The Price of Wisdom - 高山雪 Snow Hill

Continuing from the previous article < Subjective Probability Estimation >, a nother thing we should deal with caution is other peoples' subjective probability. Clarifying Expert's Estimation As mentioned, we should understand what people mean when they speak "chance" - a descriptive probability.  If an expert or a consultant says his estimation for a possibility of an event happening is "more likely", you have to be very cautious about this word, and should seek further clarification by what does he mean by that. Because you will never know if there is any difference between your understanding about "more likely" and his. If you don't clarify, you'll never know.   You can guide him through the following example conversation. You should start from the average and guide him through by questions: You: Would you say it is 50%? Expert: No, more than that. I said it is more likely. You: 70%? Expert: I would say it is a bit more than 70%. Y...

機率分布大致有兩類：離散型 Discrete Distribution，和連續型 Continuous Distribution。離散型分布是指獨立離散的機率，而連續型分布是指機率是無縫緊連地出現。 例如： 離散型分布 ：P(10) = 0.16 連續型分布 ：P(10-20) = 30 離散型分布 ，包括：伯努利分布 Bernoulli Distribution、二項分布 Binomial Distribution、卜瓦松分布 Poisson Distribution。 我會在本篇文章簡述離散型的機率分布。

在不確定情況下，我們可以利用 Principle of Insufficient Reason  來先進行平均機率假設，即：把每個「假說 Hypothesis」 的 Prior Probability 假設為一樣的平均機率，再計算 Posterior Probability (事後機率分佈)。 如有 N 個假說 Hypothesis ，它們各自的 Prior Probability  便假定為 1/N 。 然後把新資訊納入計算，把第一次計算出來，每個 Hypothesis 的 Posterior Probability 變成下次更新的 Prior Probability，再計算每個 Hypothesis 的新的 Posterior Probability。如此類推，一直更新。這就是「 貝氏更新 (Bayesian Updating) 」。

In this article, we will continuously go through Mr K's decision making process in Example 4 in < Decision Tree > by examining his risk tolerance. Risk Tolerance Risk tolerance is the willingness of a person to take risk for better consequences. It means how the person weigh the downside of the consequences as compared to the upside, i.e. how significance of the downside of the consequences he would be impacted?  Most   risk averse people will weigh the downside (loss) heavier than the upside (gains), even the probability for both sides are equal.  Risk tolerance is a crucial factor to determine the diversification of an asset portfolio, which also is an attribute to tradeoff of risk/return. So, understanding the role of risk tolerance  is important not only for making daily decisions but also beneficial for making investment decisions.  

In the previous article < Subjective Probability Estimation >, I have mentioned the difficulty in assigning chance for decision making. One of the crucial tools I mentioned is to the Principle of Insufficient Reason (also known as Principle of Indifference ) to assign probability of events in the absence of knowledge about the situation.   

一些無形事件、事物的價值估算是很困難的，例如：精神折磨、時間損耗等是難以量化和估算。正如我在 < Trade-offs in Decision Making > 寫道，若要用 Cancel-out method 來抹去某考慮條件 (objectives or criteria) 的話，我們必須要學懂 Trade-off 「交換」這個概念。尤其在量化無形或有形事件、事物的價值時，人類會被很多因素、 捷思 、 偏 誤 所影響， 其中一個較少人被提及的是 匱乏度 scarcity ！即： 你 個人現時 的匱乏程度； 那 物件或事項 的匱乏程度。 第二點是指：一般來說，若某物件、資源、服務愈是匱乏 scarcity，其估值會愈高，因為供應量低，可擁有機會也小。 有時，這個物件、資源、服務的估值會跟其價值有矛盾，這也是經濟學家 Adam Smith 提出的 Paradox of Value: Diamond and Water。 Adam Smith 在他著作 ＜Wealth of Nations（國富論）＞寫道："Nothing is more useful than water, but it will purchase scarce anything"。鑽石比水對人類的生存或實用價值為低，但鑽石的價格卻比水高，這是因為：(i) 鑽石的匱乏程度高、(ii) 供應量低、(iii) Marginal Utility（邊際效用）。 邊際效用可用主觀效用值來解說，即：對你個人的滿足度。而這滿足度亦跟你個人的匱乏程度有關，牽涉 Law of Diminishing、Value of Use、Value in Exchange。 本文看的估值，不是從第二點的「物件或事項的匱乏程度」來評估，而是從第一點「個人現時的匱乏程度」。    究竟匱乏程度 Scarcity 如何影響價值估算？ 根據 Zhu & Ratner (2014) 的研究指出，  窮人在決定是否買一件物品時，他們 會用「交換」 Tradeoff 的思維來衡量 。他們會想：「如買了此物件，我將不能買別的物件」。 窮人的腦子會被一些迫切而且必要的支出擠滿，例如：腦子總是充斥著，公共服務、水電煤、租金、稅務、學費等的支出。 他們 因為資源匱乏，很容...

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 .     

This article is an elaboration on assigning chance subjectively - the hardest bit for many people - in the article < Uncertainty and Chance >. This article is by no means serves as a deep-dive about risk or whatever, it is about pointing out which parts of chance assignment is hard and how to resolve them.  

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.

不確定時 如果在完全沒有資料和數據下，我們唯有用自己的 本能 (instinct) 或 直覺 (gut feeling) ，作最合理的決策。因為有時有些事情，人的腦子不能逐一拆解，但能記下那複雜系統引伸的後果或記下用來處理的手法，這就形成了人的本能 (instinct) 或 直覺 (gut feeling)。這套思考習慣、捷徑又叫「捷思 Heuristic」。 Gerd Gigerenzer 提倡用直覺來解決複雜系統內的問題。例如：攬球員是用凝視捷思 Gaze Heuristic 來接下飛來攬球，而非運算那複雜數式來計算飛球的軌跡。所以在決策上，要善用自己的本能或直覺。 筆者要強調 用 直覺 進行的決策， 只限於 : 1) 高不確定性 high uncertainty 而 時間緊迫 時使用， 而非 在有明確數據資料顯示是高風險 high risk 又時間充裕時使用。因為如數據資料清晰，而後果又影響深遠時，我們必須經過適合思維模型進行理性分析、估 算 可能 和 最有可能 出 現的後果，判斷風險及自己的承受範圍後, 才可以下決定。相反，如要做出 即時決定 ，我們只能靠自己的直覺 (Heuristics) 作最快的計算來得出結果。 2) 樣品數量太少，不夠代表性 時 (Number of samples is too small to be representative)。因為數量太少我們不能依賴數據分析，得出 statistical significant 的機會率來協助做決定。在 沒有曆史數據或太少數據 的情況下，我們只能夠用 Uniform Distribution 來形容機率分布。亦即是說，假定是相同機率。Refer to < Principle of Insufficient Reason > 要知道， 可思考的時間愈短，犯錯的機會愈高 。因為時間充裕，你可以反覆思考關鍵條件，例如，需要甚麼的條件會導致災難，甚麼條件會是成功？那你可以轉注那些關鍵條件的出現。但若然要當下做 即時決定 ，可用 直覺 並以 保守 為原則來作決策。(保守的意思是盡量減低風險。) 若要運用到捷思來做即時決策時，最好要假設這個決策有佷高可能性會出錯，想像其後果，自己能否承受？若非，最好還是 Status quo。 即時決策可能只有數分鐘內便要下決定，請不要在這類性況下，作重...

I've recently got hold of a voice clip by Alain de Botton, a popular British philosopher, specialising in answering questions about human nature such as love, relationship, happy and fulfilling life; and he is a founder of School of Life. This time the topic was " What's Wrong With Living an Ordinary Life? ". What he said about simple ordinary life really resonates with me, I can't agree more. The voice clip on YouTube is worth listening. I have quoted some words from Alain de Botton in the lower part of the article. ********************************** I write this article because: Many university/school students across the world had chosen to end their lives after or around exams or graduation time, even some old people/ the needy/ the caregivers had chosen to kill themselves because of the feeling of loss of value, long-term tiredness/ hopelessness, long-term emotional and physical torture etc , which saddened me. My soul was disturbed. More and more of them had ...

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...