Stochastic Block Model Dynamics

The past few years have seen an increasing focus on fairness and the long-term impact of algorithmic decision making in the context of Machine learning, Artificial Intelligence and other disciplines. In this thesis, we model hiring processes in enterprises and organizations using dynamic mechanism design. Using a stochastic block model to simulate the workings of a hiring process, we study fairness and long-term evolution in the system.

We first present multiple results on a deterministic variant of our model including convergence and an accurate approximate solution describing the state of the deterministic variant after any time period has elapsed. Using the differential equation method, it can be shown that this deterministic variant is in turn an accurate approximation of the evolution of our stochastic block model with high probability.

Finally, we derive upper and lower bounds on the expected state at each time step, and further show that in the limiting case of the long-term, these upper and lower bounds themselves converge to the state evolution of the deterministic system. These results offer conclusions on the long-term behavior of our model, thereby allowing reasoning on how fairness in organizations could be achieved. We conclude that without sufficient, systematic incentives, under-represented groups will wane out from organizations over time.