scholarly journals On coalitional manipulation for multiwinner elections: shortlisting

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Robert Bredereck ◽  
Andrzej Kaczmarczyk ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Strategic Voting ◽  
Evaluation Functions ◽  
Group Evaluation ◽  
Voting Rule ◽  
Comprehensive Picture ◽  
Depth Study ◽  
Special Case

AbstractShortlisting of candidates—selecting a group of “best” candidates—is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the perhaps most basic voting rule in this scenario, $$\ell $$ ℓ -Bloc (every voter approves $$\ell $$ ℓ  candidates). In particular, we investigate the influence of several different group evaluation functions (e.g., egalitarian versus utilitarian) and tie-breaking mechanisms modeling pessimistic and optimistic manipulators. Among other things, we conclude that in an egalitarian setting strategic voting may indeed be computationally intractable regardless of the tie-breaking rule. Altogether, we provide a fairly comprehensive picture of the computational complexity landscape of this scenario.

scholarly journals On Coalitional Manipulation for Multiwinner Elections: Shortlisting

2017 ◽  
Author(s):  
Robert Bredereck ◽  
Andrzej Kaczmarczyk ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Strategic Voting ◽  
Evaluation Functions ◽  
Group Evaluation ◽  
Voting Rule ◽  
Comprehensive Picture ◽  
Depth Study ◽  
Special Case

Shortlisting of candidates—selecting a group of “best” candidates—is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the most natural and simple voting rule in this scenario, l-Bloc (every voter approves l candidates). In particular, we investigate the influence of several tie-breaking mechanisms (e.g. pessimistic versus optimistic) and group evaluation functions (e.g. egalitarian versus utilitarian) and conclude that in an egalitarian setting strategic voting may indeed be computationally intractable regardless of the tie-breaking rule. We provide a fairly comprehensive picture of the computational complexity landscape of this neglected scenario.

Adding flexibility to the links of a rigid-link dynamic model of an articulated robot

Robotica ◽  
1989 ◽  
Vol 7 (2) ◽  
pp. 165-168 ◽  
Author(s):  
A. Bodner
Keyword(s):  
Computational Complexity ◽  
Dynamic Model ◽  
Euler Equations ◽  
Inverse Dynamics ◽  
Small Degree ◽  
End Effector ◽  
Rigid Link ◽  
Link Model ◽  
Articulated Robot ◽  
Special Case

SUMMARYA method was developed that takes into account flexibility of robot links in the inverse dynamics calculations. This method uses the Newton-Euler equations and is applicable for special case systems that allow for only a small degree of flexibility. Application of the method should improve the accuracy of the position of the end effector during motion of the robot.The results of this study show that the method can be based entirely on an existing rigid-link model with only minimal changes required as additions. The computational complexity of the method is discussed briefly as well and indicates an increase of computations of slightly more than a factor of two as compared to a rigid-link model for the same robot geometry.

scholarly journals Adapting Stable Matchings to Evolving Preferences

2020 ◽  
Vol 34 (02) ◽  
pp. 1830-1837 ◽  
Author(s):  
Robert Bredereck ◽  
Jiehua Chen ◽  
Dušan Knop ◽  
Junjie Luo ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Computational Cost ◽  
Modern Society ◽  
Stable Matching ◽  
Stable Marriage ◽  
Fixed Parameter Tractability ◽  
Stable Matchings ◽  
Changing Environments ◽  
Fixed Parameter ◽  
Comprehensive Picture

Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing “incrementalized versions” of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters “degree of change” both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter “distance between old and new stable matching”.

Literacy, Information, and Party System Fragmentation in India

2017 ◽  
Vol 51 (5) ◽  
pp. 555-586
Author(s):  
Arturas Rozenas ◽  
Anoop Sadanandan
Keyword(s):  
Party System ◽  
Strategic Voting ◽  
Access To Information ◽  
Aggregate Level ◽  
Individual Level ◽  
Common Information ◽  
Voting Rule ◽  
Level Data ◽  
Duverger's Law ◽  
Individual Information

A rich theoretical literature argues that, in contradiction to Duverger’s law, the plurality voting rule can fail to produce two-party system when voters do not share their common information about the electoral situation. We present an empirical operationalization and a series of tests of this informational hypothesis in the case of India using constituency- and individual-level data. In highly illiterate constituencies where access to information and information sharing among voters is low, voters often fail to coordinate on the two most viable parties. In highly literate constituencies, voters are far more successful at avoiding vote-wasting—in line with the informational hypothesis. At a microlevel, these aggregate-level patterns are driven by the interaction of individual information and the informational context: In dense informational environments, even low-information voters can successfully identify viable parties and vote for them, but in sparse informational environments, individual access to information is essential for successful strategic voting.

On the computational complexity of the Jones and Tutte polynomials

1990 ◽  
Vol 108 (1) ◽  
pp. 35-53 ◽  
Author(s):  
F. Jaeger ◽  
D. L. Vertigan ◽  
D. J. A. Welsh
Keyword(s):  
Computational Complexity ◽  
Jones Polynomial ◽  
Tutte Polynomial ◽  
Wide Range ◽  
Tutte Polynomials ◽  
Special Points ◽  
Alternating Link ◽  
Special Case

AbstractWe show that determining the Jones polynomial of an alternating link is #P-hard. This is a special case of a wide range of results on the general intractability of the evaluation of the Tutte polynomial T(M; x, y) of a matroid M except for a few listed special points and curves of the (x, y)-plane. In particular the problem of evaluating the Tutte polynomial of a graph at a point in the (x, y)-plane is #P-hard except when (x − 1)(y − 1) = 1 or when (x, y) equals (1, 1), (−1, −1), (0, −1), (−1, 0), (i, −i), (−i, i), (j, j2), (j2, j) where j = e2πi/3

scholarly journals Cycles and Intractability in a Large Class of Aggregation Rules

2018 ◽  
Vol 61 ◽  
pp. 407-431 ◽  
Author(s):  
William S. Zwicker
Keyword(s):  
Computational Complexity ◽  
Related Problem ◽  
Borda Count ◽  
Impossibility Theorem ◽  
Approval Voting ◽  
Winner Determination ◽  
Voting Rule ◽  
Special Cases ◽  
The Mean ◽  
Cyclic Part

We introduce the (j,k)-Kemeny rule -- a generalization of Kemeny's voting rule that aggregates j-chotomous weak orders into a k-chotomous weak order. Special cases of (j,k)-Kemeny include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally tractable for each of these other rules, but intractable for Kemeny? We show that intractability of winner determination for the (j,k)-Kemeny rule first appears at the j=3, k=3 level. The proof rests on a reduction of max cut to a related problem on weighted tournaments, and reveals that computational complexity arises from the cyclic part in the fundamental decomposition of a weighted tournament into cyclic and cocyclic components. Thus the existence of majority cycles -- the engine driving both Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem -- also serves as a source of computational complexity in social choice.

scholarly journals Simplified group activity selection with group size constraints

2021 ◽  
Author(s):  
Andreas Darmann ◽  
Janosch Döcker ◽  
Britta Dorn ◽  
Sebastian Schneckenburger
Keyword(s):  
Computational Complexity ◽  
Simple Model ◽  
Lower Bounds ◽  
Group Activity ◽  
Core Stability ◽  
Upper And Lower Bounds ◽  
Size Constraints ◽  
Broad Variety ◽  
Special Case ◽  
Additional Constraints

AbstractSeveral real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.

The Study of Strategic Voting

2019 ◽  
pp. 291-309 ◽  
Author(s):  
André Blais ◽  
Arianna Degan
Keyword(s):  
Survey Data ◽  
Empirical Research ◽  
Strategic Voting ◽  
Conventional Wisdom ◽  
Strategic Vote ◽  
Plurality Rule ◽  
Voting Rules ◽  
Electoral Outcomes ◽  
Lab Experiments ◽  
Voting Rule

This chapter stresses the necessity of distinguishing between a strategic vote and a strategic voter. The sincere voter always casts a sincere vote, while the strategic voter casts a sincere or strategic vote depending on the context and the voting rule. This leads to two definitions of strategic voting: a broad one, where a strategic vote is one that is partly based on expectations about the outcome of the election, and a narrow one, where a strategic vote also entails not voting sincerely. The chapter then reviews three types of empirical research that differ with respect to the type of data used: the observation of electoral outcomes, survey data, and lab experiments. That literature has confirmed that indeed some voters cast a strategic vote, though many studies have found most votes to be sincere. That research has also shown that there is some degree of strategic voting under all kinds of voting rules; that, contrary to conventional wisdom, there is as much strategic voting under proportional representation as under plurality rule; and that the propensity to vote strategically depends very much on the type of information that is available.

scholarly journals Winner Determination and Strategic Control in Conditional Approval Voting

2021 ◽  
Author(s):  
Evangelos Markakis ◽  
Georgios Papasotiropoulos
Keyword(s):  
Computational Complexity ◽  
Polynomial Algorithms ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Strategic Control ◽  
Approval Voting ◽  
Winner Determination ◽  
Bounded Treewidth ◽  
Voting Rule ◽  
Necessary And Sufficient

Our work focuses on a generalization of the classic Minisum approval voting rule, introduced by Barrot and Lang (2016), and referred to as Conditional Minisum (CMS), for multi-issue elections. Although the CMS rule provides much higher levels of expressiveness, this comes at the expense of increased computational complexity. In this work, we study further the issue of efficient algorithms for CMS, and we identify the condition of bounded treewidth (of an appropriate graph that emerges from the provided ballots), as the necessary and sufficient condition for polynomial algorithms, under common complexity assumptions. Additionally we investigate the complexity of problems related to the strategic control of such elections by the possibility of adding or deleting either voters or alternatives. We exhibit that in most variants of these problems, CMS is resistant against control.

scholarly journals Algebraic Bayesian networks: Checking backbone connectivity

2021 ◽  
Vol 8 (2) ◽  
pp. 305-316
Author(s):  
Anatolii G. Maksimov ◽  
◽  
Aleksandr L. Tulupyev ◽  
Keyword(s):  
Machine Learning ◽  
Inverse Problem ◽  
Computational Complexity ◽  
Bayesian Networks ◽  
Primary Structure ◽  
Global Structure ◽  
Graph Theoretic ◽  
Theoretical Significance ◽  
First Time ◽  
Special Case

The paper investigates the construction of a joint graph as a global structure of network based on its primary structure, one of the problems arising in machine learning of bases of knowledge patterns with uncertainty, presented in the form of algebraic Bayesian networks. The aim of the research is to propose methods for solving the inverse problem. As the results, algorithms for checking a graph for belonging to a family of joint graphs and a family of minimal joint graphs are proposed, and estimates of their computational complexity are made. An improved version for the special case and an improvement for the general case on average are also proposed for the algorithm for checking membership in a family of joint graphs. The problem of recognition of joint graphs has not been previously researched; issue is being addressed for the first time as currently drafted. The theoretical significance lies in the possibilities for applying the results in further researches of graph-theoretic invariants in the global structures of algebraic Bayesian networks.

Sign in / Sign up

Export Citation Format

Share Document