171 research outputs found
On the manipulability of approval voting and related scoring rules
We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of alternatives: by comparison of worstalternatives, best alternatives, or by comparison based on stochastic dominance. We perform a similar exercise for -approval rules, where voters approve of a fixed number of alternatives. These results can be used to compare (-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of for which the -approval rule is minimally manipulable -- has the smallest number of manipulable preference profiles -- under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the -approval rule with around half the number of alternatives is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that -approval rules may improve on the approval rule as far as manipulability is concerned.public economics ;
How Hard Is It to Control an Election by Breaking Ties?
We study the computational complexity of controlling the result of an
election by breaking ties strategically. This problem is equivalent to the
problem of deciding the winner of an election under parallel universes
tie-breaking. When the chair of the election is only asked to break ties to
choose between one of the co-winners, the problem is trivially easy. However,
in multi-round elections, we prove that it can be NP-hard for the chair to
compute how to break ties to ensure a given result. Additionally, we show that
the form of the tie-breaking function can increase the opportunities for
control. Indeed, we prove that it can be NP-hard to control an election by
breaking ties even with a two-stage voting rule.Comment: Revised and expanded version including longer proofs and additional
result
Detecting Possible Manipulators in Elections
Manipulation is a problem of fundamental importance in the context of voting
in which the voters exercise their votes strategically instead of voting
honestly to prevent selection of an alternative that is less preferred. The
Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule
that simultaneously satisfies certain combinations of desirable properties.
Researchers have attempted to get around the impossibility results in several
ways such as domain restriction and computational hardness of manipulation.
However these approaches have been shown to have limitations. Since prevention
of manipulation seems to be elusive, an interesting research direction
therefore is detection of manipulation. Motivated by this, we initiate the
study of detection of possible manipulators in an election.
We formulate two pertinent computational problems - Coalitional Possible
Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW),
where a suspect group of voters is provided as input to compute whether they
can be a potential coalition of possible manipulators. In the absence of any
suspect group, we formulate two more computational problems namely Coalitional
Possible Manipulators Search (CPMS), and Coalitional Possible Manipulators
Search given Winner (CPMSW). We provide polynomial time algorithms for these
problems, for several popular voting rules. For a few other voting rules, we
show that these problems are in NP-complete. We observe that detecting
manipulation maybe easy even when manipulation is hard, as seen for example, in
the case of the Borda voting rule.Comment: Accepted in AAMAS 201
10101 Abstracts Collection -- Computational Foundations of Social Choice
From March 7 to March 12, 2010, the Dagstuhl Seminar 10101
``Computational Foundations of Social Choice \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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