  Fair re-ranking aims to redistribute ranking slots among items more equitably
to ensure responsibility and ethics. The exploration of redistribution problems
has a long history in economics, offering valuable insights for conceptualizing
fair re-ranking as a taxation process. Such a formulation provides us with a
fresh perspective to re-examine fair re-ranking and inspire the development of
new methods. From a taxation perspective, we theoretically demonstrate that
most previous fair re-ranking methods can be reformulated as an item-level tax
policy. Ideally, a good tax policy should be effective and conveniently
controllable to adjust ranking resources. However, both empirical and
theoretical analyses indicate that the previous item-level tax policy cannot
meet two ideal controllable requirements: (1) continuity, ensuring minor
changes in tax rates result in small accuracy and fairness shifts; (2)
controllability over accuracy loss, ensuring precise estimation of the accuracy
loss under a specific tax rate. To overcome these challenges, we introduce a
new fair re-ranking method named Tax-rank, which levies taxes based on the
difference in utility between two items. Then, we efficiently optimize such an
objective by utilizing the Sinkhorn algorithm in optimal transport. Upon a
comprehensive analysis, Our model Tax-rank offers a superior tax policy for
fair re-ranking, theoretically demonstrating both continuity and
controllability over accuracy loss. Experimental results show that Tax-rank
outperforms all state-of-the-art baselines in terms of effectiveness and
efficiency on recommendation and advertising tasks.
