Homophily and the Glass Ceiling Effect in Social

Homophily and the Glass Ceiling Effect in Social Networks Speaker: Lukas Walker

What do we talk about? The Glass Ceiling Effect Homphily The unseen, yet unbreakable barrier that keeps minorities and women from rising to the upper rungs of the corporate ladder, regardless of their qualifications or achievements. The tendency of individuals to prefer connections to those who are similar to themselves. (Example: Boys tend to become friends with other boys more easily than with girls. )

Who wrote this paper? Fields of study from top left to bottom right: Theoretical Computer Science TCS; TCS; TCS

Why is this paper interesting? • algorithmic growth > organic growth Example: Facebook recommends new friends • specific conditions can influence the Glass Ceiling effect

In short, what does this paper present? • formal definition of the Glass Ceiling effect in social networks • mathematical model of a social network with a glass ceiling • Proof: Specific conditions are necessary for the glass ceiling effect Interesting:

Success in Social Networks

Three phenoma in the model The Biased Referential Attachment Model: 1. «The rich get richer» : preferential attachment 2. Minority-majority partition 3. Homophily

«The richer get richer» Preferential Attachment Model • Grows over time • For any node, the probability for a new connection is proportional to its degree.

Minority-majority •

Homophily •

One time step 4. Retry connection according to preferential attachment X 2. Choose entry point according to preferential attachment

Initial state (Paper proves that it doesn’t matter)

Examples given in the paper

Examples given in the paper

Three phenoma in the model: Necessary and sufficient! 1. Preferential Attatchment 2. Minority-majority partition 3. Homophily Glass Ceiling Effect

What’s a Glass Ceiling in this model? •

What’s a Glass Ceiling in this model? •

What’s a Glass Ceiling in this model? •

Power Law in a graph •

Idea behind the proof

Proof: This leads to a Glass Ceiling! Given •

Proof: This leads to a Glass Ceiling! Given •

Proof: This leads to a Glass Ceiling! Given •

Proof: This leads to a Glass Ceiling! Given •

Visualization ✓ preferential attachment ✓ red minority ✓ homophily Glass Ceiling

Visualization ✓ preferential attachment ✓ red minority ✓ homophily no Glass Ceiling

Visualization ✓ preferential attachment ✓ red minority ✓ homophily no Glass Ceiling

Visualization ✓ preferential attachment ✓ red minority ✓ absolute homophily no Glass Ceiling

Examples in the real world

Conclusion • Homophily + minority Glass Ceiling • Removing one «ingredient» removes Glass Ceiling • Minority-Majority partition and homophily is bad for individuals!

Criticism • Is the degree a good measure? • Over-simplified model • No new conclusion

Thank you!