197 research outputs found
Combining Voting Rules Together
We propose a simple method for combining together voting rules that performs
a run-off between the different winners of each voting rule. We prove that this
combinator has several good properties. For instance, even if just one of the
base voting rules has a desirable property like Condorcet consistency, the
combination inherits this property. In addition, we prove that combining voting
rules together in this way can make finding a manipulation more computationally
difficult. Finally, we study the impact of this combinator on approximation
methods that find close to optimal manipulations
Dominating Manipulations in Voting with Partial Information
We consider manipulation problems when the manipulator only has partial
information about the votes of the nonmanipulators. Such partial information is
described by an information set, which is the set of profiles of the
nonmanipulators that are indistinguishable to the manipulator. Given such an
information set, a dominating manipulation is a non-truthful vote that the
manipulator can cast which makes the winner at least as preferable (and
sometimes more preferable) as the winner when the manipulator votes truthfully.
When the manipulator has full information, computing whether or not there
exists a dominating manipulation is in P for many common voting rules (by known
results). We show that when the manipulator has no information, there is no
dominating manipulation for many common voting rules. When the manipulator's
information is represented by partial orders and only a small portion of the
preferences are unknown, computing a dominating manipulation is NP-hard for
many common voting rules. Our results thus throw light on whether we can
prevent strategic behavior by limiting information about the votes of other
voters.Comment: 7 pages by arxiv pdflatex, 1 figure. The 6-page version has the same
content and will be published in Proceedings of the Twenty-Fifth AAAI
Conference on Artificial Intelligence (AAAI-11
Most Equitable Voting Rules
In social choice theory, anonymity (all agents being treated equally) and
neutrality (all alternatives being treated equally) are widely regarded as
``minimal demands'' and ``uncontroversial'' axioms of equity and fairness.
However, the ANR impossibility -- there is no voting rule that satisfies
anonymity, neutrality, and resolvability (always choosing one winner) -- holds
even in the simple setting of two alternatives and two agents. How to design
voting rules that optimally satisfy anonymity, neutrality, and resolvability
remains an open question.
We address the optimal design question for a wide range of preferences and
decisions that include ranked lists and committees. Our conceptual contribution
is a novel and strong notion of most equitable refinements that optimally
preserves anonymity and neutrality for any irresolute rule that satisfies the
two axioms. Our technical contributions are twofold. First, we characterize the
conditions for the ANR impossibility to hold under general settings, especially
when the number of agents is large. Second, we propose the
most-favorable-permutation (MFP) tie-breaking to compute a most equitable
refinement and design a polynomial-time algorithm to compute MFP when agents'
preferences are full rankings
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