133,342 research outputs found
The Complexity of Fully Proportional Representation for Single-Crossing Electorates
We study the complexity of winner determination in single-crossing elections
under two classic fully proportional representation
rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for
these rules is known to be NP-hard for unrestricted preferences. We show that
for single-crossing preferences this problem admits a polynomial-time algorithm
for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our
algorithm for Chamberlin--Courant's rule can be modified to work for elections
with bounded single-crossing width. To circumvent the hardness result for
Monroe's rule, we consider single-crossing elections that satisfy an additional
constraint, namely, ones where each candidate is ranked first by at least one
voter (such elections are called narcissistic). For single-crossing
narcissistic elections, we provide an efficient algorithm for the egalitarian
version of Monroe's rule.Comment: 23 page
Multiwinner Voting with Fairness Constraints
Multiwinner voting rules are used to select a small representative subset of
candidates or items from a larger set given the preferences of voters. However,
if candidates have sensitive attributes such as gender or ethnicity (when
selecting a committee), or specified types such as political leaning (when
selecting a subset of news items), an algorithm that chooses a subset by
optimizing a multiwinner voting rule may be unbalanced in its selection -- it
may under or over represent a particular gender or political orientation in the
examples above. We introduce an algorithmic framework for multiwinner voting
problems when there is an additional requirement that the selected subset
should be "fair" with respect to a given set of attributes. Our framework
provides the flexibility to (1) specify fairness with respect to multiple,
non-disjoint attributes (e.g., ethnicity and gender) and (2) specify a score
function. We study the computational complexity of this constrained multiwinner
voting problem for monotone and submodular score functions and present several
approximation algorithms and matching hardness of approximation results for
various attribute group structure and types of score functions. We also present
simulations that suggest that adding fairness constraints may not affect the
scores significantly when compared to the unconstrained case.Comment: The conference version of this paper appears in IJCAI-ECAI 201
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