← Thinking, Fast and Slow
第 5 章 · 22 分钟
Prospect theory: reference points and loss aversion
The one place the book gives a formal model.
概念地图
Reference point
Gains and losses are measured against a baseline that wording can set.
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Locus01
延伸阅读
Bernoulli · eighteenth century · expected utility and log utility of wealth
Explained with diminishing utility why people do not bet by expected amount, against equating decision with computing an expected value. The cost is that utility is defined over total wealth, so it cannot explain why the same sum is valued quite differently in different situations — which is prospect theory's entry point.
Foundational
von Neumann and Morgenstern · 1940s · the axiomatisation of expected utility
Gave axioms under which preferences admit an expected-utility representation. It moved the discussion from 'how do people choose' to 'which axiom is violated', so every later counterexample has had to name one.
Turn
Allais · 1950s · the Allais paradox
Constructed choice patterns that systematically violate the independence axiom — the most famous counterexample to expected utility, and one that points at a specific axiom rather than at irrationality in general.
Counterexample
Kahneman and Tversky · 1979 · prospect theory
Offered a replacement: value over gains and losses relative to a reference point, a steeper loss side, and non-linear probability weighting. The book's popular retelling omits the probability weighting half; the first crack lands there.
Subject of this course
机制02
The reference point defines gain and loss
The same thousand can be 'I had two thousand and am down to one' or 'I had nothing and now have one thousand'. Prospect theory defines evaluation over changes relative to a baseline rather than over total wealth, and that baseline is the reference point. This is the model's hinge: as long as the baseline can be moved from outside, the same objective outcome can be scored as a gain or as a loss.
机制An outcome, through being converted into a gain or loss relative to a baseline, changes the value assigned to it.
可迁移性测试
Move it to performance review: the same quarterly result is growth against last quarter and a shortfall against the annual target, and the two baselines give opposite verdicts. The isomorphism breaks in that a review's baseline is written down and contestable, while an everyday reference point is set by nobody and noticed by no one.
机制03
The loss side is steeper
The value function is asymmetric around the reference point, and Kahneman and Tversky named that asymmetry loss aversion. Its place in the argument is specific: it explains why people refuse symmetric bets, and it does not explain their risk attitude on either side — that is set by curvature. Running the two properties together is the book's most frequent misreading, and the worked example below takes it apart.
机制A loss of equal size, through a steeper value slope, has a stronger effect on evaluation than a gain.
可迁移性测试
Move it to project management: cutting a feature already invested in draws far more resistance than the original hesitation about whether to build it. The isomorphism breaks in that the sunk investment in a project is an accountable number, while the reference point in an experiment is set by instructions with nothing invested at all.
Derivation04
From the reference point to 'framing can flip a choice'
What is being derived is the model's strongest prediction: change the wording without changing the outcomes and the majority choice flips.
Value is defined over changes relative to a reference point, not over total wealth
Chosen, and the step at which the model parts from expected utility.
is concave over gains, convex over losses, and steeper on the loss side
Chosen: curvature sets risk attitude, steepness sets loss aversion — two separate assumptions.
The reference point is set by the wording of the problem
Chosen, and the most fragile of the three. Chapter 6 shows that expectations and history can set it too; wording is only one source.
推导 · 0 / 4
Worked derivation05
Loss aversion is not risk aversion
The same person refuses a coin flip that wins 120 or loses 100, yet adds to a position already down. Is that a contradiction?
Separate the ratio of the two slopes from the curvature on each side.
裂缝06
Cracks in this framework
争议地形07
本书主张
Evaluation is defined over gains and losses relative to a reference point with a steeper loss side, so equivalent wordings change choices and preferences violate the independence axiom.
另一种看法
The defence of expected utility holds that most counterexamples come from small, one-shot, no-learning laboratory settings, and that in repeated markets with learning and real money, arbitrage and experience compress the violations to very little.
分歧扎在
The disagreement is rooted in whether the laboratory setting extrapolates to settings with learning and arbitrage, not in the data. Both sides accept that the reversals in the laboratory are real.
什么证据能裁决
What would settle it is the same people with and without learning: have participants repeat the same class of decision over many rounds with outcome feedback and compare the framing effect in the first and last rounds. A significant shrinkage would show learning compresses it; no change would show it is a stable preference.
The evidence points to 'learning compresses but does not flatten': repetition with feedback shrinks framing effects, and professional traders deviate less within their own domain, but neither eliminates it. What is missing is a way to separate learning from selection — the professionals' advantage may come from who was hired rather than from training.
Falsification08
The reference point as a preregistrable test
The mechanism under test: an outcome, through being converted into a gain or loss relative to a baseline, changes the value assigned to it.
Data source: newly collected choice data with the reference point set directly by the experimenter and stated in the registration
The reference point has to be a manipulated variable, never one inferred afterwards.
Sample: a pre-computed sample size analysed in full, with no exclusion on comprehension checks
Comprehension checks correlate with response style, so post hoc exclusion introduces selection.
Window: a single session, within-subject, with the two reference points assigned at random across items
Within-subject nets out individual risk attitudes.
Threshold: the difference in choice proportions between the two reference points reaches a pre-registered minimum effect size
A minimum effect size, not significance alone.
Failure condition: the difference runs the wrong way, or the effect size falls below the registered minimum
The second also counts as refutation: too small an effect has no practical content.
推导 · 0 / 3
接口09
Which slot it hangs on
挂在哪个槽位The conclusion you already hold is probably 'I hate losing money, so I am conservative' — loss aversion and risk attitude merged into one. This chapter goes at that merger.
Does this chapter (a) replace 'hating losses equals being conservative', or (b) open a new slot about wording changing choices?
慢变量Register two slow variables: how often you write down your reference point before a decision, and how often you add to a position already down. Look at the second first.
小结10
本章小结
01Prospect theory defines evaluation over changes relative to a reference point, not over total wealth.
02'Concavity over gains implies preferring the certain option' is an arithmetic consequence of the assumed shape.
03Loss aversion (ratio of slopes) and risk attitude (curvature on each side) are two independent properties.
04The popular retelling omits probability weighting, and part of the framing effect comes from overweighted small probabilities.
05Reference points are unobservable in natural settings, so explanations that infer them afterwards carry no empirical risk.
提取练习 · 合上书，先自己答一遍。
?Is 'concavity over gains implies preferring the certain option in a gain frame' (a) an identity or (b) an empirical claim?
?Does adding to a losing position reflect (a) convexity on the loss side or (b) the ratio of the two slopes?
Forced choice11
A · Identify the mechanism
Which of these is a mechanism?
二选一
Forced choice12
C · Locate the crack
In which situation does this framework give a confident and wrong answer?
二选一
读到这里，把它记为已读。