花了一天时间阅读了 Thinking, Fast and Slow 的 Appendix A：JUDGEMENT UNDER UNCERTAINTY: 3 HEURISTICS AND BIASES
这是全书中相对独立的一个单元，作者是Amos Tversky and Daniel Kahneman。
看完本文，通过很多例子学到了很多有趣的认知知识。在这里用自己的语言分享，若有不对欢迎指正。以及摘抄一些原文。也有一些没有读懂的地方，请读者不吝赐教。
许多时候，人们做的决策依赖于对于许多不确定性事件的判断。本文不是教你怎么做决策，而是谈人们在对不确定性事件进行概率估计/数值预测时，是怎样通过一些启发性的规则进行简化的，以及这些经济有效的方法会带来哪些系统性和可预测的认知偏差。
有以下三大类方法
- 相似性
通常在估计 物体 A 属于 B 类别/C 过程导致 D 事件 的概率时使用 - 易想到性
通常在估计类别的频率 - 从认知锚点进行调整
通常在预测数值并且有个大致相关的值可参考时使用
REPRESENTATIVENESS 相似性
Insensitivity to prior probability of outcomes
对先验概率不敏感
哪怕告诉你一个先验概率，然后给你一段描述，哪怕是毫不相关的，也会极大影响你的判断
However, prior probabilities were effectively ignored when a description was introduced, even when this description was totally uninformative.
When no specific evidence is given, prior probabilities are properly utilized; when worthless evidence is given, prior probabilities are ignored.3
Insensitivity to sample size 对样本大小不敏感
人往往对样本大小对概率的影响不敏感
Misconceptions of chance 对概率的误解
gambler’s fallacy
抛一个标准的硬币很多次都是正面，那么接下来是正是反？很多人会觉得都那么多次正了，那么接下来的一次是反的概率更大。
非也。机会均等：
Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not“corrected”as a chance process unfolds, they are merely diluted.
Insensitivity to predictability 对信息是否有预测作用不敏感
某些信息对你要预测的对象的某些属性（例如公司利润）无直接关系（例如只是对公司的整体性描述），信息中流露的整体印象的好坏却往往能影响人对公司利润的判断。
The illusion of validity 对信息的真实有效性不敏感
有时候你根本不对别人给你的信息本身进行思考，就拿来做预测，而该信息本身可能单薄、不可靠、或者过时。
The unwarranted confidence which is produced by a good fit between the predicted outcome and the input information may be called the illusion of validity
However, an elementary result in the statistics of correlation asserts that, given input variables of stated validity, a prediction based on several such inputs can achieve higher accuracy when they are independent of each other than when they are redundant or correlated.
Misconceptions of regression 对回归的错误认识
If one selects individuals whose average X score deviates from the mean of X by k units, then the average of their Y scores will usually deviate from the mean of Y by less than k units. These observations illustrate a general phenomenon known as regression toward the mean, which was first documented by Galton more than 100 years ago.
这里作者讲了一个相信很多人也有切身体会的事情：
考试考好了，老师表扬，但下次考试往往就会考差。考得不好，老师批评，下次考试往往就会考好。所以我们往往得出结论：学生不能表扬，不能中场开香槟，要多批评。
这是错误的。
Because the instructors had praised their trainees after good landings and admonished them after poor ones, they reached the erroneous and potentially harmful conclusion that punishment is more effective than reward.
AVAILABILITY 易想到性
However, availability is affected by factors other than frequency and probability. Consequently, the reliance on availability leads to predictable biases, some of which are illustrated below.
Biases due to the retrievability of instances 样本可检索性造成的认知偏差
念一串名人的名字，判断其中男人多还是女人多。
假如其中的男（女）人大多更有名，那么受试者往往觉得男（女）人多。
When the size of a class is judged by the availability of its instances, a class whose instances are easily retrieved will appear more numerous than a class of equal frequency whose instances are less retrievable.
In addition to familiarity, there are other factors, such as salience, which affect the retrievability of instances.
Biases due to the effectiveness of a search set
搜索空间的有效性（effectiveness）造成的偏差
英语中第三个字母是 r 还是第一个字母是 r 的单词更多？
因为在脑海中检索第一个字母是 r 的单词更容易，所以会得出错误的结论。
Different tasks elicit different search sets.
Biases of imaginability 可想象性造成的偏差
Conversely, the risk involved in an undertaking may be grossly underestimated if some possible dangers are either difficult to conceive of, or simply do not come to mind.
Illusory correlation 虚假的相关性
有些东西本身就是有自然关联性，但通过数据分析重新发现，是没有意义的。
The judgment of how frequently two events co-occur could be based on the strength of the associative bond between them. When the association is strong, one is likely to conclude that the events have been frequently paired.
It persisted even when the correlation between symptom and diagnosis was actually negative, and it prevented the judges from detecting relationships that were in fact present.
ADJUSTMENT AND ANCHORING 从认知锚点进行调整
The judgment of how frequently two events co-occur could be based on the strength of the associative bond between them. When the association is strong, one is likely to conclude that the events have been frequently paired.
Insufficient adjustment 不充分的调整
Biases in the evaluation of conjunctive and disjunctive events 对于连续、非连续事件评估的不同偏见
The judgment of how frequently two events co-occur could be based on the strength of the associative bond between them. When the association is strong, one is likely to conclude that the events have been frequently paired.
Biases in the evaluation of compound events are particularly significant in the context of
planning.
Even when the likelihood of failure in each component is slight, the probability of an overall failure can be high if many components are involved. Because of anchoring, people will tend to underestimate the probabilities of failure in complex systems. Thus, the direction of the anchoring bias can sometimes be inferred from the structure of the event. The chain-like structure of conjunctions leads to overestimation, the funnel-like structure of disjunctions leads to underestimation.
Anchoring in the assessment of subjective probability distributions 主观概率分布的锚点
Subjective probability distributions for a given quantity (the Dow Jones average) can be obtained in two different ways: (i) by asking the subject to select values of the Dow Jones that correspond to specified percentiles of his probability distribution and (ii) by asking the subject to assess theprobabilities that the true value of the Dow Jones will exceed some specified values.
The two procedures are formally equivalent and should yield identical distributions. However, they suggest different modes of adjustment from different anchors. In procedure (i), the natural starting point is one’s best estimate of the quantity. In procedure (ii), on the other hand, the subject may be anchored on the value stated in the question. Alternatively, he may be anchored on even odds, or a 50–50 chance, which is a natural starting point in the estimation of likelihood. In either case, procedure (ii) should yield less extreme odds than procedure (i).
DISCUSSION
This article has been concerned with cognitive biases that stem from the reliance on judgmental heuristics. These biases are not attributable to motivational effects such as wishful thinking or the distortion of judgments by payoffs and penalties.
The reliance on heuristics and the prevalence of biases are not restricted to laymen. Experienced researchers are also prone to the same biases—when they think intuitively.
What is perhaps surprising is the failure of people to infer from lifelong experience such fundamental statistical rules as regression toward the mean, or the effect of sample size on sampling variability. Although everyone is exposed, in the normal course of life, to numerous examples from which these rules could have been induced, very few people discover the principles of sampling and regression on their own. Statistical principles are not learned from everyday experience because the relevant instances are not coded appropriately.
However, it is not natural to group events by their judged probability.