A Modern Guide to Thinking, Fast and Slow

Part IV - Choices

25. Bernoulli's Errors
26. Prospect Theory
27. The Endowment Effect
28. Bad Events
29. The Fourfold Pattern
30. Rare Events
31. Risk Policies
32. Keeping Score
33. Reversals
34. Frames and Reality

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Chapter 25: Bernoulli's Errors

Overview
Bernoulli’s expected utility theory—evaluating options by final wealth with diminishing marginal utility—cannot describe how people actually choose. Economists model “Econs” as rational, selfish agents with stable tastes, but psychologists study “Humans,” whose System 1, limited information, and changing preferences make them sensitive to reference points. Choices depend on perceived gains and losses from a reference point, not on end wealth alone. Humans are also influenced by framing effects, where small changes in wording can reverse preferences.

Kahneman and Tversky's prospect theory is a descriptive alternative that modifies expected utility to explain these patterns.

Replications & Reliability

• Prospect theory: Kahneman & Tversky’s 1979 Econometrica paper is foundational and remains highly cited. The main update is cumulative prospect theory (Tversky & Kahneman, 1992), now the standard formulation in economics and finance. Core components are broadly supported; see Gisbert-Pérez et al., 2022 for a bibliometric and systematic review of the literature.
• Framing effects: The Science article on risky-choice framing (Tversky & Kahneman, 1981) has held up well. A meta-analysis finds a reliable framing effect overall (Kühberger, 1998), and a re-appraisal of it using p-curve methods concludes the effect is real with no evidence of heavy p-hacking (Steiger & Kühberger, 2018).

Recommendations
This chapter is replication-crisis safe and highly valuable. Prospect theory and risky-choice framing are well supported across replications and meta-analyses, and the move from final-wealth utility to reference-dependent evaluation is now standard in economics.

Chapter 26: Prospect Theory

Overview
Kahneman and Tversky's prospect theory is a model of decision making under risk in which people evaluate outcomes as gains or losses relative to a reference point (often the status quo, what they expected, or what they feel entitled to).

The three cognitive features at the heart of prospect theory are reference dependence, diminishing sensitivity, and loss aversion. People tend to be risk averse when it comes to gains and risk seeking when facing sure losses.

Replications & Reliability

• Loss aversion ratio: The claim that the "loss aversion ratio" is usually in the range of 1.5 to 2.5 is reliable. In a 2021 meta-analysis, Brown and colleagues found that the mean loss aversion coefficient is between 1.8 and 2.1.
• "Thinking like a trader": The claim that thinking like a trader reduces loss aversion is based on Sokol-Hessner and colleagues' 2009 study. While the study showed strong effects, the sample size was small (about 30 for both samples) and I am not aware of any independent replications.

Recommendations
This chapter expands on the explanation of prospect theory—Kahneman’s major contribution to economics—and is well worth reading. The core content is useful for understanding real-world choice patterns. Note that the “think like a trader” result is based on a small sample size and would benefit from independent follow-up research.

Chapter 27: The Endowment Effect

Overview
Willingness to pay (WTP) is the most someone would pay to get an item they don’t own, and willingness to accept (WTA) is the least they would accept to give up an item they already own. In practice, WTA is often much higher than WTP. This is called the endowment effect.

Replications & Reliability
A systematic review of WTA/WTP studies (Horowitz and Mcconnell, 2000) found that WTA is usually substantially higher than WTP, with the WTA/WTP ratio largest for non-market goods, smaller for ordinary private goods, and smallest in experiments involving money.

The 1990 mug study by Kahneman, Knetsch, and Thaler has been disputed. Plott and Zeiler (2005) reported that the WTA–WTP gap can be greatly reduced or even eliminated by changing instructions, training, and elicitation procedures. They argue that the classic results reflect subject misconceptions rather than true preferences. However, other researchers (e.g., Isoni et al., 2011) criticized their research, pointing to additional data not reported in the original paper that show sizeable gaps.

In a more recent meta-analysis with three new experiments (Archtypi et al., 2020), researchers argue that “the endowment effect may largely reflect 'adaptively rational' behavior on the part of both buyers and sellers (given their beliefs about relevant markets) rather than any ownership-induced bias or change in intrinsic preferences.”

Recommendations
The endowment effect itself is generally well supported. While the mug study has been criticized on methodological grounds, this criticism has also been disputed. We can treat the mug study as a clear illustration of the endowment effect, but not as definitive evidence about its size or universality.

Chapter 28: Bad Events

Overview
System 1 is tuned to detect threats and negative events more quickly and intensely than opportunities, which helps explain why we cling to the status quo, resist reforms that create obvious losers, and work especially hard to avoid falling short of targets. The same asymmetry shapes our sense of fairness and the law: people treat existing prices, wages, and contracts as entitlements, see imposed losses as more unfair than withheld gains, and legal rules are more willing to restore losses than to compensate for missed opportunities.

Replications & Reliability

• Amygdala response to eyes: This is a reference to a 2005 study by Whalen and colleagues. They found that people’s amygdalas showed a more intense response when they were shown the eyes of a wide-eyed, fearful-looking person than when they were shown the eyes of a happy person, even though they only saw the images for a fraction of a second. A lot of follow-up research has been done, but a recent critical review of the amygdala fMRI literature highlights common issues like small samples and publication bias, and urges caution about strong claims of fully automatic, awareness-independent amygdala responses (Varkevisser et al., 2024).
• Long-term relationship success: Kahneman cites John Gottman’s claims that the long-term success of a relationship depends far more on avoiding the negative than on seeking the positive, and that good interactions must outnumber bad ones 5:1. The exact 5:1 number and the very strong predictive claims around it look more like an overconfident extrapolation than a robust, repeatedly replicated finding. A community-sample replication (Kim et al, 2007) did not reproduce many of Gottman’s findings, and critics have argued that Gottman’s highly publicized “over 90% accuracy” divorce-prediction claims rest on small, non-random samples and questionable statistical modeling.
• Pope and Schweitzer’s golf analysis: Pope and Schweitzer’s 2011 analysis of 2.5 million golf putts, which found that players tried harder and performed better when putting for par than when putting for a birdie, is not a randomized experiment but a very large, well-analyzed observational dataset that rules out obvious alternatives (e.g., learning from previous putts, different lies on the green, tournament-round effects). This finding appears robust.
• Customer antagonism towards price reduction of a previously-bought product: This finding comes from a robust study—a 28-month randomized field experiment involving over 50,000 customers (Anderson and Simester, 2008).
• Altruistic punishment and reward regions: The claim that altruistic punishment activates the brain’s “pleasure centers” comes from imaging studies showing that the brain’s reward-related regions are involved when people punish norm violations. A 2004 PET study (De Quervain et al., 2004) and a 2011 fMRI study (Strobel et al., 2011) both found that reward-related regions of the brain were activated by punishment of norm violations.

Recommendations
The reliability of the studies in this chapter is mixed. The fearful-eyes amygdala work and Gottman’s “5:1” relationship pattern are methodologically shaky and subject to some criticism, so they should be treated as provisional. By contrast, the golf analysis and the customer antagonism field experiment are large-scale and methodologically strong. Overall, the core theme of negativity dominance is plausible, but the individual studies vary in robustness.

Chapter 29: The Fourfold Pattern

Overview
Instead of weighting outcomes by their actual probabilities (as expected utility theory says we “should”), our minds apply non-linear decision weights. We give extra value to changes in probability that turn impossibility into possibility, such as the 0% to 5% (the possibility effect) as well as to small changes that turn an almost certain outcome into a sure thing, such as 95% to 100% (the certainty effect). Changes in the middle feel less significant, such as the difference between 60% probability and 65%.

When you combine this probability distortion with loss aversion and diminishing sensitivity to gains and losses, you get the fourfold pattern:

• For high-probability gains, people are usually risk averse (preferring a sure, slightly smaller gain over a risky larger one).
• For low-probability gains, they become risk seeking (buying lottery tickets).
• For high-probability losses, they are risk seeking (rather than accepting a sure big loss, they’d rather gamble on an even bigger one).
• For low-probability losses, they are risk averse (buying insurance to eliminate small risks).

Replications & Reliability

• Insecticide survey: The survey that found that parents were willing to pay $2.40 extra per bottle to cut each poisoning risk from 15 in 10,000 to 5, but over $8.09 to eliminate a risk entirely was from a study by Vicusi and colleagues (1987) of over 1500 parents. Subsequent work supports the pattern, which is now called the "zero risk bias," that people pay a disproportionate premium to drive small risks to zero. For example, a 2012 study by Botzen and colleagues found that "a majority of homeowners (52%) is willing to make a substantial investment of €10,000 to elevate a new house to a level that is safe from flooding. Differences between willingness to pay (WTP) for flood insurance and WTP for risk elimination through elevation indicate that individuals place a considerable value on the latter adaptation option." This is now called the zero-risk bias.
• The fourfold pattern: Empirically, the fourfold pattern is reasonably well supported, but its strength depends on how you measure it. Tversky and Kahneman’s 1992 paper introducing the idea reviewed earlier experiments and added new data supporting the pattern. Later, Harbaugh, Krause, and Vesterlund (2010) tested the pattern with real-money gambles using two methods: in one, people stated how much they were willing to pay for each gamble, and those prices lined up cleanly with the fourfold pattern; in the other, the same people simply chose between each gamble and a sure amount equal to its expected value, and their choices did not show the pattern. Their results suggest that the fourfold pattern is a genuine tendency in risk attitudes, but one that is highly sensitive to elicitation method, stakes, and cognitive load. For more recent research see "Your money and your life: Risk attitudes over gains and losses" (Oliver, 2018).

Recommendations
The fourfold pattern is supported by a fair amount of evidence, but it is not a precise, universal law of human behaviour. This chapter offers a useful picture of how people usually respond to small vs large probabilities in gains and losses, but it should not be treated as a reliable predictor of what people will do in every situation that fits the fourfold pattern.

Chapter 30: Rare Events

Overview
Rare events often get treated as more important than their probabilities justify. When an outcome is vivid, emotionally charged, repeatedly discussed, or presented in a concrete way, it feels more likely than it is. That leads people to both overestimate rare probabilities and overweight rare outcomes in their choices, especially when they focus on one specific scenario while the alternative remains vague. Rare events are often overweighted when they’re described explicitly, but neglected when decisions are based on lived experience where rare outcomes may never show up.

Replications & Reliability

• Basketball fans study: Kahneman cites a study by Craig Fox and Amos Tversky (1998) that found that when NBA fans estimated each team’s chance of winning one at a time, the probabilities added up to over 100%. I have not been able to find any direct replications of that study, but the underlying effects (partition-dependence and subadditivity) have been repeatedly demonstrated in other settings. Later research linked the size of the effect to limits on attention and memory (e.g., Dougherty & Hunter, 2003; Sprenger et al., 2011).
• Princeton psychologists' study: This was a reference to a 2010 study by McGraw and colleagues. They found that people were less sensitive to probabilities for non-monetary outcomes and making the outcome more emotional didn’t further reduce probability sensitivity. I'm not aware of any direct replications. Later studies found that affect-rich (i.e., emotionally impactful) outcomes do reduce attention to probability information (for example, Pachur et al., 2014). One study in particular found that "The affect gap persisted even when affect-rich outcomes were supplemented by numerical information, thus providing no support for the thesis that choices in affect-rich and affect-poor problems diverge because the information provided in the former is nonnumerical" (Suter et al., 2015).
• Denominator neglect: This bias has been extensively studied and is well supported by empirical evidence, and a great deal of research has been done on how reduce it to communicate risk more clearly (for example, Garcia-Retamero et al., 2010, Brust-Renck et al., 2017, Ancker et al., 2025).

Recommendations
I haven’t found strong evidence supporting Kahneman’s prediction that adding vivid (but irrelevant) details to an outcome, whether it is emotional or not, makes people less sensitive to probability, but the chapter’s other main takeaways are solid: rare events often feel more likely than they are, and denominator neglect is a common, well-supported bias that is important to consider when communicating risk.

Chapter 31: Risk Policies

Overview
People often evaluate risky choices one at a time. This narrow framing can make our preferences inconsistent with what we’d choose if we treated related choices as a bundle instead of separate decisions. Taking a broader view helps us overcome loss aversion: while a single favorable gamble can feel unacceptable, an opportunity to take that gamble a hundred times is attractive. One way to make more rational long-run economic decisions is to use risk policies—default rules for repeated choices involving things like insurance policies and extended warranties.

Replications & Reliability

• The finding that evaluating the gain and loss decisions separately can cause people to pick a combination that is inferior once the outcomes are combined (“73% chose A and D; 3% chose B and C”) due to risk aversion in the domain of gains and risk seeking in losses comes from Tversky and Kahneman’s 1981 Science paper on framing. In 2009, Rabin & Weizsäcker reproduced the core result with real incentives (at lower rates than the original), and showed that the error largely vanishes when choices are presented in a way that forces broad framing. This supports the interpretation that narrow bracketing is the mechanism.
• Kahneman's claim that "a commitment not to change one’s position for several periods (the equivalent of “locking in” an investment) improves financial performance” is consistent with strong evidence that frequent trading harms typical retail investors’ net returns (Barber & Odean, 2000; Odean, 1999). The proposed mechanism of loss-aversion is supported by experimental work by Gneezy & Potters, 1997, which found that when people evaluate outcomes less frequently, they take more long-run-favorable risk.

Recommendations
This chapter is solid. Narrow framing can make an inferior option feel “right” in the moment. The practical advice is useful: setting a few default risk policies can lead to more rational, long-run-beneficial economic decisions.

Chapter 32: Keeping Score

Overview
People don’t pursue money only for what it can buy. For most people, money also functions as “points” that signal competence, achievement, and self-regard—and we keep score of those points. Because the score is emotional, people often avoid admitting failure, hesitate to cut losses, and steer away from choices that might produce regret. We expect more regret when a bad outcome follows action rather than inaction—and even more when that action deviates from the default—so we tend to stick with inaction or routine choices even when a different action is more likely to lead to a better outcome.

Replications & Reliability

• The disposition effect (we are more likely to sell winners than losers) is well-established in both field data and experiments. The term “disposition effect” comes from Shefrin & Statman (1985), who theorized a tendency to realize gains too quickly and ride losses too long. The most-cited field evidence is a paper by Odean (1998), which examined records of 10,000 brokerage accounts and found a strong preference for realizing gains over losses even though it was costly in performance terms. The effect also shows up in controlled trading experiments (e.g., Weber & Camerer (1998)). A recent meta-analysis found that, under baseline conditions, “investors realise 10% more opportunities to sell winning compared to losing assets, despite optimal choice dictating the opposite” (Cheung, 2024).
• The sunk-cost fallacy is a widely-studied bias with strong empirical support. For a literature review, see Falchetta’s “The Sunk Cost Fallacy: A Literature Review and an Empirical Test”.
• Instruction can reduce sunk cost errors: Kahneman supports this claim with a 1988 study on the effect of graduate training in reasoning and a 2006 study showing that trading experience and being empoyed in professional occupations reduce the disposition effect. A 1993 paper found that training in economics is "associated with use of cost-benefit rules," but an older field study found that "the sunk cost effect was not lessened by having taken prior courses in economics" (Arkes and Blumer, 1985). More recent studies have found that some interventions to reduce the sunk cost fallacy, such as being told to focus on thoughts and feelings, are effective (see Strough et al., 2017 and the studies cited in its introduction).
• Blackjack regret demonstration: The finding that answering “yes” to “Do you want a hit?” or “Do you want to stand?” produces more regret than saying “no” after a bad outcome (regardless of which action “yes” implies) is from Miller & Taylor’s chapter in the 2002 book, Heuristics and Biases: The Psychology of Intuitive Judgment. While I did not see direct replications of that experiment, the general result that deviations from a default/normal option carry more anticipated regret is supported by other research. For example, Ritov & Baron (1992) found that “Subjects reacted more strongly to adverse outcomes caused by action, whether the status quo was maintained or not, and subjects preferred inaction over action even when inaction was associated with change,” and Carlin & Robinson (2009) found that “80% of the mistakes at the table are caused by playing too conservatively.”

Recommendations
The main points in this chapter are robust. The disposition effect and sunk cost fallacy are well supported, and although the specific blackjack framing demo has not been directly replicated, it is consistent with broader evidence on regret and defaults.

The claim that economics instruction reduces the sunk cost fallacy is shaky (presumably it depends on what is included in their courses), but there is evidence that some targeted interventions can reduce sunk cost behavior.

Chapter 33: Reversals

Overview
Preference reversals are cases where your evaluation of an option changes depending on whether you see it alone or alongside an alternative. In single evaluation, you assign a value with little context; WYSIATI, substitution, and intensity matching let System 1 translate whatever is most available—poignancy, a vivid detail, an anchor—into value. Single evaluations also lean on categories: each case quietly supplies its own “normal” yardstick, so judgments can feel coherent within a category but become inconsistent when different categories are involved.

In joint evaluation, you see two options side by side, so they are judged on the same yardstick. Features that were hard to interpret on their own become easier to evaluate and System 2 is more likely to be involved. The same object can therefore receive one value in isolation and a different value when seen next to another—producing the reversals that challenge the idea that preferences are stable and context-free.

Replications & Reliability
While I couldn't find direct replications of the studies mentioned in this chapter, preference reversal in general is well-supported. A recent large-scale meta-analysis aggregates decades of preference-reversal experiments and finds "a robust asymmetric pattern of preference reversals, accompanied by substantial variation across study contexts, suggesting that this pattern is susceptible to moderating factors or study designs" (Lu, 2025).

Recommendations
The main point in this chapter holds up: preference reversals reliably occur, even though their size varies across tasks and designs. Read this chapter as well supported conceptually: even when an exact scenario hasn’t been re-run, the same pattern has been demonstrated many times in different forms.

Chapter 34: Frames and Reality

Overview
Due to framing effects, logically equivalent descriptions can produce different judgments and choices. System 1 responds to the associative and emotional meaning of words rather than the underlying state of the world. As a result, preferences are often not “reality-bound.” Because System 1 is sensitive to reference points, the very same outcome can be framed as a gain or as a loss—keeping versus losing—even when nothing in the objective situation changes. This can make a choice seem acceptable in one formulation and unacceptable in another. System 2 can correct for this, but it is usually passive and effort-averse.

Replications & Reliability
Recent evidence supports the existence of the risky-choice framing effect.

A meta-analytic reappraisal that checks for publication bias concludes that “although there is discussion on the adequate explanation for framing effects, there is no doubt about their existence: risky-choice framing effects are highly reliable and robust” (Steiger and Kühberger, 2018). In a newer systematic review (Kühberger, 2023), Kühberger notes that the size of the effect varies a lot across study designs and argues that “the existence of framing effects points to the adaptiveness of the processes underlying human judgment and choice rather than simply showing human irrationality.”

During COVID-19, researchers ran versions of the classic “Asian disease” framing problem across dozens of countries with tens of thousands of participants. They still found the expected pattern overall, although “the framing effect varied substantially across nations” (Rachev et al., 2021).

Newer work by DeKay and Dou (2024) shows that the size of the classic “gain vs. loss” framing pattern depends heavily on whether the two frames are truly equivalent in what they tell you. Many experiments use mismatched or incomplete option descriptions across frames (for example, one version highlighting only the positive or only the negative side). When they systematically compared matched and mismatched versions across many variants, they found that these description differences explained a lot of the variation in risk-taking. However, a sizable framing effect still remained even in a balanced, carefully matched design.

Recommendations
Risky-choice framing effects have been observed repeatedly in modern research, including large-scale datasets. Read the chapter as broadly reliable, but be aware that some of the most dramatic preference reversal demonstrations change more than the frame—they also change what information is made explicit in each option. When the versions are carefully matched to convey the same content, a framing effect often remains, but its size can be smaller.

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