Recognizing Top-Monotonic Preference Profiles in Polynomial Time

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/46 ◽

2017 ◽

Author(s):

Krzysztof Magiera ◽

Piotr Faliszewski

Keyword(s):

Polynomial Time ◽

Median Voter ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Recognition Problem ◽

Median Voter Theorem ◽

Weak Preference ◽

Single Peakedness ◽

Preference Orders

We provide the first polynomial-time algorithm for recognizing if a profile of (possibly weak) preference orders is top-monotonic. Top-monotonicity is a generalization of the notions of single-peakedness and single-crossingness, defined by Barbera and Moreno. Top-monotonic profiles always have weak Condorcet winners and satisfy a variant of the median voter theorem. Our algorithm proceeds by reducing the recognition problem to the SAT-2CNF problem.

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Recognizing Top-Monotonic Preference Profiles in Polynomial Time

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.11331 ◽

2019 ◽

Vol 66 ◽

pp. 57-84 ◽

Cited By ~ 1

Author(s):

Krzysztof Magiera ◽

Piotr Faliszewski

Keyword(s):

Polynomial Time ◽

Median Voter ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Recognition Problem ◽

Median Voter Theorem ◽

Weak Preference ◽

Single Peakedness ◽

Preference Orders

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Computational Aspects of Nearly Single-Peaked Electorates

Journal of Artificial Intelligence Research ◽

10.1613/jair.5210 ◽

2017 ◽

Vol 58 ◽

pp. 297-337 ◽

Cited By ~ 2

Author(s):

Gábor Erdélyi ◽

Martin Lackner ◽

Andreas Pfandler

Keyword(s):

Polynomial Time ◽

Strategic Behavior ◽

Distance Measure ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Distance Measures ◽

Voting Rules ◽

Single Peakedness ◽

Computational Aspects ◽

And Control

Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting rules are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to single-peaked electorates, these rules suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra studied the computational complexity of strategic behavior in nearly single-peaked electorates. These are electorates that are not single-peaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding single-peakedness. We prove that determining whether a given profile is nearly single-peaked is NP-complete in many cases. For one case we present a polynomial-time algorithm. In case the single-peaked axis is given, we show that determining the distance is always possible in polynomial time. Furthermore, we explore the relations between the new notions introduced in this paper and existing notions from the literature.

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ERROR CORRECTING ANALYSIS FOR TREE LANGUAGES

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001400000234 ◽

2000 ◽

Vol 14 (03) ◽

pp. 357-368 ◽

Cited By ~ 9

Author(s):

DAMIÁN LÓPEZ ◽

JOSÉ M. SEMPERE ◽

PEDRO GARCÍA

Keyword(s):

Pattern Recognition ◽

Polynomial Time ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Error Model ◽

Recognition Problem ◽

Tree Automaton ◽

Pattern Recognition Problem ◽

Syntactic Approach ◽

Tree Languages

To undertake a syntactic approach to a pattern recognition problem, it is necessary to have good grammatical models as well as good parsing algorithms that allow distorted samples to be classified. There are several methods that obtain, by taking two trees as input, the editing distance between them. In the following work, a polynomial time algorithm which processes the distance between a tree and a tree automaton is presented. This measure can be used in pattern recognition problems as an error model inside a syntactic classifier.

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Learning Importance of Preferences

10.29007/v68w ◽

2018 ◽

Author(s):

Ying Zhu ◽

Mirek Truszczynski

Keyword(s):

Polynomial Time ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Scoring Rules ◽

Np Hard ◽

Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

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