General Tiebreaking Schemes for Computational Social Choice

In (computational) social choice, how ties are broken can affect the axiomatic and computational properties of a voting rule. In this paper, we first consider settings where we may have multiple winners. We formalize the notion of parallel universes tiebreaking with respect to a particular tree that represents the computation of the winners, and show that the specific tree used does not matter if certain conditions hold. We then move on to settings where a single winner must be returned, generally by randomized tiebreaking, and examine some drawbacks of existing approaches. We propose a new class of tiebreaking schemes based on randomly perturbing the vote profile. Finally, we show that one member of this class uniquely satisfies a number of desirable properties.

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