I presented a model I am very proud of on mathematical models of the glass ceiling in the Knesset (joint work with Chen Avin BGU, Claire Mathieu ENS, David Peleg Weizmann, Yvonne-Anne Pignolet IBB Zurich, Barbara Keller ETHZ, Hadassa Daltrophe BGU, Yinon Nahum Weizmann). The conorance Was interesting

1. The mathematics of gender
Prof. Zvi Lotker(1,2)
(1) Ben-Gurion University
(2) Bar Ilan University

2. Barbara
Keller
ETHZ
Collaborators
Chen
Avin
BGU
David
Peleg
Weizmann
Yvonne-Anne
Pignolet
IBM Zurich
Claire
Mathieu
Brown/ENS
Yinon
Nahum
Weizmann
Hadassa
Daltrophe
BGU

3. What math has to contribute to gender?

4. What math has to contribute to gender?
The Tribes’ argument
Philosophers
Politicians

5. The unseen argument
What math has to contribute to gender?

6. Minimal argument
What math has to contribute to gender?

7. Main contribution

8. Models for social networks
• Graphs 𝑮 𝟏, 𝑮 𝟐, 𝑮 𝟑 … where 𝑮 𝒕+𝟏 is derived from 𝑮 𝒕
• How? Vertex/edge arrival events
• Probabilistic Model

9. Preferential attachment
• Proposed by [Price ‘76] and [Barabási ,Albert ‘99] to explain
Power Law.
9
“The rich get richer”
• Dynamic, randomized
joining process
• Rule: a new site
attaches itself to each
site with probability
proportional to its
degree and the and
depend no the colors

10. Definition [Federal glass ceiling commission, 1995]:
“The unseen, yet unbreachable barrier that keeps minorities and women
from rising to the upper rungs of the corporate ladder, regardless of their
qualifications or achievements”
The glass ceiling effect
Our motivating question:
What prevents women
from reaching the stars?
Disclaimer: Potential solutions
are left for future study…

11. Individualsno.
Power level
How does it look?
The glass ceiling effect

12. How does it look?Individualsno.
Power level
The glass ceiling effect

13. A. Possible causes for inequality
The model considers
1. Minority
2. Homophily
3. The Rich Get Richer
One other possible cause:
4. Leaky pipeline
Individualsno.
Power level

14. Another possible cause for inequality
3. Leaky pipeline:
Members of the red population may quit work (or take
extended vacations) at a higher rate than members of the
blue population
Thanks
to David
Peleg for
the Slide

15. Leaky pipeline in STEM
[USA 2010 statistics]
Students
51% Male
49% Female
Graduates
54% Male
46% Female
First Ph.D. post
56% Male
44% Female
Next level
positions
63% Male
37% Female
Highest level
80% Male
20% Female
Thanks
to David
Peleg for
the Slide

16. Interpretation
To break the glass ceiling:
One should ensure
𝓡minority ⋅ 𝓡leakage ⋅ 𝓡homophily ≥ 1
or
𝑟
𝑏
⋅
𝑞 𝑅
𝑞 𝐵
⋅
𝜌 𝐵 1−𝜌 𝑅
𝜌 𝑅 1−𝜌 𝐵
≥ 1
Increase
women
entrance rate
Increase
women
activity rate
Reduce bias
against
women
Thanks
to David
Peleg for
the Slide

17. Conclusion
• 1 We saw two explanations for the glass ceiling
• 2 We have a formula that measures whether there is a glass ceiling or not
• 𝓡minority ⋅ 𝓡leakage ⋅ 𝓡homophily ≥ 1
• 3 Equality will increase if both parents go on maternity leave
• 4 Equality will increase if everyone went out of retirement at the same age
• Equality would increase if there were more collaborations