Algorithms for Public Decision Making
In public decision making, we are confronted with the problem of aggregating the conflicting preferences of many individuals about outcomes that affect the group. Examples of public decision making include allocating shared public resources and social choice or voting. We study these problems from the perspective of an algorithm designer who takes the preferences of the individuals and the constraints of the decision making problem as input and efficiently computes a solution with provable guarantees with respect to fairness and welfare, as defined on individual preferences.
Concerning fairness, we develop the theory of group fairness as core or proportionality in the allocation of public goods. The core is a stability based notion adapted from cooperative game theory, and we show extensive algorithmic connections between the core solution concept and optimizing the Nash social welfare, the geometric mean of utilities. We explore applications in public budgeting, multi-issue voting, memory sharing, and fair clustering in unsupervised machine learning.
Regarding welfare, we extend recent work in implicit utilitarian social choice to choose approximately optimal public outcomes with respect to underlying cardinal valuations using limited ordinal information. We propose simple randomized algorithms with strong utilitarian social cost guarantees when the space of outcomes is metric. We also study many other desirable properties of our algorithms, including approximating the second moment of utilitarian social cost. We explore applications in voting for public projects, preference elicitation, and deliberation.
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