385 research outputs found
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
On Optimal Mechanisms in the Two-Item Single-Buyer Unit-Demand Setting
We consider the problem of designing a revenue-optimal mechanism in the
two-item, single-buyer, unit-demand setting when the buyer's valuations, , are uniformly distributed in an arbitrary rectangle
in the positive quadrant. We provide a complete and
explicit solution for arbitrary nonnegative values of . We
identify five simple structures, each with at most five (possibly stochastic)
menu items, and prove that the optimal mechanism has one of the five
structures. We also characterize the optimal mechanism as a function of , and . When is low, the optimal mechanism is a posted price
mechanism with an exclusion region; when is high, it is a posted price
mechanism without an exclusion region. Our results are the first to show the
existence of optimal mechanisms with no exclusion region, to the best of our
knowledge
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