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Electronic Letters to:
- BehavioralSystemsCognitive:
Dominik R. Bach, Ben Seymour, and Raymond J. Dolan- Neural Activity Associated with the Passive Prediction of Ambiguity and Risk for Aversive Events
J. Neurosci. 2009; 29: 1648-1656[Abstract] [Full text] [PDF]
eLetters: Submit a response to this article
Electronic letters published:
The correct definition of risk and ambiguity would have provided different results
- Angela A Stanton (12 February 2009)
- Dominik R. Bach, Ben Seymour, and Raymond J. Dolan (25 February 2009)
The correct definition of risk and ambiguity would have provided different results 12 February 2009 
Angela A Stanton,
Visiting Scholar
Center for Neuroeconomics Studies, Claremont Graduate University, Claremont, CA 91711Send letter to journal:
Re: The correct definition of risk and ambiguity would have provided different results
angela{at}angelastanton.com Angela A Stanton
In Bach et al. (2009) the authors state the definition of risk and ambiguity incorrectly. They write (in the abstract) "In economic decision making, outcomes are described in terms of risk (uncertain outcomes with certain probabilities) and ambiguity (uncertain outcomes with uncertain probabilities)." Both of these statements are incorrect. In economic theory, risk is defined as fully known outcomes and fully known probabilities (what is unknown is the "specific" outcome that will materialize) and ambiguity is defined as fully known outcomes and unknown probability distribution (the probability distribution can be estimated by beliefs).
Furthermore, the authors define "ignorance" suggesting that ignorance is that in which probabilities of outcomes are unknown and are unknowable "unless exploration and learning are permitted" (page 1648). Placed in this context, there is no difference between ambiguity and ignorance, because in both cases, some information is missing and beliefs can be used to make up the missing information--even if exploration and learning are not permitted. I suggest that rather than ignorance, they tested a version of ambiguity in which the experimenters knew the difference between the types of ambiguity forthcoming but the experimental subjects did not. Hence the unsurprising result of no distinction in brain activation between the cases of ambiguity and ignorance.
Equivalent definitions, misquoted results 25 February 2009 
Dominik R. Bach,
Postdoctoral Research Fellow
University College London, WC1N 3BG,
Ben Seymour, and Raymond J. DolanSend letter to journal:
Re: Equivalent definitions, misquoted results
d.bach{at}fil.ion.ucl.ac.uk Dominik R. Bach, et al.
Stanton's (2009) definition of risk and ambiguity would most certainly not have led to different results, as her definition is equivalent to the one used in our study. However, our results are misquoted in her letter.
Stanton refers to the “unsurprising result of no distinction in brain activation between the cases of ambiguity and ignorance”. We would have found this result quite surprising, and fortunately our study shows exactly the opposite. In fact, there is a distinction in brain activity between ignorance and ambiguity, and it's the same as between risk and ambiguity. This demonstrates that not only the experimenter, but also the participants gathered a difference between ambiguity and ignorance.
Stanton is correct in pointing out that in risk, it's only the ultimate outcome that is unknown while the stakes (or possible outcomes) are known. Our definition of risk ("unknown outcomes with known probabilities") could thus be extended to “unknown ultimate outcomes with known possible outcomes and known probabilities”. This reflects precisely what is described in the methods section of our article and is equivalent to Stanton's definition.
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