Showing papers by "Piotr Faliszewski published in 2012"

Campaigns for lazy voters: truncated ballots

Abstract: We study elections in which voters may submit partial ballots consisting of truncated lists: each voter ranks some of her top candidates (and possibly some of her bottom candidates) and is indifferent among the remaining ones. Holding elections with such votes requires adapting classical voting rules (which expect complete rankings as input) and these adaptations create various opportunities for candidates who want to increase their chances of winning. We provide complexity results regarding planning various kinds of campaigns in such settings, and we study the complexity of the possible winner problem for the case of truncated votes.

Clone structures in voters' preferences

Abstract: In elections, a set of candidates ranked consecutively (though possibly in different order) by all voters is called a clone set, and its members are called clones. A clone structure is the family of all clone sets of a given election. In this paper we study properties of clone structures. In particular, we give an axiomatic characterization of clone structures, show that they are organized hierarchically, and analyze clone structures in single-peaked and single-crossing elections. We describe a polynomial-time algorithm that finds a minimal collection of clones that need to be collapsed for an election to become single-peaked, and we show that this problem is NP-hard for single-crossing elections.

Possible winners in noisy elections

Abstract: We consider the problem of predicting winners in elections given complete knowledge about all possible candidates, all possible voters (together with their preferences), but in the case where it is uncertain either which candidates exactly register for the election or which voters cast their votes. Under reasonable assumptions our problems reduce to counting variants of election control problems. We either give polynomial-time algorithms or prove #P-completeness results for counting variants of control by adding/deleting candidates/ voters for Plurality, k-Approval, Approval, Condorcet, and Maximin voting rules.

Rationalizations of Condorcet-consistent rules via distances of hamming type

Abstract: In voting, the main idea of the distance rationalizability framework is to view the voters’ preferences as an imperfect approximation to some kind of consensus. This approach, which is deeply rooted in the social choice literature, allows one to define (“rationalize”) voting rules via a consensus class of elections and a distance: a candidate is said to be an election winner if she is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance-rationalized. In this article, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance-rationalize the Young rule and Maximin using distances similar to the Hamming distance. It has been claimed that the Young rule can be rationalized by the Condorcet consensus class and the Hamming distance; we show that this claim is incorrect and, in fact, this consensus class and distance yield a new rule, which has not been studied before. We prove that, similarly to the Young rule, this new rule has a computationally hard winner determination problem.

Weighted manipulation for four-candidate Llull is easy

Abstract: Our main contribution is a surprising polynomial-time algorithm for weighed coalitional manipulation of four-candidate Copeland1 (also known as Llull) elections. On the technical side, our algorithm relies on a polynomial-time routine that solves a variant of the partition problem. We also show that there is a pseudopolynomial-time algorithm for weighted coalitional manipulation with a fixed number of candidates under any anonymous rule with a polynomial-time winner-determination procedure.

Fully Proportional Representation as Resource Allocation: Approximability Results

Abstract: We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no constant-factor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe's and Chamberlin and Courant's voting systems).