# Mathematics and Gender Relations

#### the consequences of nonrandom sampling Do our experiences accurately reflect the greater world?

Written 2001

Formatted 2009

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 well-defined characteristics. Although we believe that communication style and world-views, as described in "In another voice," "You just don't Understand," and "Men are from Mars," 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 one-sided simply reverse the labels "men" and "women" and correspondingly change other titles that may appear gender-specific.

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?"

### [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 non-jerks, 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 non-jerks for 10 relationships the rest out of 1 are "jerks" determine the percent 1 - 5% / 100 = 0.95 0.9510 = 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 non-jerks + 5 "jerks" + 5 more "jerks" 95 / (95+5+5) = 0.905 0.37 never date a jerk , 1-0.37 = 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) = 1-0.42 = 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, non-aggressor 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 non-aggressors 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 non-jerks 89 - 2 = 88 non-jerks 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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