  Women have become better represented in business, academia, and government
over time, yet a dearth of women at the highest levels of leadership remains.
Sociologists have attributed the leaky progression of women through
professional hierarchies to various cultural and psychological factors, such as
self-segregation and bias. Here, we present a minimal mathematical model that
reveals the relative role that bias and homophily (self-seeking) may play in
the ascension of women through professional hierarchies. Unlike previous
models, our novel model predicts that gender parity is not inevitable, and
deliberate intervention may be required to achieve gender balance in several
fields. To validate the model, we analyze a new database of gender
fractionation over time for 16 professional hierarchies. We quantify the degree
of homophily and bias in each professional hierarchy, and we propose specific
interventions to achieve gender parity more quickly.
