This is a beta version cover page for general readers.
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.
- Philosophy, logic and basic mathematics of probability and statistics
exemplified by Hacking's
An Introduction to Probability and Inductive Logic.
- 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:
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.