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54 Daniel Bernoulli’s work in probability theory: W. W. Rouse Ball, A Short Account of the History of Mathematics, 4th ed. (Mineola, NY: Dover Publications, 2010); and http://www-history.mcs.st-and.ac.uk/Biographies/Bernoulli_Daniel.html. The formula for expected utility: Alan Schwartz, George Bergus, Medical Decision Making : A Physician’s Guide (Cambridge, UK: Cambridge University Press, 2008).

54 An examination of the methodology of determining utilities and preferences can be found in Alan Schwartz, George Bergus, Medical Decision Making: A Physician’s Guide (Cambridge, UK: Cambridge University Press, 2008); George W. Torrance, “Measurement of health state utilities for economic appraisal: A review,” Journal of Health Economics 5 (1986), pp. 1–30.

55 The complexity of trying to project future feelings has been studied extensively in cognitive psychology; see George Loewenstein, David Schkade, “Wouldn’t it be nice ? Predicting future feelings,” in D. Kahneman, E. Diener, and N. Schwarz (eds.), Well-Being: The Foundation of Hedonic Psychology (New York: Russell Sage Foundation, 1998),pp. 85–105. Also see Norman F. Boyd et al., “Whose utilities for decision analysis ?” Medical Decision Making 10 (1990),pp. 58–67; Nick Sevdalis, Nigel Harvey, “Predicting preferences: Aneglected aspect of shared decision-making ,” Health Expectations 9 (2006), pp. 245–251. The dilemma of forecasting is wonderfully illuminated in Daniel Gilbert, Stumbling on Happiness (New York: Vintage Books, 2007).

57 Constructing preferences “on the spot” is addressed in Sarah Lichtenstein and Paul Slovic, “The Construction of Preference: An Overview,” in Lichtenstein and Slovic (eds.), The Construction of Preference (New York: Cambridge University Press, 2006). See also Ronald M. Epstein, Ellen Peters, “Beyond information: Exploring patients’ preferences,” JAMA 302 (2009), pp. 195–197.

57 The importance of the default option and how it may be used in changing health behaviors and other social issues: Richard H. Thaler, Cass R. Sunstein, Nudge: Improving Decisions About Health, Wealth, and Happiness (New York, Penguin Books, 2009).

58 On the challenge of teaching physicians and other health care professionals how to elicit preferences in an objective manner while providing clear information, see Ronald M. Epstein, Ellen Peters, “Beyond information: Exploring patients’ preferences,” JAMA 302 (2009), pp. 195–197. For differences in how patients and physicians weigh the importance of facts about clinical problems and the goals and concerns about available treatments: Karen R. Sepucha et al., “Developing instruments to measure the quality of decisions: Early results for a set of symptom-driven decisions,” Patient Education and Counseling 73 (2008), pp. 504–510; Karen Sepucha et al., “An approach to measuring the quality of breast cancer decisions,” Patient Education and Counseling 65 (2007), pp. 261–269.

59 The studies cited on atrial fibrillation are P. J. Devereaux et al., “Differences between perspectives of physicians and patients on anticoagulation in patients with atrial fibrillation: Observational study,” BMJ 323 (2001), pp. 1218–1222; Malcolm Man-Son-Hing et al., “The effect of qualitative vs. quantitative presentation of probability estimates on patient decision-making : A randomized trial,” Health Expectations 5 (2002), pp. 246–255.

60 The new anticoagulant approved by the FDA in 2010: Stuart J. Connolly et al., “Dabigatran versus warfarin in patients with atrial fibrillation,” NEJM 361 (2009), pp. 1139–1151; Brian F. Gage, “Can we rely on RE-LY ?” NEJM 361 (2009), pp. 1200–1202. Also see Stuart J. Connolly et al., “Apixaban in patients with atrial fibrillation,” NEJM (Online First, February 10, 2011). The risks and benefits of bleeding versus stroke prevention: B. Nhi Beasley, Ellis F. Unger, Robert Temple, “Anticoagulant options: Why the FDA approved a higher but not a lower dose of dabigatran,” NEJM (Online First, April 13, 2011).

The application of Bernoulli’s formula to atrial