The Robert Example (corrected)
The Robert example is an instance of a class of uncertainty-centered
problems which lie beyond the reach of classical probability theory and
Bayesian techniques. However, the questions posed in the Robert example
fall within the reach of a perception-based generalization of probability
theory. The Robert example relates to everyday commonsense reasoning. It is
intended to draw attention to a major shortcoming of classical probability
theory and decision analysis the inability to operate on perception-based
information.
More specifically, assume that I am considering calling Robert
at home at 6:30 pm. The question is: Should I call him
person-to-person or station-to-station, given that the calls cost a
and b, respectively.
The decision-relevant information is the probability, P, that
Robert is home at 6:30 pm. Thus, the question is: What is P?
There are three versions of the information which I have -- in
order of increasing difficulty of analysis.
Version l. My perception is that Robert usually returns from work at about
6:00 pm.
Version 2. My perceptions are:
(a) Robert usually leaves his office at about 5:30 pm; and
(b) it usually takes him about 30 minutes to get home.
Version 3. My perceptions are:
(a) Robert usually leaves his office at about 5:30 pm; and
(b) the travel time depends on the time when he leaves office.
More specifically:
when Robert leaves at about 5:l5 pm, the travel time is usually about
25 minutes.
when Robert leaves at about 5:30 pm, the travel time is usually about
30 minutes.
when Robert leaves at about 5:45 pm, the travel time is usually about
35 minutes.
An additional question: What is the earliest time at which the
probability that Robert is home is high?
It is understood that in the Robert example, terms such as high,
usually, about 6:00 pm, etc., do not have a crisp meaning.
=====
Lotfi A. Zadeh
Professor in the Graduate School, Computer Science Division, Department of
EECS,
University of California, Berkeley, CA 94720-1776.
Director, Berkeley Initiative in Soft Computing (BISC)
Tel (office): (510) 642-4959, Fax (office): (510) 642-1712
Tel (home): (510) 526-2569, Fax (home): (510) 526-2433, (510) 526-5181
zadeh@cs.berkeley.edu,
http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html
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