The Price of Wisdom - 高山雪 Snow Hill

作者友野在書中用到「雙曲折現」(hyperbolic discounting) 來展現人對時間的感受或看法，是受到框架效應的影響，導致「時間不一致性」(time inconsistency)，形成「雙曲折現偏誤」。 意思是，人會因為時間的延遲，而把物件的價值評估得大大降低。 雙曲折現偏誤 的特徵是， 重視當前，寧願要現時較少的獲利，也不願等未來更大的利益 。

 心理帳戶 (Mental Accounting) 是 Richard Thaler 主張的一個決策框架。Thaler 說：「當人類在進行與金錢有關的決策時，並不是評估不同因素和選項後，才理性地決定，而是自己在心裏形造一個狹窄框架後，才進行決定。」Thaler 將這個建造框架的行為，叫做「心理帳戶」。 心理帳戶是一個人類的行為偏誤，把自己的主觀價值加諸在自己的錢之上，從而影響自己的決定，再影響消費行為。

框架效應 (Framing Effect) 框架效應 就是指，當人們要決策或回答、分析問題時，人會 選擇把問題以某種方式呈現， 這 種呈現的方式或方法叫 做 「框架」(Frame)。 因為用了不同的框架，而導致我們對同一問題有不同的判斷，稱為「框架效應」 (Framing Effect)。 框架效應是以框架來限制人的注意力在框架以內 。

  捷思 (Heuristics) 捷思是指在未能掌握資訊的情況下，卻沒有頭緒，但又要做判斷，為了解決問題，人類會利用某種思維方式來對機率和頻率作判斷。 這種思維方式是一種思考捷徑 (mental shortcut) ，被稱為 「捷思」 。簡單來說， 捷思是一種直覺判斷。 常識是一種即時的直覺，直接地浮現腦海，不需思考，所以 常識也是捷思的一種 。 透過捷思而作出的判斷，經常與客觀的機率判斷，相差甚遠。例如，強烈情緒造成的情緒加權，而導致客觀機率大大被扭曲，這就是「 機率忽視偏誤 (Probability Neglect) 」。 所以，在不確定性高的情況下作決策時，必須要計算客觀機率，再用機率作預測。有些人會認為捷思是一種思考陷阱。大部分時候，人都會用某種捷思來做判斷。而 捷思伴隨的是「偏誤」(Biases)。

  ＜ 有限理性：行為經濟學入門首選＞，作者：友野典男 作者友野典男在書中寫出行為經濟學的原由、重點、理性決策的困難、捷思與偏誤、展望理論、機率的誤解。我在 2021 年已看畢這本書，我認為友野能把較複雜的展望理論、貝氏定理、賽局理論、機率和捷思簡化，及用淺白的數學來解釋這些理論是我非常欣賞的地方。 這本書能協助讀者快速拿揑何為 捷思與偏誤 ，如何避免用捷思與偏誤來作決策，明白應該如何運用機率來正確思考。所以，如果你是對行為經濟學有興趣，又想明白一些基礎知識，我是十分推薦這本書。 我會把這個題目分為五部分： 我的書架 | 有限理性 (1): 機率究竟怎理解？ 我的書架 | 有限理性 (2): 捷思 (Heuristics) 與偏誤 (Biases) 我的書架 | 有限理性 (3):  框架效應 (Framing Effect) 我的書架 | 有限理性 (4): 心理帳戶 (Mental Account) 我的書架 | 有限理性 (5): 雙曲折現 (Hyperbolic Discounting)與現時偏誤 (Present Bias) 機率思維 | 蒙堤霍爾困境 (Monty Hall Problem) 至於 展望理論 和 貝氏定理 ， 可以看我的其他文章。 =============================== 機率的誤解 背景 ：Peter 家中有兩個孩子，但你不知道是男是女。 問題 1 - 3 的背景 相同 --------------------------------------------- 問題 1： 某天，你問 Peter：「 你家 有女兒嗎 ？ 」，他答：「有」。那你估計 Peter 的另一個孩子也是女兒的機率是多少？ 誤解： 很多人會認為另一個孩子也是女兒的機率是 1/2，因為世上只有男或女的兩個生理性別。 答案： 正確的機率是 1/3。 解釋： 列出兩個孩子的男女組合：女女、女男、男女、男男。各有 1/4 的出現機率。 從 Peter 提供的資訊：「你家有女兒」，那麼「男男」的出現機率 = 0，我們便可以把它刪掉。剩下來的可能組合是：女女、女男、男女，各出現機率 = 1/3。 -------------------------------------------- 問題 2： 某天，你問 ...

The book, "Recovering From Losses in Life" by H. Norman Wright, is a comforting and supporting book that helps ease the pain of loss while you are in the midst of it. The feeling of a permanent loss is like: "It hurts so much so that I feel hollow inside of me",  "I feel like a half-man, I can't function as normal",  "I feel loneliness and isolation without the person I lost",  "I have a void in my life",  "I feel insecure that anyone may suddenly leave me",  "I feel helpless and lifeless",  "It feels like I have shut down myself, and detached from others", "The fear is paralysing". When there is a loss, there is a grieving or mourning process undergoing, grief is absolutely necessary and normal. 

Decision Tree Another way to present the consequences together with probabilities and outcomes is decision tree . A decision tree can be a more efficient representation of the present uncertainties, alternatives and consequences than a consequence table.  When drawing a decision tree, using quantitative measures, the hardest part is how to assign chance (probability) because it involves a high degree of subjective probability estimation   where it is easily affected by heuristics and biases .     

A good quote from the book of Smart Choices, "The quality of our decision making is not judged by the quality of consequences." The authors put it, you may end up: A smart choice, a bad consequence : the decision is fine, but it is only things happen. The rare bad case scenario happens which ruins the result. How do you know the rare bad thing could happen before make the decision? We never know! This is uncertainty. A poor choice, a good consequence: even the decision is poor but outcome is good, it is just because of luck.  Once you have made the decision right, the outcome may be subject to uncertainties.     What uncertainty means to us? The authors put it: " you may know what might happen, but you won't know what will happen ." This is because of uncertainty .  Uncertainties can be arisen from:  (a) information/ data uncertainties,  (b) model uncertainties,  (c) calculation/ mathematical uncertainties,  (d) result/ outcome uncertaintie...

We have difficulty in decision making is because very often there are more than one alternative to choose from, where one alternative would better satisfy one objective but worse in the other. In a real world situation, we can't always have all goods in one alternative. In such a situation, we have to make trade-off, i.e. seek balance amongst all alternatives and make a relatively balanced decision. The more objectives and the more alternatives you have in your decision making process, the more trade-offs you will have to make, and more difficult a task the decision maker has to do.  An excellent method called "Even Swap Method" is useful to get one or more objectives removed from your consequence table so as to simply a complex decision, which adopts the concept of trade-off  . I term it "Cancel-Out" method .  The key to it is "compensation" . 

  In order to construct a consequence table, we must list out objectives (on rows) and alternatives (on columns) to be able to build a consequence table.   Objectives Setting Objectives are the criteria and your guide for your decision, so they are important in your decision process. Think about:  What are the things you most want, The concerns you want to address,  The outcomes you most want to avoid ,  Always ask "why" can help you to find out the fundamental objectives.  Using the fundamental objectives to evaluate and compare alternatives, From the fundamental objectives, you can think about some mean objectives to achieve those fundamental ones. Or you can grow some sub-objectives from one fundamental objectives (see Figure 1). Ask yourself, " are you happy with the alternative that satisfies the objectives you've listed? " If no, there may be some objectives missing, Ask yourself, "are the objectives you wrote just the means or the end?"....

  The following is the summary of  the PrOACT approach taken out from the book, Smart Choices, by Hammond et al (1999).  The first part of the book review: Smart Choices (1) | Focus and Defining Problem   As said in the first part, this PrOACT approach is to resolve a complex decision problem by breaking it into the following eight elements, think systematically, focus on those that are critical  to the problem.

I've been reading a book, Smart Choices . Here I just want to jot down a quick note of some valuable ideas of what I have underlined in the book. I have completed a couple of chapters, and find it very relevant to what I had been searching out for, and it is useful and applicable.    Quotes from the book: " A decision is a means to an end ."  "Ask yourself what you most want to accomplish and which of your interests, values, concerns, fears, and aspirations are most relevant to achieving your goal. Thinking through your objectives will give directions to your decision making "  "... a good decision doesn't necessarily guarantee a good result, just as a bad decision doesn't necessarily guarantee a bad result . The careless can hit it lucky, the careful can be shot down. But a good decision does increase the odds of success and at the same time satisfies our very human desire to control the forces that affect our lives." "Always focus yo...

   ＜思考的框架＞，作者：夏恩、派瑞許 思考的框架 (1): 第一原理 (First Principle) 思考的框架 (2a): 機率思考 - 貝氏思維 (Bayes Thinking) 思考的框架 (2b): 機率思考 - 肥尾曲線   (Fat-tailed Distribution) 思考的框架 (3): 逆向思維 (Inversion Thinking) 思考的框架 (4): 第二層思維 (Second-Order Thinking)

＜思考的框架＞，作者：夏恩、派瑞許 原著: "The Great Mental Models", written by Shane Parrish (Farnam Street Blog Author) 思考的框架 (1): 第一原理 (First Principle) 思考的框架 (2a): 機率思考 - 貝氏思維 (Bayes Thinking) 思考的框架 (2b): 機率思考 - 肥尾曲線 (Fat-tailed Distribution) 思考的框架 (3): 逆向思維 (Inversion Thinking) 思考的框架 (4): 第二層思維 (Second-Order Thinking)

  ＜ 思考的框架＞，作者：夏恩、派瑞許 逆向思維 (反演法) (Inversion Thinking) (以下是筆者的理解， 不是 Shane Parrish 在書寫的。) 多數人思考問題的方法，都是從單一方向，平舖直敍來思考。逆向思維是透過改變視角、反轉方向、上下顛倒、內外反轉、正反反轉，來提升思考力的強大工具。

＜思考的框架＞，作者：夏恩、派瑞許 肥尾曲線 (Fat-tailed Distribution) 先看 Figure 1 的肥尾曲線 (Fat-tailed Distribution) 跟常態分佈 (Normal Distribution) 的比較圖：

＜思考的框架＞，作者：夏恩、派瑞許 思考的框架 (1): 第一原理 機率思考 (Probabilistic Thinking) 作者 Shane Parrish 認為，未來永遠是不可知的，而且我們無法可以知道全部資訊。對未來影響的變數太多，數據只要出現稍微誤差，結果會偏離真實甚遠，所以未來是無法預測的。但是，我們可以從了解某事件的發生機率，確認並計算真實而有用的機率，我們可以藉此找出最有可能發生的結果，幫助我們做出更精確的決策。

＜ 思考的框架＞，作者：夏恩、派瑞許 原著: "The Great Mental Models", written by Shane Parrish (Farnam Street Blog Author) 這是一本非常簡單易讀的書，寫的是簡單但十分有用的 思維模式，說的是實用真智慧。看畢這本書，好像自己的思考工具箱內，多了幾件 有用的 工具似的 。   如作者 Shane Parrish 所說，這 不是 一本教人如何做決策的書，但是書中說出的一些簡單知識，的確會使筆者多了些不同 的 思考 方法。 筆者個人得著不少， 非常推薦。

猶太人快速致富的101條商規 - 破譯＜塔木德＞ ，作者：韓冰     為什麼猶太人做生意那麼出色呢？筆者嘗試從書中找出答案。 筆者在書中可以看到一些以色列人的特質，以下是我重新編排的要點：  

<行為投資金律>，作者： 丹尼爾 . 克羅斯比。 原著： The Laws of Wealth: Psychology and the Secret to Investing Success, by Daniel Crosby 續上篇：  行為投資金律 (1/4): 人類行為風險 行為投資金律 (2/4): 行為投資金律(上) 行為投資金律 (3/4): 行為投資金律(下) 以下是 我 以自己的理解寫下 的 得著， 亦加入了自己的一些資料和意見 ，與原文不盡相同。