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20201025 – Calculated Risk



The main idea of this book to demonstrate how often people misunderstand data and how easy it is to manipulate people who are innumerate or at least poorly understand statistics and their representation. Even more important, it is to provide people with tools that allow practical methods of problem’s representation that make it a lot easier achieve statistically valid understanding.


Part l: Dare to Know
1: Uncertainty
This starts with the story of pain and suffering of women who has false positive for HIV, then discuss similar problems with Prozac, Mammograms, DNA ID for courts, and so on. Author’s main point is that reality is filled with uncertainty, while people seek certainty and, because it is often impossible, they settle for illusion of certainty. Author provides a good advice how avoid it:” When thinking and talking about risks, use frequencies rather than probabilities. Frequencies can facilitate risk communication”

2: The Illusion of Certainty
Here author start discussion of illusion of certainty by using picture:

Then author discusses source of illusion: human mind does not just transmit information about reality, it actually constract internal image of reality. Important thing to understand is that evolution selected individuals not on the basis of their ability correctly represent reality, but rather on the basis of their ability to act on such perception of reality that increases their chances of procreation.  Author then discusses a number of examples such as fingerprinting, believe religious and/or  trivial based purely on authority, marketing, and political propaganda. He also tells the story of physisians and their relations with patients, in which they usually have problems communicating real levels of their certanty or lack thereof about diagnosis and treatment. Finally author summarizes it in such way:” Learning to live with uncertainty is a daring task for individuals as well as societies. Much of human history has been shaped by people who were absolutely certain that their kin, race, or religion was the one most valued by God or destiny, which made them believe they were entitled to get rid of conflicting ideas along with the bodies polluted with them. Modern societies have come a long way toward greater tolerance of uncertainty and diversity. Nevertheless, we are still far from being the courageous and informed citizens whom Kant envisaged—a goal that can be expressed in just two Latin words: Sapere aude. Or in three English words: “Dare to know.””

3: Innumeracy
Here author looks at reasons for difficulties that people experience in dealing with uncertainty such as inability to manage probability, misunderstanding of statistical analysis, and other forms of innumeracy. Then author discusses connection between illusion of certainty and innumeracy, providing this list:

• Illusion of certainty. Franklin’s law is a mind tool to overcome the illusion of certainty, to help make the transition from certainty to uncertainty.

• Ignorance of risk. This is an elementary form of innumeracy in which a person does not know, not even roughly, how large a personally or professionally relevant risk is. This differs from the illusion of certainty in that the person is aware that there may be uncertainties, but does not know how great these are. The major tool for overcoming the ignorance of risk consists of various forms of information search (for example, scientific literature).

• Miscommunication of risk. In this form of innumeracy, a person knows the risks but does not know how to communicate these so that others understand them. The mind tool for overcoming miscommunication is representations that facilitate understanding.

• Clouded thinking. In this form of innumeracy, a person knows the risks but not how to draw conclusions or inferences from them. For instance, physicians often know the error rates of a clinical test and the base rate of a disease, but not how to infer from this information the chances that a patient with a positive test actually has the disease

After this author moves to defining Risk and quantifiable uncertainty and reviewing three major versions of probability interpretations: Degree of believe, Propensity, and Frequencies.

Then author discusses ignorance of risk and its miscommunication. As example, author applies this approach to communicating medical benefit for a drug:

Author ends this chapter with recommendation:” Overcoming innumeracy is like completing a three-step program to statistical literacy. The first step is to defeat the illusion of certainty. The second step is to learn about the actual risks of relevant events and actions. The third step is to communicate the risks in an understandable way and to draw inferences without falling prey to clouded thinking. The general point is this: Innumeracy does not simply reside in our minds but in the representations of risk that we choose.”4: Insight
Here author describes his work with physicians on decreasing their innumeracy and ignorance. Specifically, he used technic of modelling change from probabilities to frequencies. Here is graphic example:

Part II: Understanding Uncertainties in the Real World
In this part author reviews application of his approach in the following specific areas, providing some conclusion for each:

5: Breast Cancer Screening; 6: (Un) lnformed Consent; 7: AIDS Counseling;

8: Wife Battering; 9: Experts on Trial; 10: DNA Fingerprinting; 11: Violent People

Part III: From Innumeracy to Insight
12: How Innumeracy Can Be Exploited
Here author reviews a few examples when innumeracy of people in authorities effectively used to get money. Here is graph for 2 of them:

In short, effective presentation is a great tool to get whatever one wants from other people.

13: Fun Problems
This chapter presents a few funny applications and here is the one clearly demonstrating that majority does indeed could be much better than average:

14: Teaching Clear Thinking

Here author provides tips on how to improve understanding of reality:

Step 1 – Remember that everything is at least somewhat uncertain.

Step 2 – Analyze Risks

Step 3 – Analyze Communication and Representation

At the end author provides an interesting review of cultural differences in learning, but consistency of eventual ability to retain knowledge depending on training approach:


This is a very useful book that facilitates sound approach to understanding multitude of data provided by media and businesses in such form as to manipulate individual perception to achieve intendent political or business outcome. Analytical tools provided in this book make it a lot easier to see through manipulated data and therefore avoid being manipulated either into support of some party that is acting against one’s interest or buying something that one does not needs or really wants.

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