impersonality of procedures: Fo {i>How Doctors Think (New York: Mariner Books, 2008), 6.

planning fallacy: Daniel Kahneman and Amos Tversky, "Intuitive Prediction: Biases and Corrective Procedures," Management Science 12 (1979): 31327.

Scottish Parliament building: Rt. Hon. The Lord Fraser of Carmyllie, "The Holyrood Inquiry, Final Report," September 8, 2004, www.holyroodinquiry.org/FINAL_report/report.htm.

did not become more reliant on it: Brent Flyvbjerg, Mette K. Skamris Holm, and Sren L. Buhl, "How (In)accurate Are Demand Forecasts in Public Works Projects?" Journal of the American Planning Association 71 (2005): 13146.

survey of American homeowners: "2002 Cost vs. Value Report," Remodeling, November 20, 2002.

completion times: Brent Flyvbjerg, "From Nobel Prize to Project Management: Getting Risks Right," Project Management Journal 37 (2006): 515.

sunk-cost fallacy: Hal R. Arkes and Catherine Blumer, "The Psychology of Sunk Cost," Organizational Behavior and Human Decision Processes 35 (1985): 12440. Hal R. Arkes and Peter Ayton, "The Sunk Cost and Concorde Effects: Are Humans Less Rational Than Lower Animals?" Psychological Bulletin 125 (1998): 591600.24: The Engine of Capitalismyou already feel fortunate: Miriam A. Mosing et al., "Genetic and Environmental Influences on Optimism and Its Relationship to Mental and Self-Rated Health: A Study of Aging Twins," Behavior Genetics 39 (2009): 597604. David Snowdon, Aging with Grace: What the Nun Study Teaches Us About Leading Longer, Healthier, and More Meaningful Lives (New York: Bantam Books, 2001).

bright side of everything: Elaine Fox, Anna Ridgewell, and Chris Ashwin, "Looking on the Bright Side: Biased Attention and the Human Serotonin Transporter Gene," Proceedings of the Royal Society B 276 (2009): 174751.

"triumph of hope over experience": Manju Puri and David T. Robinson, "Optimism and Economic Choice," Journal of Financial Economics 86 (2007): 7199.

more sanguine than midlevel managers: Lowell W. Busenitz and Jay B. Barney, "Differences Between Entrepreneurs and Managers in Large Organizations: Biases and Heuristics in Strategic Decision-Making," Journal of Business Venturing 12 (1997): 930.

admiration of others: Entrepreneurs who have failed are sustained in their confidence by the probably mistaken belief that they have learned a great deal from the experience. Gavin Cassar and Justin Craig, "An Investigation of Hindsight Bias in Nascent Venture Activity," Journal of Business Venturing 24 ( {>

influence on the lives of others: Keith M. Hmieleski and Robert A. Baron, "Entrepreneurs' Optimism and New Venture Performance: A Social Cognitive Perspective," Academy of Management Journal 52 (2009): 47388. Matthew L. A. Hayward, Dean A. Shepherd, and Dale Griffin, "A Hubris Theory of Entrepreneurship," Management Science 52 (2006): 16072.

chance of failing was zero: Arnold C. Cooper, Carolyn Y. Woo, and William C. Dunkelberg, "Entrepreneurs' Perceived Chances for Success," Journal of Business Venturing 3 (1988): 97108.

given the lowest grade: Thomas Astebro and Samir Elhedhli, "The Effectiveness of Simple Decision Heuristics: Forecasting Commercial Success for Early-Stage Ventures," Management Science 52 (2006): 395409.

widespread, stubborn, and costly: Thomas Astebro, "The Return to Independent Invention: Evidence of Unrealistic Optimism, Risk Seeking or Skewness Loving?" Economic Journal 113 (2003): 22639.

bet small amounts of money: Eleanor F. Williams and Thomas Gilovich, "Do People Really Believe They Are Above Average?" Journal of Experimental Social Psychology 44 (2008): 112128.

"hubris hypothesis": Richard Roll, "The Hubris Hypothesis of Corporate Takeovers," Journal of Business 59 (1986): 197216, part 1. This remarkable early article presented a behavioral analysis of mergers and acquisitions that abandoned the assumption of rationality, long before such analyses became popular.

"value-destroying mergers": Ulrike Malmendier and Geoffrey Tate, "Who Makes Acquisitions? CEO Overconfidence and the Market's Reaction," Journal of Financial Economics 89 (2008): 2043.

"engage in earnings management": Ulrike Malmendier and Geoffrey Tate, "Superstar CEOs," Quarterly Journal of Economics 24 (2009), 15931638.

self-aggrandizement to a cognitive bias: Paul D. Windschitl, Jason P. Rose, Michael T. Stalk-fleet, and Andrew R. Smith, "Are People Excessive or Judicious in Their Egocentrism? A Modeling Approach to Understanding Bias and Accuracy in People's Optimism," Journal of Personality and Social Psychology 95 (2008): 25273.

average outcome is a loss: A form of competition neglect has also been observed in the time of day at which sellers on eBay choose to end their auctions. The easy question is: At what time is the total number of bidders the highest? Answer: around 7:00 p.m. EST. The question sellers should answer is harder: Considering how many other sellers end their auctions during peak hours, at what time will there be the most bidders looking at my auction? The answer: around noon, when the number of bidders is large relative to the number of sellers. The sellers who remember the competition and avoid prime time get higher prices. Uri Simonsohn, "eBay's Crowded Evenings: Competition Neglect in Market Entry Decisions," Management Science 56 (2010): 106073.

"diagnosis antemortem": Eta S. Berner and Mark L. Graber, "Overconfidence as a Cause of Diagnostic Error in Medicine," American Journal of Medicine 121 (2008): S2S23.

"disclosing uncertainty to patients": Pat Croskerry and Geoff Norman, "Overconfidence in Clinical Decision Making," American Journal of Medicine 121 (2008): S24S29.

background of risk taking: Kahneman and Lovallo, "Timid Choices and Bold Forecasts."

Royal Dutch Shell: J. Edward Russo and Paul J. H. Schoemaker, "Managing Overconfidence," Sloan Management Review 33 (1992): 717.25: Bernoulli's ErrorsMathematical Psychology: Clyde H. Coombs, Robyn M. Dawes, and Amos Tversky, Mathematical Psychology: An Elementary Introduction (Englewood Cliffs, NJ: Prentice-Hall, 1970).

for the rich and for the poor: This rule applies approximately to many dimensions of sensation and perception. It is known as Weber's law, after the German physiologist Ernst Heinrich Weber, who discovered it. Fechner drew on Weber's law to derive the logarithmic psychophysical function.

$10 million from $100 million: Bernoulli's intuition was correct, and economists still use the log of income or wealth in many contexts. For example, when Angus Deaton plotted the average life satisfaction of residents of many countries against the GDP of these countries, he used the logarithm of GDP as a measure of income. The relationship, it turns out, is extremely close: Residents of high-GDP countries are much more satisfied with the quality of their lives than are residents of poor countries, and a doubling of income yields approximately the same increment of satisfaction in rich and poor countries alike.

"St. Petersburg paradox": Nicholas Bernoulli, a cousin of Daniel Bernoulli, asked a question that can be paraphrased as follows: "You are invited to a game in which you toss a coin repeatedly. You receive $2 if it shows heads, and the prize doubles with every successive toss that shows heads. The game ends when the coin first shows tails. How much would you pay for an opportunity to play that game?" People do not think the gamble is worth more than a few dollars, although its expected value is infinite-because the prize keeps growing, the expected value is $1 for each toss, to infinity. However, the utility of the prizes grows much more slowly, which explains why the gamble is not attractive.

"history of one's wealth": Other factors contributed to the longevity of Bernoulli's theory. One is that it is natural to formulate choices between gambles in terms of gains, or mixed gains and losses. Not many people thought about choices in which all options are bad, although we were by no means the first to observe risk seeking. Another fact that favors Bernoulli's theory is that thinking in terms of final states of wealth and ignoring the past is often a very reasonable thing to do. Economists were traditionally concerned with rational choices, and Bernoulli's model suited their goal.26: Prospect Theory

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subjective value of wealth: Stanley S. Stevens, "To Honor Fechner and Repeal His Law," Science 133 (1961): 8086. Stevens, Psychophysics.

The three principles: Writing this sentence reminded me that the graph of the value function has already been used as an emblem. Every Nobel laureate receives an individual certificate with a personalized drawing, which is presumably chosen by the committee. My illustration was a stylized rendition of figure 10.

"loss aversion ratio": The loss aversion ratio is often found to be in the range of 1. 5 and 2.5: Nathan Novemsky and Daniel Kahneman, "The Boundaries of Loss Aversion," Journal of Marketing Research 42 (2005): 11928.

emotional reaction to losses: Peter Sokol-Hessner et al., "Thinking Like a Trader Selectively Reduces Individuals' Loss Aversion," PNAS 106 (2009): 503540.

Rabin's theorem: For several consecutive years, I gave a guest lecture in the introductory finance class of my colleague Burton Malkiel. I discussed the implausibility of Bernoulli's theory each year. I noticed a distinct change in my colleague's attitude when I first mentioned Rabin's proof. He was now prepared to take the conclusion much more seriously than in the past. Mathematical arguments have a definitive quality that is more compelling than appeals to common sense. Economists are particularly sensitive to this advantage.

rejects that gamble: The intuition of the proof can be illustrated by an example. Suppose an individual's wealth is W, and she rejects a gamble with equal probabilities to win $11 or lose $10. If the utility function for wealth is concave (bent down), the preference implies that the value of $1 has decreased by over 9% over an interval of $21! This is an extraordinarily steep decline and the effect increases steadily as the gambles become more extreme.

"Even a lousy lawyer": Matthew Rabin, "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica 68 (2000): 128192. Matthew Rabin and Richard H. Thaler, "Anomalies: Risk Aversion," Journal of Economic Perspectives 15 (2001): 21932.

economists and psychologists: Several theorists have proposed versions of regret theories that are built on the idea that people are able to anticipate how their future experiences will be affected by the options that did not materialize and/or by the choices they did not make: David E. Bell, "Regret in Decision Making Under Uncertainty," Operations Research 30 (1982): 96181. Graham Loomes and Robert Sugden, "Regret Theory: An Alternative to Rational Choice Under Uncertainty," Economic Journal 92 (1982): 80525. Barbara A. Mellers, "Choice and the Relative Pleasure of Consequences," Psychological Bulletin 126 (2000): 91024. Barbara A. Mellers, Alan Schwartz, and Ilana Ritov, "Emotion-Based Choice," Journal of Experimental Psychology-General 128 (1999): 33245. Decision makers' choices between gambles depend on whether they expect to know the outcome of the gamble they did not choose. Ilana Ritov, "Probability of Regret: Anticipation of Uncertainty Resolution in Choice," Organiz {an>y did not ational Behavior and Human Decision Processes 66 (1966): 22836.27: The Endowment EffectWhat is missing from the figure: A theoretical analysis that assumes loss aversion predicts a pronounced kink of the indifference curve at the reference point: Amos Tversky and Daniel Kahneman, "Loss Aversion in Riskless Choice: A Reference-Dependent Model," Quarterly Journal of Economics 106 (1991): 103961. Jack Knetsch observed these kinks in an experimental study: "Preferences and Nonreversibility of Indifference Curves," Journal of Economic Behavior & Organization 17 (1992): 13139.

period of one year: Alan B. Krueger and Andreas Mueller, "Job Search and Job Finding in a Period of Mass Unemployment: Evidence from High-Frequency Longitudinal Data," working paper, Princeton University Industrial Relations Section, January 2011.

did not own the bottle: Technically, the theory allows the buying price to be slightly lower than the selling price because of what economists call an "income effect": The buyer and the seller are not equally wealthy, because the seller has an extra bottle. However, the effect in this case is negligible since $50 is a minute fraction of the professor's wealth. The theory would predict that this income effect would not change his willingness to pay by even a penny.

would be puzzled by it: The economist Alan Krueger reported on a study he conducted on the occasion of taking his father to the Super Bowl: "We asked fans who had won the right to buy a pair of tickets for $325 or $400 each in a lottery whether they would have been willing to pay $3,000 a ticket if they had lost in the lottery and whether they would have sold their tickets if someone had offered them $3,000 apiece. Ninety-four percent said they would not have bought for $3,000, and ninety-two percent said they would not have sold at that price." He concludes that "rationality was in short supply at the Super Bowl." Alan B. Krueger, "Supply and Demand: An Economist Goes to the Super Bowl," Milken Institute Review: A Journal of Economic Policy 3 (2001): 2229.

giving up a bottle of nice wine: Strictly speaking, loss aversion refers to the anticipated pleasure and pain, which determine choices. These anticipations could be wrong in some cases. Deborah A. Kermer et al., "Loss Aversion Is an Affective Forecasting Error," Psychological Science 17 (2006): 64953.

market transactions: Novemsky and Kahneman, "The Boundaries of Loss Aversion."

half of the tokens will change hands: Imagine that all the participants are ordered in a line by the redemption value assigned to them. Now randomly allocate tokens to half the individuals in the line. Half of the people in the front of the line will not have a token, and half of the people at the end of the line will own one. These people (half of the total) are expected to move by trading places with each other, so that in the end everyone in the first half of the line has a token, and no one behind them does.

Brain recordings: Brian Knutson et al., "Neural Antecedents of the Endowment Effect," Neuron 58 (2008): 81422. Brian Knutson an {an utson et ad Stephanie M. Greer, "Anticipatory Affect: Neural Correlates and Consequences for Choice," Philosophical Transactions of the Royal Society B 363 (2008): 377186.

riskless and risky decisions: A review of the price of risk, based on "international data from 16 different countries during over 100 years," yielded an estimate of 2.3, "in striking agreement with estimates obtained in the very different methodology of laboratory experiments of individual decision-making": Moshe Levy, "Loss Aversion and the Price of Risk," Quantitative Finance 10 (2010): 100922.

effect of price increases: Miles O. Bidwel, Bruce X. Wang, and J. Douglas Zona, "An Analysis of Asymmetric Demand Response to Price Changes: The Case of Local Telephone Calls," Journal of Regulatory Economics 8 (1995): 28598. Bruce G. S. Hardie, Eric J. Johnson, and Peter S. Fader, "Modeling Loss Aversion and Reference Dependence Effects on Brand Choice," Marketing Science 12 (1993): 37894.

illustrate the power of these concepts: Colin Camerer, "Three Cheers-Psychological, Theoretical, Empirical-for Loss Aversion," Journal of Marketing Research 42 (2005): 12933. Colin F. Camerer, "Prospect Theory in the Wild: Evidence from the Field," in Choices, Values, and Frames, ed. Daniel Kahneman and Amos Tversky (New York: Russell Sage Foundation, 2000), 288300.

condo apartments in Boston: David Genesove and Christopher Mayer, "Loss Aversion and Seller Behavior: Evidence from the Housing Market," Quarterly Journal of Economics 116 (2001): 123360.

effect of trading experience: John A. List, "Does Market Experience Eliminate Market Anomalies?" Quarterly Journal of Economics 118 (2003): 4771.