Fair Social Choice in Dynamic Settings

We study a dynamic social choice problem in which an alternative is chosen at each round according to the reported valuations of a set of agents. In the interests of obtaining a solution that is both efficient and fair, we aim to maximize the Nash social welfare, which is the product of all agents’ utilities. We present three novel rules and discuss some of their properties. Two are greedy algorithms and the third attempts to explicitly learn the distribution over inputs, updating its decisions by solving a convex program at each round. We also take a more generally applicable algorithm from existing literature and apply it to our problem. Finally, we compare all four algorithms against the offline optimal solution in simulations.

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