A Modern Guide to Thinking, Fast and Slow

Part IV - Choices

Bernoulli's Errors
Prospect Theory
The Endowment Effect
Bad Events
The Fourfold Pattern
Rare Events
Risk Policies
Keeping Score
Reversals
Frames and Reality

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 willingness to 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 mugs 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: The claim that people who learned from a new catalog that a merchant was now charging less for a product that they had recently bought reduced their future purchases from that supplier by 15% 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 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 to 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 patter: 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 than 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 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.