Calculating the Morris Number - Hypotheticals (Morris Number 04)

The ordinary Morris Number, described here, is the number of men you pass, starting at the top of an organizational chart, on your way to finding the fifth highest ranking woman. 

Here are some illustrative examples.  A note on notation:  Female #3 or F3 means the 3rd highest ranking female.

A.  WOMEN'S ORGANIZATIONS

In a nunnery, the Morris Number is probably 0. If the Mother Superior is not really the top person but reports to a male Priest, the Morris Number is 1.

Note:  I thought the Girl Scouts might have a Morris Number of 0 but then I found the senior leadership here and realized I was wrong.  There is one man on that page and six women: Is the Morris Number 0 or 1?  We can infer that it is 1. The man apparently ranks third overall. This is suggested by the fact that the various Chiefs below the CEO and Chief of Staff are not in alphabetical order by title nor last name.  Mr. Boockvar, Chief Customer Officer, is listed above Chief Officers for Development, Information, and Financial, and the General Counsel (named, respectively, Taft, Miller, Olden and Rochon). If we were to use weights in calculating Morris Numbers, we would need to know M1's rank vis-a-vis F1 through F5. See Part 06 of this series.

Is a female as highly placed in the Boy Scouts organization? No. Their leadership team consists of eight men: three holding positions called "National" and designated volunteer -- the President, Commissioner and President-Elect, then four Scout Executives of different ranks and last the Chief Financial Officer.

B.  SOME POWERFUL FEMALES

This hypothetical organization has
    - one CEO, a female (F1)
              Contribution to Morris Number =   0
    - a COO, CFO and CTO, all reporting to the CEO; the first two are male and the CTO is female (F2): 
              Contribution to Morris Number =   2
    - five Executive Vice Presidents (EVPs); one is female (F3):
              Contribution to Morris Number =   4
    - eleven Senior Vice Presidents (SVP); one is female (F4): 
               Contribution to Morris Number = 10
    - one Associate Senior Vice President, a female (F5, so we can stop looking)
               Contribution to Morris Number =   0
                               The Morris Number is 16

Note that in this example we do not have to know the standing of Female #3 or Female #4, the lone female EVP and SVP, respectively, relative to the men with the same title because all those males are above Female #5. 


C.  ALL-MALE TOP MANAGEMENT

In this hypothetical organization:
    - The highest ranked woman is an Account Representative (AR).  Above her, there are 100 positions, all filled by males. 
            Contribution to Morris Number = 100.
     - There are 420 ARs, 20 of whom are women.   Without reliable information to know about the rank of the 5th women among the 420 ARs, we can nevertheless make some educated guesses.

       1. We can estimate the Morris Number assuming that the women and men in this organization have the same range of abilities. 

This may not be the case, especially given the absence of women in the first 100 positions and the widely accepted belief that people who do not conform to homosocial reproduction, which in this hypothetical means women, have to be better than men to attain the same level. Here is one citation for that proposition from thirty years ago: "Neutralizing Sexism in Mixed-Sex Groups: Do Women Have to Be Better Than Men?" by M. D. Pugh and Ralph Wahrman, American Journal of Sociology, 88:746-782 (Jan. 1983), available at http://www.jstor.org/stable/2779483, which references a study by the same authors from 1974 ("Sex, Noncomformity and Influence," Sociometry 37:137-47) in which they found that "[M]ale groups refused to be influenced by an obviously competent female despite the fact that without her they clearly failed at their task and lost money." Forty years later, how much has changed?

The 5th woman out of 20 is above 3/4 of the women.  She should therefore also rank above 3/4 of the men and therefore below 1/4 of them.
            Contribution to Morris Number:  1/4 of 400 = 100
            Morris Number assuming equal gender abilities:  200.
OR
        2. We can caculate the range of Morris Numbers, and the average within that range, obtained by calculating the lowest and highest possible numbers:
    - the Lowest Morris Number is obtained if the first five women are above all the men: 
            Contribution to Morris Number: 0 
            and
            the Morris Number is at least 100
    and
    - the Highest Morris Number:  all 400 men are above the first five women: 
            Contribution to Morris Number: 400
            and
            the Morris Number is at most 500

Morris Number Range: [100,400]. Average: 250

March 19, 2014; rev 1 20140328,0403