Results 1  10
of
14
Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders
"... Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of part ..."
Abstract

Cited by 48 (13 self)
 Add to MetaCart
Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of partial orders and a candidate c, two important questions arise: first, is c guaranteed to win, and second, is it still possible for c to win? These are the necessary winner and possible winner problems, respectively. We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We prove that for Copeland, maximin, Bucklin, and ranked pairs, the possible winner problem is NPcomplete; also, we give a sufficient condition on scoring rules for the possible winner problem to be NPcomplete (Borda satisfies this condition). We also prove that for Copeland and ranked pairs, the necessary winner problem is coNPcomplete. All the hardness results hold even when the number of undetermined pairs in each vote is no more than a constant. We also present polynomialtime algorithms for the necessary winner problem for scoring rules, maximin, and Bucklin.
Towards a Dichotomy for the Possible Winner Problem in Elections Based on Scoring Rules
, 2010
"... To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This direc ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, whether a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, kapproval, and Borda. Generalizing previous NPhardness results for some special cases, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSIBLE WINNER is NPcomplete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2, 1,...,1, 0), while it is solvable in polynomial time for plurality and veto.
Possible Winners When New Alternatives Join: New Results Coming Up!
"... In a voting system, sometimes multiple new alternatives will join the election after the voters’ preferences over the initial alternatives have been revealed. Computing whether a given alternative can be a cowinner when multiple new alternatives join the election is called the possible cowinner wi ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
In a voting system, sometimes multiple new alternatives will join the election after the voters’ preferences over the initial alternatives have been revealed. Computing whether a given alternative can be a cowinner when multiple new alternatives join the election is called the possible cowinner with new alternatives (PcWNA) problem, introduced by Chevaleyre et al. [4, 5]. In this paper, we show that the PcWNA problems are NPcomplete for the Bucklin, Copeland0, and Simpson (a.k.a. maximin) rule, even when the number of new alternatives is no more than a constant. We also show that the PcWNA problem can be solved in polynomial time for plurality with runoff. For the approval rule, we define three different ways to extend a linear order with new alternatives, and characterize the computational complexity of the PcWNA problem for each of them. 1
Computational complexity of two variants of the possible winner problem
 In Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems
, 2011
"... A possible winner of an election is a candidate that has, in some kind of incompleteinformation election, the possibility to win in a complete extension of the election. The first type of problem we study is the Possible coWinner with respect to the Addition of New Candidates (PcWNA) problem, whic ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
A possible winner of an election is a candidate that has, in some kind of incompleteinformation election, the possibility to win in a complete extension of the election. The first type of problem we study is the Possible coWinner with respect to the Addition of New Candidates (PcWNA) problem, which asks, given an election with strict preferences over the candidates, is it possible to make a designated candidate win the election by adding a limited number of new candidates to the election? In the case of unweighted voters we show NPcompleteness of PcWNA for a broad class of pure scoring rules. We will also briefly study the case of weighted voters. The second type of possible winner problem we study is Possible Winner/coWinner under Uncertain Voting System (PWUVS and PcWUVS). Here,
On problem kernels for possible winner determination under the kapproval protocol
, 2009
"... Abstract. The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes (partial orders) are extended into complete ones (linear orders) in a favorable way. Under the kapproval protocol, for every voter, the best k candida ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract. The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes (partial orders) are extended into complete ones (linear orders) in a favorable way. Under the kapproval protocol, for every voter, the best k candidates of his or her preference order get one point. A candidate with maximum total number of points wins. The POSSIBLE WINNER problem for kapproval is NPcomplete even if there are only two votes (and k is part of the input). In addition, it is NPcomplete for every fixed k ∈ {2,..., m − 2} with m denoting the number of candidates if the number of votes is unbounded. We investigate the parameterized complexity with respect to the combined parameter k and “number of incomplete votes ” t, and with respect to the combined parameter k ′: = m − k and t. For both cases, we use kernelization to show fixedparameter tractability. However, we show that whereas there is a polynomialsize problem kernel with respect to (t, k ′), it is very unlikely that there is a polynomialsize kernel for (t, k). We provide additional fixedparameter algorithms for some special cases. 1
New Candidates Welcome! Possible Winners with respect to the Addition of New Candidates
, 2010
"... In some voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. We give a computational study of the latter problem, focusi ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
In some voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. We give a computational study of the latter problem, focusing on scoring rules, and we give a formal comparison with related problems such as control via adding candidates or cloning.
Winner determination in voting trees with incomplete preferences and weighted votes
 Journal of Autonomous Agents and MultiAgent Systems
"... In multiagent settings where agents have different preferences, preference aggregation can be an important issue. Voting is a general method to aggregate preferences. We consider the use of voting tree rules to aggregate agents ’ preferences. In a voting tree, decisions are taken by performing a seq ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
In multiagent settings where agents have different preferences, preference aggregation can be an important issue. Voting is a general method to aggregate preferences. We consider the use of voting tree rules to aggregate agents ’ preferences. In a voting tree, decisions are taken by performing a sequence of pairwise comparisons in a binary tree where each comparison is a majority vote among the agents. Incompleteness in the agents ’ preferences is common in many reallife settings due to privacy issues or an ongoing elicitation process. We study how to determine the winners when preferences may be incomplete, not only for voting tree rules (where the tree is assumed to be fixed), but also for the Schwartz rule (in which the winners are the candidates winning for at least one voting tree). In addition, we study how to determine the winners when only balanced trees are allowed. In each setting, we address the complexity of computing necessary (respectively, possible) winners, which are those candidates winning for all completions (respectively, at least one completion) of the incomplete profile. We show that many such winner determination problems are computationally intractable when the votes are weighted. However, in some cases, the exact complexity remains unknown. Since it is generally computationally difficult to find the exact set of winners for voting trees and the Schwartz rule, we propose several heuristics that find in polynomial time a superset of the possible winners and a subset of the necessary winners which are based on the completions of the (incomplete) majority graph built from the incomplete profiles. 1
The Possible Winner Problem with Uncertain Weights
"... Abstract. The original possible winner problem is: Given an unweighted election with partial preferences and a distinguished candidate c, can the preferences be extended to total ones such that c wins? We introduce a novel variant of this problem in which not some of the voters ’ preferences are unc ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. The original possible winner problem is: Given an unweighted election with partial preferences and a distinguished candidate c, can the preferences be extended to total ones such that c wins? We introduce a novel variant of this problem in which not some of the voters ’ preferences are uncertain but some of their weights. Not much has been known previously about the weighted possible winner problem. We present a general framework to study this problem, both for integer and rational weights, with and without upper bounds on the total weight to be distributed, and with and without ranges to choose the weights from. We study the complexity of these problems for important voting systems such as scoring rules, Copeland, ranked pairs, plurality with runoff, and (simplified) Bucklin and fallback voting. 1
Cloning in Elections: Finding the Possible Winners
"... We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. The outcome of the resulting election may then depend onthenumberofclonesaswellasonhoweachvoterordersthecloneswithintheblock. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of common voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimumcost cloning manipulation. Finally, we compare cloning with two related problems: the problem of control by adding candidates and the problem of possible (co)winners when new alternatives can join. 1.