The Strong Maximum Circulation Algorithm: A New Method for Aggregating Preference Rankings
CoRR(2023)
摘要
We present a new optimization-based method for aggregating preferences in
settings where each voter expresses preferences over pairs of alternatives. Our
approach to identifying a consensus partial order is motivated by the
observation that a collection of votes that form a cycle can be treated as
collective ties. Our approach then removes unions of cycles of votes, or
circulations, from the vote graph and determines aggregate preferences from the
remainder. Specifically, we study the removal of maximal circulations attained
by any union of cycles the removal of which leaves an acyclic graph. We
introduce the strong maximum circulation, the removal of which guarantees a
unique outcome in terms of the induced partial order, called the strong partial
order. The strong maximum circulation also satisfies strong complementary
slackness conditions, and is shown here to be solved efficiently as a network
flow problem. We further establish the relationship between the dual of the
maximum circulation problem and Kemeny's method, a popular optimization-based
approach for preference aggregation. We also show that a minimum maximal
circulation – i.e., a maximal circulation containing the smallest number of
votes – is an NP-hard problem with multiple solutions and that the partial
orders induced by their removal may conflict.
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