Wednesday, March 19, 2014

The Weighted Morris Number (Morris Number 06)


When I calculated the range of ordinary Morris Numbers (OMNs) for the five tech companies discussed in Julianne Pepitone's CNN Money article, I thought about adding weights. Weights help to discriminate (npi) between companies with the same OMN but a different ordering of females and males. Weights are a way to take account of the gender pattern above the fifth highest ranking woman.


Two companies have an ordinary Morris Number (OMN) of 5: there are 5 men above the 5th highest ranking women. In one company the top 10 positions alternate between M and F. In the other company the top five positions are held by men, the next five by women.

To distinguish between such situations, we can use weights. Counting down from the top, the more men above each successive woman, the higher (worse) the metric will be.

The Weighted Morris Number (WMN) is calculated by using different weighting factors for the number of men whose position at the company is higher than one or more of the top five woman. The weights go down as you go down the hierarchy. The number of men higher than the top woman is multiplied by the biggest factor. Let us set it at 15. If the CEO is a woman, the contribution to the Morris Number for Female #1 is 0. If the top woman is 6th in the company, the contribution is 75 (5 x 15).

The set of multipliers might be:
     15 for the number of men above Female #1
     10 for the number of men between Female #1 and Female #2
       6 for the number of men between Female #2 and Female #3
       3 for the number of men between Female #3 and Female #4
       1 for the number of men between Female #4 and Female #5
The size of the steps between weights are 5-4-3-2.


If men and women alternate in the top 10 positions, the ordinary Morris Number is either 4, if a woman is at the top, or 5, if a man is at the top. The difference between the OMNs for those two situations is 1. The difference between the two WMNs is more dramatic. With a man in the number 1 position, the weighted Morris Number is
     1 x 15
     1 x 10
     1 x   6
     1 x   3
     1 x   1
for a total of 35. If a woman is in the top position, the weighted Morris Number is 20.
The bonus for a female CEO might make the weighted Morris Number a less desirable metric: it could encourage companies to rely on the Indira Phenomenon rather than ending discrimination.

Company 1: There are 50 men before you reach any women. The next 5 positions are held by women. The OMN is 50.

Company 2: The CEO is a woman. Then there are 5 men between her and F2, 35 men between F2 and the next two women, F3 and F4, then 10 more men between F4 and F5. The OMN is 50.

In Company 1, the top 5 females are below the executive tier. (I say that because it is rare for an organization to have more than 50 people with substantial executive clout.) Company 2 has a female CEO and another female also within the top 10. So far so good, but the Indira Phenomenon may dominate after F2.

Now consider the WMNs for these two companies: Company 1:
     750 = 50 men above F1 x 15
         0 = No men between F1 and F5
     750 = WMN

Company 2:
          0 = 15 x  0 men above F1
       50 = 10 x  5 men between F1 and F2
     210 =  6 x 35 men between F2 and F3
         0 =  3 x  0 men between F3 and F4
        10 = 1 x 10 men between F4 and F5
     270 = WMN

Company 2's WMN is about a third of Company 1's. Imagine if that fact were publicized at job fairs and university career offices and in a tweet that went viral. Company 2 would attract more and better women job seekers and more and better women customers. It would be able to achieve a level of excellence that company 1 could only envy until its top management finally realized that quality women should replace mediocre men.

March 19, 2014; rev 1 20140331,0403

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