This talk explores how an equitable distribution of benefits and costs might be achieved through optimization of a social welfare function (SWF). Such a function can be embedded in an optimization or machine learning model to obtain a fair solution, or used to assess the outcome of such a model for fairness. Emphasis is placed on SWFs that combine equity and efficiency, including alpha fairness (including the special case of proportional fairness, or the Nash bargaining solution), the Kalai-Smorodinsky bargaining solution, and recently proposed threshold functions. Structural properties of optimal solutions are derived, as a guide to selecting a suitable SWF for a given application. An assessment of popular group parity metrics used in AI is also presented, based on SWF analysis.
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