The Possible Winner Problem with Uncertain Weights
نویسندگان
چکیده
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.
منابع مشابه
The Possible Winner Problem with Uncertain Weights1
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 prob...
متن کاملA Novel Hybrid Modified Binary Particle Swarm Optimization Algorithm for the Uncertain p-Median Location Problem
Here, we investigate the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain. We propose a programming model for the uncertain p-median location problem with tail value at risk objective. Then, we show that it is NP-hard. Therefore, a novel hybrid modified binary particle swarm optimization algorithm is presented to obtai...
متن کاملThe robust vertex centdian location problem with interval vertex weights on general graphs
In this paper, the robust vertex centdian location problem with uncertain vertex weights on general graphs is studied. The used criterion to solve the problem is the min-max regret criterion. This problem is investigated with objective function contains $lambda$ and a polynomial time algorithm for the problem is presented. It is shown that the vertex centdian problem on general graphs i...
متن کاملClassical Center Location Problem Under Uncertain Environment
This paper investigates the $p$-center location problem on a network in which vertex weights and distances between vertices are uncertain. The concepts of the $alpha$-$p$-center and the expected $p$-center are introduced. It is shown that the $alpha$-$p$-center and the expected $p$-center models can be transformed into corresponding deterministic models. Finally, linear time algorithms for find...
متن کاملComputational complexity of two variants of the possible winner problem
A possible winner of an election is a candidate that has, in some kind of incomplete-information election, the possibility to win in a complete extension of the election. The first type of problem we study is the Possible co-Winner 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 d...
متن کامل