participant should choose the greater cloud only for a ratio > 1/(success probability). The authors take this as evidence for a common mechanism underlying magnitude estimation and risky choice, but it really just shows that people take into consideration the success probability in risky choice. \n\n* In risky choice, non-symbolic representations are more noisy.\n\n* Risk aversion correlates with precision in number estimation\n\n\n* behavioural precision, $\\gamma_{perceptual}$, significantly mediated (\\alpha \\times \\beta) the effect between neural precision and risk aversion, \\pi, for both non-symbolic($p_MCMC$ =0.013) and symbolic (p_{MCMC} = 0.019) visual displays (Fig 7a,b).},\n completed = {2023-09-25},\n country = {England},\n doi = {10.1038/s41562-023-01643-4},\n file = {:/Users/endress/Articles/Individual_risk_attitudes_arise_from_noise_in_neur.pdf:PDF},\n groups = {Moral learning by numbers},\n issn-linking = {2397-3374},\n issue = {9},\n keywords = {Humans; Choice Behavior; Magnetic Resonance Imaging; Parietal Lobe; Attitude},\n nlm-id = {101697750},\n owner = {NLM},\n pii = {10.1038/s41562-023-01643-4},\n pmc = {3065064},\n pmid = {37460762},\n pubmodel = {Print-Electronic},\n pubstate = {ppublish},\n revised = {2023-09-27},\n}\n\n","author_short":["Barretto-García, M.","de Hollander, G.","Grueschow, M.","Polanía, R.","Woodford, M.","Ruff, C. 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