Willful Ignorance: The Mismeasure of Uncertainty

Herbert Weisberg's historical exploration of the roots and meaning of what we call 'Probability' should be on the desk (or on the professional bookshelf) of every undergraduate student, and every graduate student for whom knowledge of statistics and probability are necessary professional requirements. That would also include students at professional schools that include law, business administration, public administration, banking and finance, and every other professional discipline engaged in forecasting future events and trend-lines. In short, any job or profession whose practitioners are tasked with discovering the likelihood of future happenings.I awarded Mr. Weisberg's treatise the customary 'five stars' denoting excellence; but I also rate books, and this would be one of them, on the basis of how many heavy-duty highlighters I consume in identifying significant passages within those books that I want to bookmark for future reference. In this case, Mr. Weisberg also earns my 'four-highlighter' designation simply on the basis of the wealth of information that he includes. On top of that, the book is eminently readable, and Mr. Weisberg is a thoroughly engaging storyteller as he walks the reader through the truly fascinating history of how we come to educate ourselves to the likelihood that certain kinds of events will, to a greater or lesser extent, happen at some future time.The science of ascertaining and describing probabilities is really less than 500 years old. Neither classical Greece nor Imperial Rome were able to develop the type of thinking and intellectual inquiry that are necessary for even thinking about probabilities in the abstract, and then calculating the odds of something actually happening, to occur. For the Ancients, mathematics was all about geometry and Platonic ideals. Fast-forward a thousand years, and Arabic mathematicians built upon what the Ancients had begun, but by adding their own contribution mathematical thinking and practice, beginning with what we now call algebra.Fast forward again another 500 years, we now have mathematical thinkers in France and elsewhere in Europe who were also inveterate gamblers. These men apparently spent most of their leisure time working to develop a coherent science of calculating gambling odds, whether through flipping coins or rolling dice in various multiples. Although gambling, per se, frequently met with social disapproval, for many of the well-to-do it was a guilty pleasure. And being avid competitors with one another (as well as being risk-aversive) those brilliant minds went to work trying to figure out how to win consistently at betting. In this regard, the world has changed little from its Sixteenth Century counterpart.As one might expect, that type of mathematical mental prowess was not confined to the gaming tables, and it certainly proved to be useful by Dutch merchants engaged in overseas trade who needed to hedge their risks in the form of ships lost at sea, along with their cargoes.Using translations of original essays, treatises, and interpersonal letters, Mr. Weisberg walks the reader through the history of probabilistic thinking, showing how other developments in science and mathematics than being developed and refined in parallel with explorations into the laws of probability, eventually effectuated a convergence of the concepts of odds that something would happen with mathematics that could be used to calculate a numerical statement that could be used to show precisely what degree of potentiality existed for the event being examined to occur.Mr. Weisberg goes on to show that mathematics made probabilistic thinking possible in today's world, and with huge success. That high level of success has all but supplanted the earlier notions of probability based upon the more ambiguous notions of likelihood that an event would occur, or not occur, and that mathematically-calculated probabilities are now being overused to the point that scientists are now achieving inconsistent results that cannot be replicated by subsequent researchers, which is essentially a negation of the scientific method.All in all, Mr. Weisberg has done a thoroughly admirable job. My only comment, not to be overly critical in light of the overall excellence of his book, would be to suggest that many of the tools of behavioral economics, especially those regarding the identification and modulation of what are known as Heuristics and Biases are subjects for future exploration. If, as Mr. Weisberg suggests, mathematically-generated probabilities that are so important in STEM disciplines are markedly less effective in describing and predicting probabilities in the social sciences where inconsistent thinking and ambiguities abound, that is where future research ought to occur.As a lawyer whose métier was in negotiation and dispute resolution I would have to agree. Every settlement conference that I attended had the opposing lawyers throwing exaggerated or unsubstantiated probabilities dressed up as curve-balls at one another, hoping to bully or con the other side into thinking that they stood little or no chance of prevailing if the case went to trial. Entirely apart from that being a 'dialogue of the deaf', none of these people really knew what they were talking about. For the lawyers, it was an exercise in shamanism, a ritual that every trial lawyer goes through on the way to settlement, dramatic but wholly unedifying in the way it is practiced nowadays. As a mediator working to bring the opposing parties together, the legal profession's pervasive lack of understanding about statistics and probabilities made settlement negotiations all the more difficult, especially where the research findings of Behavioral Economics have become widely known only in the last decade or two.Even where research findings in statistical probabilities have been publicized, assimilating that knowledge and understanding the assumptions implicit in applying that knowledge have been a long time in coming. Law school courses on the Rules of Evidence, likewise, have not kept up with research findings in behavioral psychology, particularly in the area of cognitive biases and judgment-making heuristics nowhere to be found in the law school curriculum. It seems rather odd that in a legal proceeding that is intended to determine the truth of the matter at hand based upon probabilities, i.e., that one party's version of the fact is more likely to be true than his opponent's, has nothing in the way of probabilistic thinking to support the fact-finding and legal argument that follow. This may be attributed to failures of imagination on the part of the trial bar and bench, and lawyers who skimp on pretrial discovery because the time and expense impact their bottom line. It also gives unfair advantage to institutional defendants who use their enormous databases to justify settlements based upon what they claim to be 'typical' or 'average' fact patterns. If we have learned anything over the last decade or two, it is that extreme random events do occur that confound every expectation. Used to be that judgments were made on the basis of one's life experience, or those of close neighbors, or others with whom we are constantly in contact. Nowadays, there are arguably more computers than there are people, and it is possible to create hypothetical scenarios that explore the 'what if's' that are the basis of probability studies. It is fashionable, indeed even de rigueur for a lawyer or someone in authority to declare that 'he could not imagine' an event happening that could cause the injuries suffered to occur, and yet it happens and with increasing regularity. Not only are outliers predictable, they are measurable. We need better teachers and training in probabilistic thinking. I have fervent hopes that Mr. Weisberg will eventually be able to lend his expertise to that effort.In the meantime, Mr. Weisberg's engaging and well-conceived book on how we measure, or mismeasure, uncertainty and evaluate ambiguities in any sort of situation are well worth reading, just for their own sake. I would even go so far as to say that his book is so accessible that even high school students would be able to read and understand it, despite the stresses and distractions they have to endure on a daily basis simply by being teenagers. I would love to of had it when I was in high school six decades ago.

Willful Ignorance: The Mismeasure of Uncertainty by Herbert Weisberg addresses uncertainty in the information all of us use to make decisions, for example, decisions about medications, medical procedures, transportation options, investments, life style practices. Willful Ignorance is a well-written, enlightening book that explains and demystifies the characteristics of information uncertainty. The material is presented at a non-technical level that can be enjoyed and comprehended by anyone interested in gaining an understanding of information uncertainty; also, researchers, analysts, and clinicians working in the biomedical and social sciences as well as lawyers and judges who deal with legal arguments based on probabilities can benefit by reading the book. Probability is the central theme of the book, but, as the author explains, the book does not focus on the mathematics of probability, but on the conception of probability as a measure of uncertainty. What is probability, and if we know the answer to that question, under what circumstances is probability a useful measure of uncertainty? Willful Ignorance provides answers to these questions. Along the way, the book includes the historical development of probability, which is written in an entertaining style enhanced by the author’s efforts to develop his treatment of the history of probability directly from original historical treatises, articles, and letters. But the principal message in the book is that probability is currently an ineffective measure of uncertainty because to calculate a probability many ambiguities are and must be knowingly ignored. Therefore, willful ignorance, i.e., ignoring known ambiguities, leads to a dilemma: willful ignorance is necessary to make scientific progress; at the same time willful ignorance stifles scientific progress. The vast majority of the book is devoted to defining and explaining the dilemma. In the final chapter, the author proposes a “solution” (his quotation marks) - looking toward “big data” (my quotation marks) to study and corral ambiguities and mindful rather than willful ignorance to address the dilemma. I found Willful Ignorance enlightening and entertaining; I recommend it for biomedical and social science researchers, analysts, and clinicians; lawyers and judges; and anyone else interested in understanding information uncertainty.

Willful Ignorance is a great read on multiple levels.First, it is great history that is enjoyable to read, making the person stories of the great mathematicians really come alive.Second, you will come away with a more intuitive feel for the strengths and weakness of various approaches, in particular Bayes Theorm, Fisherian stats testing and contemporary stats testing.Third, this is a critical piece of the history of statistics and probability. Daston's history uncovers the fundamental importance of contracts in 17th century Europe, but Weisberg uncovers the role of metaphor in classical probabilism, demonstrating that the frequent use of gambling in early probabilistic math was bound with the role of a metaphorical lottery in Bernoulli and subsequent probabilists. The role of a perfectly random lottery was metaphorical because early probabilists understood that their models accounted for doubt, but not for ambiguity. Ambiguity over what features have a causal role in a phenomenon binds mathematicians to domain experts in a dialectical process of "trust, but verify" that never ends. However, this metaphor "died" over time, such that the reified lottery needed to be located somewhere - either out in reality or in our minds - leading to the misleading contemporary debate around objective vs subjective probability.Fourth, this text is a call to arms for contemporary researchers and statisticians to retrieve the notion of a methaphorical lottery, and the mission to "trust, but verify". This call has rarely been more urgent, in particular in AI where there is little to no concern with causation. This is a great example of learning from our history to inform our craft today.

No debate corriqueiro sobre dados, que cresceu com o hype de "Big data", dados expressam certeza e probabilidades são precisas. Weisberg mostra o quanto falta de estofo a esse debate aparentemente profundo e o quanto é antigo esse debate aparentemente moderno.

Probability and statistics play a huge and ever-increasing role in public policy discussions. Is the climate changing? Do PSA tests save lives? Have early childhood education programs helped poor children? The list is endless. All of these involve complex statistical arguments. There is a tendency these days to apply statistical tests blindly to individual cases, often with poor results.Here is just one example. Suppose that a doctor has diagnosed a patient with disease X. Scientific studies show 70% of the patients given treatment A are cured while only 40% of patients given treatment B are cured. The government and insurance companies may use these data to pressure (or insist) that doctors use treatment A. However, suppose that treatment A requires the patient to take a complex sequence of multiple pills several times a day, never missing one and doing this accurately with respect to mealtimes while treatment B consists of taking just one pill at dinner time. Now suppose a doctor has just diagnosed a patient with disease X but in his or her clinical judgment does not believe the patient to be capable of maintaining the regime required for treatment A. Should the doctor prescribe treatment B? Probability theory and advanced statistical tests don’t provide much guidance here.Dr. Weisberg’s book is about the application of probability and statistics to social, economic, and medical applications, but is not mathematical at all. It is about the larger context of what probability and statistics really mean, their history, and their misuse due to lack of understanding what the concepts can and cannot do. People have a hard time grasping the idea of uncertainty and how to deal with it. Given the importance of this subject and how many things in daily life and the public policy sphere are uncertain, this book should be required reading for anyone having to make major decisions involving uncertainty and is worthwhile reading for anyone interested in the long history of dealing with uncertainty and how we got where we are now.

This book provides an original account of willful ignorance and how this principle relates to modern probability and statistical methods.Its intended readership includes professionals in statistics and related fields, including practicing and research clinicians, biomedical and social science researchers, business leaders, and policy-makers. The author is certainly well qualified: Herb Weisberg graduated from Columbia University and received his doctorate in statistics from Harvard. After a brief stint in academia, he has spent the bulk of his career as a statistical consultant.This book combines the history of a big idea, with a prescription for change. It is well illustrated and packed with original quotations. Extensive references are included.I'd say it was suitable for an academic and specialist audience, and that university libraries would do well to stock it. The very well informed lay reader might have a crack at it, but this is no book for the statistical dilettante!

An intriguing book that is both ambitious and necessary in it's critique of modern culture's obsession with analysis. Weisberg looks in depth and with a fair bit of thought provoking insight on the differing approaches of qualitative and quantitative methods of information gathering and dissemination and charts not just the societal advantages but the weaknesses inherent in statistical analysis- something recently brought home in the Real World by the catastrophic failure of the biggest polling operations to predict the shape of the General election outcome correctly.Although well written and an 'accessible' narrative this is nonetheless a book for professionals involved in the field, who will glean much from this book.

Fascinating, intriguing & divisive are the three words I would use to sum up this book. By examining the divide between qualitative & quantitative research methodologies - both historic & current; Dr Weisberg discusses why he believes that our current approaches to research need to be reassessed & redesigned to allow a more productive application. Brilliantly researched, and well referenced this is not a book for the uninitiated, but it's a book that will certainly provoke further discussion.