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Explore the concept of equitable distribution of benefits and costs through social welfare function optimization in this 50-minute lecture by John Hooker from Carnegie Mellon University. Delve into the integration of social welfare functions in optimization and machine learning models to achieve fair solutions. Examine various functions that balance equity and efficiency, including alpha fairness, proportional fairness, the Nash bargaining solution, and the Kalai-Smorodinsky bargaining solution. Gain insights into the structural properties of optimal solutions to guide the selection of appropriate social welfare functions for specific applications. Analyze popular group parity metrics used in AI through the lens of social welfare function analysis. Recorded at IPAM's Mathematical Foundations for Equity in Transportation Systems Workshop, this talk provides a comprehensive overview of using mathematical approaches to address equity in complex systems.
