The Price of Wisdom - 高山雪 Snow Hill

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，很容易會 用「交換」 Tradeoff

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.