Satisfying Complex Top-𝑘 Fairness Constraints by Preference Substitutions

Senjuti Basu Roy

Abstract:

Given 𝑚 users (voters), where each user casts her preference for
a single item (candidate) over 𝑛 items (candidates) as a ballot, the
preference aggregation problem returns 𝑘 items (candidates) that
have the 𝑘 highest number of preferences (votes). Our work studies
this problem considering complex fairness constraints that have to
be satisfied via proportionate representations of different values of
the group protected attribute(s) in the top-𝑘 results. Precisely, we
study the margin finding problem under single ballot substitutions,
where a single substitution amounts to removing a vote from can-
didate 𝑖 and assigning it to candidate 𝑗 and the goal is to minimize
the number of single ballot substitutions needed to guarantee that
the top-𝑘 results satisfy the fairness constraints. We study several
variants of this problem considering how top-𝑘 fairness constraints
are defined, (i) MFBinaryS and MFMultiS are defined when the
fairness (proportionate representation) is defined over a single,
binary or multivalued, protected attribute, respectively; (ii) MF-
Multi2 is studied when top-𝑘 fairness is defined over two different
protected attributes; (iii) MFMulti3+ investigates the margin find-
ing problem, considering 3 or more protected attributes. We study
these problems theoretically, and present a suite of algorithms with
provable guarantees. We conduct rigorous large scale experiments
involving multiple real world datasets by appropriately adapting
multiple state-of-the-art solutions to demonstrate the effectiveness
and scalability of our proposed methods.