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# Perception of Probability in the Real World project.

Topics 1-3 here are intended to occupy about 1/3 of the actual Berkeley course I teach, but topic 3 below includes some of the most distinctive features of the project and so is emphasised on this web site. Let me introduce it by comparison with two more standard topics of academic study.
1. Philosophy, logic and basic mathematics of probability and statistics exemplified by Hacking's An Introduction to Probability and Inductive Logic.
2. Psychology of chance. The study of how "ordinary people" think about chance, with emphasis on risks and financial uncertainty, has been studied a great deal in psychology and behavioral economics, pioneered by Amos Tversy and colleagues. A nice source is the book Cognition and Chance.

In class I don't say much about topic 1, because students have been exposed to many of the basics in other courses. For the record here is a list of scattered pages loosely related to topic 1. Topic 2 is great fun to talk about in class, and a source of student projects via repeating a textbook experiment -- see e.g. example of project. But in class I just repeat standard material, so it's not posted here.

#### Brief discussion of topics 1 and 2.

Authors in topic 2 have identified -- and attached names like base rate discounting and probability matching and anchoring to -- many cognitive biases, that is ways in which people are "predictably irrational" in thinking about probability. Authors in topic 1 adopt a normative style -- this is how you should reason about probability -- and point to topic 2 as evidence that untrained intuition not only can but actually does lead people astray. Both topics are intellectually interesting -- one as philosophy of science, the other as potentially shedding light on other aspects of human cognition. At the level of non-technical books, their approaches are complementary. A book on topic 1 develops some theory from first principles, showing simplified settings in which mathematics and logic can be correctly applied. A book on topic 2 describes a cross-section of settimgs where it is easy to go wrong, as a warning about what not to do.

How close is all this to the real world? Psychology research gets real data from real people, but the data mostly consists of subjects' answers to hypothetical questions involving uncertainty, or the behavior of volunteers participating in artificial experiments. As for the logic of probability, Hacking is considerably more creative in his examples than most authors of mathematical or philosophical texts, but still writes almost entirely about suppose examples. Can we get closer to the real world?

### 3. Perception of probability

At this point I need to confess that I don't have a very organized program, but have followed a "one thing leads to another" line of thought, as follows.

The psychology research studies responses when subjects are prompted to think about chance in some specific context. I want, instead, to study first

in what contexts do people think about chance without being prompted?
I'm not sure what existing academic literature has to say about this question, but students and I have examined various kinds of data (links below). Here "data" is in contrast with "examples invented by an author". We are seeking such data from different groups of people, initially groups defined in some way not directly related to chance (e.g. not "people interested in gambling"). It's fun to compare instance of chance as perceived by real people with those invented by philosophers or mathematicians, e.g. As a digression, a more theoretical way to consider perception of probability is by contemplating the words used in English language: Now these "everyday life" contexts where we perceive chance are usually regarded as quite different from the scientific and statistical contexts where mathematical probability theory is used. I am interested in drawing the Really Big Picture; in what aspects of "Life, the Universe, and Everything" do we perceive chance as playing a role? A first step, and a foundational point of our "perception of probability" program, is simply to write down a list that seeks to touch upon all aspects:

### List of 100 contexts where we perceive chance (open while under construction).

Such a list has several purposes. I believe that writers who claim, explicitly or implicitly, to be dealing with "probability in general" tend in fact to be working within some rather narrow vision of the contexts in which Probability arises, and comparison with a reference list serves to delineate a book's scope. Similarly, reading some generalization, either descriptive (examples tend to cluster into belief-type examples and frequency-type examples) or normative, ask yourself "in how many contexts is this useful?"

A future goal is to use the list as a reference for compiling some more organized "taxonomy" of where probability plays a role. The page

collects some existing taxonomies from sub-areas; though I am in general skeptical of "top-down" taxonomies whose authors seem not to have considered numerous real-world examples.