Probability of a single event

[From Bruce Abbott (970109.1355 EST)]

Bill Powers (970108.1630 MST) to Chris Cherpas --

Of course, when you put it this way, I do have a perception of probability
or uncertainty, and I control it.

Yes, as Martin says, probability, like beauty, is a perception. However,
it's worth noting that we humans are not especially good at subjectively
evaluating the probabilities of many types of events; that's one reason why
statistical methods of evaluation were developed. One problem is that we
let our estimates of the _value_ to ourselves of those events affect our
estimation of their liklihood. We tend to overestimate the probability of
"good" consequences (e.g., winning the lottery) and underestimate the
probability of "bad" ones (e.g., being involved in a serious auto accident).

A second defect is that we tend to form opinions about the probability of
events based on the frequencies with which they come to our attention.
(Kahneman and Tversky call this the "availability heuristic.") For example,
we hear about nearly every commercial airliner crash, but rarely actually
see an airliner in flight. We vastly underestimate the number of such
flights going on each year, so it seems as though a fairly high percentage
of them end in disaster. In contrast, we hear about only a few auto
accidents (the local ones) of the thousands that happen each day, but we see
cars by the thousand on the road. The result is that we underestimate the
liklihood of auto accidents. So you have the bizarre result that many
people will take the car on a long trip because they believe they will be
safer than if they took a commercial airliner, when the reverse is true
according to objective evidence.

Perhaps another reason some prefer to drive rather than to fly is that they
feel more in control of their fate when driving. The commercial flier must
give control over to the pilot, to the air traffic controllers, and to those
who maintain the aircraft, and trust that they will do or have done their
jobs competently. And, of course, we all believe ourselves to be "better
than average" drivers!

When I'm driving my car, I don't even think about the risk under normal
circumstances; I just implicitly assume that I will get where I am going as
planned, and then drive in a way that leaves me feeling comfortable.
Certain perceptions may arise in the course of that drive that are quickly
followed by other perceptions -- the physical symptoms of anxiety -- arising
perhaps from an evaluation that I am in danger of or on the edge of losing
control. If it's not already too late, I will then act so as to reduce the
anxiety, perhaps by slowing down.

Evaluation of risk seems to be an ongoing thing, even though we may not be
conscious of it most of the time.

Regards,

Bruce