"MINORITY VIEWPOINTS, INDIVIDUALS, AND STATISTICS

Of more general concern than particular networks of personal associations is
the way that minority status-a crucial ingredient in many people's
identities-colors our view of many societal issues. In an oddly basic way, a
minority's viewpoint(s), and even an individual's, may be affected by
probability and statistics.

A thought experiment illustrates the point. (The term thought experiment
denotes an idealized investigation of a phenomenon that tries to capture its
essence without becoming bogged down in minutiae.) A supercharged area of
American life, race relations, certainly is in need of thought experiments,
simplistic though they may be. So let us experiment and assume that contrary
to fact, blacks and whites hold positions of equal importance and influence.
Assume further that about 10 percent of each group is racist, and that the
country is both residentially and professionally integrated. Given these
unrealistic assumptions it is not hard to demonstrate that since blacks
comprise approximately 13 percent of the population and whites the remaining
87 percent (for these purposes, whites are non-blacks), blacks still would
suffer disproportionately from racism.

The chance that a white will run into a black racist in any given encounter
with another person is 1.3 percent (10 percent of 13 percent), whereas the
likelihood that a black on any given encounter will do so is 8.7 percent (10
percent of 87 percent). This disparity becomes more pronounced as the number
of a person's contacts grow.

If a white person encounters 5 people, his or her chances of meeting at
least 1 racist are 6.3 percent, while the average number of racists he or
she will encounter is .07. By contrast, if a black person encounters 5
people, his or her chances of meeting at least 1 racist are 36.6 percent,
while the average number of racists he or she will encounter is .44. If a
white person encounters 25 people, his or her chances of meeting at least 1
racist rise to 27.9 percent, while the average number of racists he or she
will encounter rises to .33. If a black person encounters 25 people, his or
her chances of meeting at least 1 racist rise to 89.7 percent, while the
average number of racists he or she will encounter rises to 2.18.

The conclusion is that minority status by itself can make equal opportunity
difficult to achieve or maintain. In fact, if the already idealized above
mentioned conditions held, but now only 2 percent of whites and 10 percent
of blacks were racist, blacks would still encounter more racism than would
whites.

Most simple models can be made more realistic by introducing more
complicated assumptions. I'd like to add a couple to the example just
considered. First, replace racism with bias or general offensiveness.
Further, don't assume that individuals are biased or unbiased but rather
that they are biased to differing degrees, measured sim-plistically by
percentages. The numbers in this example would have to be massaged a bit,
but the same lesson would emerge: members of a minority group would
encounter more bias than would members of a larger group. Next, assume that
the minority group consists of only a few members, say a family. The effect,
of course, would be exacerbated. The family generally would be the recipient
of incomparably more bias or overall offensive-ness than it displayed to the
outside world ("generally" because the family might be quite nasty).

Let us take the scenario one step further and shrink the family to an
individual. Again, the individual generally would be the recipient of
incomparably more bias or offensiveness than he or she displayed to the
outside world (again, "generally" allows for the nasty exception). And we
are not only confronted with bias or offensiveness; all of us begin life as
small beings and know intimately what it is like to be powerless. Instances
of powerlessness are much more common than are instances of bias.

These elementary considerations shed some light on why so many of us feel
vulnerable and victimized. While most of us, at least by our own reckoning,
try to be kind and considerate to others, we very often find that "they" are
thoughtless and rude to us. Part of the explanation derives from arithmetic
and probability, but this insight should not be imparted to the snarling
driver stepping out of his car to contest your simultaneous discovery of
"his" parking spot.

Note that only one of the conventional elements of narrative played a role
in the aforementioned analysis: the simple notion of an agent's viewpoint.
The richness and complexity of most everyday situations make basic
arithmetic insights less visible. Similar observations hold for fictional
situations. Seeing events from the point of view of a character within a
story or through the eyes of the story's narrator is not conducive to
probabilistic reasoning. Almost any ostensibly improbable event is likely to
be explained away by the reader as resulting from some unspecified facts or
assumptions."

From "Once upon a number" by John Allen Paulos

---------------------------------------------

Regards

Lord Limbic