
A lot of things are said about gender relations, particularly when referring
to "the other gender." Mathematics, particularly probability, can give
us some insights regarding how we develop our views of other groups, such
as the other gender, by using a simple population model with welldefined
characteristics. Although we believe that communication style and worldviews,
as referenced to the side, account for most of our difficulties understanding,
still the implications of the following mathematical models need to be
considered.
This discussion will focus on, "should we expect one gender to have an
accurate view of the other, when judging from their own, and their friends
experiences?" To answer this question we will do a sequence of simple
population models. These population models are not meant to be accurate
descriptions, they are meant to give us insights into what to expect from
similar, but more complex populations. If the following discussion seems
onesided simply reverse the labels "men" and "women" and correspondingly
change other titles that may appear genderspecific.
Before reading further,
think of any two social groups that have developed distorted views of
each other, such as different religions. Ask yourself, "could this model
be generalized to describe the misunderstanding between these other two
groups?"

Gender studies:
the books previously referenced here (Men
are from Mars, You Just Don't Understand) are not recommended as they
are too simplistic.


[1] Simple Population Model
Assumptions:
 every woman will date exactly 10 men in her life
 5% of men are "jerks"
 all our relationship choices are purely random
 people do not change their personalities

These assumptions are not meant to be an accurate view of the world.
For example, we do not believe that a simple dualistic distinction
"jerks" and nonjerks, can be an accurate description of the range
of personality types, nor do we believe that our relationships are
purely random. We create this simplistic model because it is easy
to characterize and we can use the results for comparisons to real
experiences.

Doing the Math: basic probability
 determine the ratio of non"jerks"
 calculate the number of nonjerks for 10 relationships
 the rest out of 1 are "jerks"
 determine the percent

 1  5% / 100 = 0.95
 0.95^{10 }= 0.60
 1  0.60 = 0.40
 0.40*100 = 40%

On these assumptions, how many women will date an jerk? The calculation
are easy. The result for our assumptions will be that 40% of women
will date at least one jerk, even though only 5% of males are, in
fact, jerks.


What happens if we change the number of dates that we assume each
women will have? See the graph.
At 20 dates, nearly 70% of women will date at least one jerk, even
though "jerks" are only 5% of the male population.

[2] Extension 1: The male aggression model.
For this model, we keep all of the assumptions from above, but
add the assumption that "jerks", being more socially aggressive,
are twice as likely to get a date.

This model is based on the observations made by various people,
and is very easy to observe at clubs around college campuses. Certain
males, put considerably more effort into meeting girls, and meet
girls at a much greater rate than most males. These males, typically
treat girls poorly, and are known, at times, to express a certain
pride in that behavior.

Doing the math:
 figure the aggressor males as acting as likely as two males
in getting dates.
 Figure the new ratios
 follow the procedures above

 95 nonjerks + 5 "jerks" + 5 more "jerks"
 95 / (95+5+5) = 0.905
 0.37 never date a jerk , 10.37 = 0.63 date a jerk

In this model, fully 63% of women will date at least one jerk,
that is nearly 2/3,even though only 5% of males are "jerks".

What happens to our results if we give "jerks" credit for greater
aggression?
Realistic assumptions could easily put 80% of females dating jerks,
even with only 5% of the male population actually being jerks.


[3] Extension 2: The Female Choice Model
In this model we assume the same things as in our simple population
model #1, except that females do not chose males equally. Here we
assume that about 8% of the male population are "power males" and
about half of the power males are "jerks".

This model is also based on the observations of various people.
In college, we noted that females went out of their way to meet
"Zeke" and "CC." Zeke was typically a jerk and CC was not. In contrast,
other males, who were not "jerks", were typically disregarded or
even avoided. Gender equivalency occurred during a discussion in
college that went roughly: Male, "Why do girls always chose jerks,
instead of guys who will treat them with respect?" Female, "Why
do guys always chose domineering girls?"

Doing the math:
 double the number of power males who are not "jerks" and add
them to the non"jerks" group
 double the number of power males who are "jerks" and add them
to the "jerks" group
 find the new ratio
 follow the steps above

 95 + 4 = 98
 5 + 4 = 9
 98 / (98+9) =
 10.42 = 0.58

In this case, fully 58% of women will have dated at least one jerk,
even with jerks being less than 5% of males.

[4] Extension 3: The "Zelda's" Model
In this model, we recognize the male aggression in extension 1,
and the female choice in extension 2. We add two more aspects. First,
nonaggressor males may be less available, and second, some males
will temporarily emulate the behavior of more sexually successful
males. That behavior change may include dressing different, talking
different, and even trying to be a jerk.

This model is based on observations in certain college pickup joints
which were frequented by aggressor males more than passive males.
Less successful males tried to copy the behaviors more more successful
males. Scientists have observed this behavior emulation in birds,
primates, and pickup scenes. This scenario played out in the following
conversation during college. Female, "All the guys I meet are jerks!"
Male, "Why do you go to Zelda's to meet guys?"

Doing the math:
 account for the shortage on nonaggressors
 account for the activity of aggressors
 account for the "jerks" to which females respond
 account for the non "jerks" to which females respond
 account for non"jerks" emulating jerk behavior
 same
 find the new ratio
 follow the steps above

 95  10 = 85 non jerks
 5 + 5 = 10 relative "jerks"
 10 + 4 = 14 relative "jerks"
 85 + 4 = 89 nonjerks
 89  2 = 88 nonjerks
 14 + 2 = 18 relative "jerks"
 88 / (88+18) = 0.83
 only 15% never date a jerk

In this model fully 85% will date a jerk, even though "jerks" are
only 5% of the population.

Conclusions
Using very simple assumptions, we have demonstrated that
less than 5% of the male population can easily affect up to 85% of the
female population in a very negative way. (Again, the converse is, of
course, true.) So what can we learn about the world in general from
these simple models?
Lessons:
 The experiences of one group will probably not be an accurate
reflection of another group, even though they are real experiences.
 One group's perception of another group may be totally founded
in experience, yet still inaccurate.
 Parents worries about their daughters' relationships may be fully
grounded, even though the daughters trust both the guys in their
social groups and their ability to pick relationships.
 There will be many situation where a small percentage of a population
have a big effect on how we view the world.
 What others groups did you think of, where
you can apply this model to describe their misunderstandings?

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