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## Llull and Copeland voting computationally resist bribery and control (2009)

Citations: | 62 - 30 self |

### Citations

13830 |
Computers and Intractability : A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
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Citation Context ...e reduce” and “polynomial-time many-one reduction.” Our NP-hardness results typically follow via a reduction from either the exact-cover-by-3-sets problem or from the vertex cover problem (see, e.g., =-=Garey and Johnson, 1979-=-). These are wellknown NP-complete problems, but we define them here for the sake of completeness. Name: X3C (exact cover by 3-sets). Given: A set B = {b1,...,b3k}, k ≥ 1, and a family of sets S = {S1... |

10437 | Introduction to Algorithms - Cormen, Leiserson, et al. - 2009 |

1982 |
Network flows: theory, algorithms, and applications
- Ahuja, Magnanti, et al.
- 1993
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Citation Context ... literature. The definition we employ here is not the most general one but will suffice for our needs. (Readers seeking a broader discussion of the problem may wish to see, for example, the monograph =-=Ahuja, Magnanti, and Orlin, 1993-=-.) Definition 3.9 We define the min-cost-flow problem as follows: Given a flow network (K,s,t,c,a) and a target flow value F, find a flow f that has value F (if one exists) and has minimum cost among ... |

1226 | Social Choice and Individual Values - Arrow - 1970 |

528 | Strategy-proofness and Arrow's conditions: existence and correspondence theorems for voting procedures and social welfare functions - Satterthwaite - 1975 |

471 | Rank aggregation methods for the web - Dwork, Kumar, et al. - 2001 |

433 | Invitation to Fixed-Parameter Algorithms
- Niedermeier
- 2006
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Citation Context ...collection of “Copeland Outcome Tables” (to be defined later) can be obtained. Finally, we give our resistance results. 4.3.1 NOTIONS AND NOTATIONS The study of fixed-parameter complexity (see, e.g., =-=Niedermeier, 2006-=-) has been expanding explosively since it was parented as a field by Downey, Fellows, and others in the late 1980s and the 1990s. Although the area has built a rich variety of complexity classes regar... |

313 | Integer programming with a fixed number of variables - LENSTRA - 1983 |

246 | Manipulation of voting schemes - Gibbard - 1973 |

178 |
Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare
- Bartholdi, lII, et al.
- 1989
(Show Context)
Citation Context ... papers that are about the succinct-inputs case of fixed-number-of-candidates and fixed-number-of-voters claims. (The fixednumber-of-candidates and fixed-number-of-voters Dodgson winner/score work of =-=Bartholdi et al., 1989-=-b, is known to be about FPT algorithms—due to the proof of Bartholdi et al., 1989b, itself, see the discussion in Faliszewski et al., 2006a, see also Betzler, Guo, and Niedermeier, 2008. Although the ... |

172 |
The computational difficulty of manipulating an election
- Bartholdi, Tovey, et al.
- 1989
(Show Context)
Citation Context ... papers that are about the succinct-inputs case of fixed-number-of-candidates and fixed-number-of-voters claims. (The fixednumber-of-candidates and fixed-number-of-voters Dodgson winner/score work of =-=Bartholdi et al., 1989-=-b, is known to be about FPT algorithms—due to the proof of Bartholdi et al., 1989b, itself, see the discussion in Faliszewski et al., 2006a, see also Betzler, Guo, and Niedermeier, 2008. Although the ... |

165 | Single transferable vote resists strategic voting. Social Choice and Welfare - Bartholdi, I, et al. - 1991 |

154 | When Are Elections with Few Candidates Hard to Manipulate - Conitzer, Sandholm, et al. - 2007 |

138 | Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix,” Paris: L’Imprimerie Royale - Condorcet |

120 |
The complexity of Combinatorial Problems with Succinct Input Representation
- Wagner
- 1986
(Show Context)
Citation Context ... studied extensively in the case of bribery (Faliszewski et al., 2006a, 2006b), and speaking more broadly, succinctness-of-input issues are often very germane to complexity classification (see, e.g., =-=Wagner, 1986-=-). Note that proving an FPT result for the succinct case of a problem immediately implies an FPT result for the same problem (without the requirement of succinct inputs being in place), and indeed is ... |

112 | Universal Voting Protocol Tweaks to Make Manipulation Hard
- Conitzer, Sandholm
(Show Context)
Citation Context ..., a large body of research has been dedicated to the study of computational properties of election systems. Some topics that have received much attention are the complexity of manipulating elections (=-=Conitzer & Sandholm, 2003-=-, 2006; Conitzer et al., 2007; Elkind & Lipmaa, 2005; Hemaspaandra & Hemaspaandra, 2007; Procaccia & Rosenschein, 2007; Meir, Procaccia, Rosenschein, & Zohar, 2008) and of controlling elections via pr... |

108 | How hard is it to control an election
- Bartholdi, Tovey, et al.
- 1992
(Show Context)
Citation Context ...ts by an external agent (called “the chair”) to, via such actions as addition/deletion/partition of candidates or voters, make a given candidate win the election (in the case of constructive control, =-=Bartholdi, Tovey, and Trick, 1992-=-) or preclude a given candidate’s victory (in the case of destructive control, Hemaspaandra, Hemaspaandra, and Rothe, 2007a). These obstacles are very discouraging, but the field of computational soci... |

106 | Junta Distributions and the AverageCase Complexity of Manipulating Elections
- Procaccia, Rosenschein
- 2007
(Show Context)
Citation Context ...opics that have received much attention are the complexity of manipulating elections (Conitzer & Sandholm, 2003, 2006; Conitzer et al., 2007; Elkind & Lipmaa, 2005; Hemaspaandra & Hemaspaandra, 2007; =-=Procaccia & Rosenschein, 2007-=-; Meir, Procaccia, Rosenschein, & Zohar, 2008) and of controlling elections via procedural changes (Hemaspaandra et al., 2007a; Hemaspaandra, Hemaspaandra, & Rothe, 2007b; Meir et al., 2008; Erdélyi, ... |

86 | Nonexistence of Voting Rules That Are Usually Hard to Manipulate - Conitzer, Sandholm |

80 | Anyone but him: The complexity of precluding an alternative
- Hemaspaandra, Hemaspaandra, et al.
- 2007
(Show Context)
Citation Context ...d 0.5 ). Copeland 0 , where tied candidates come away empty-handed, has sometimes also been referred to as “Copeland elections” (see, e.g., Procaccia, Rosenschein, and Kaminka, 2007, and Faliszewski, =-=Hemaspaandra, Hemaspaandra, and Rothe, 2007-=-, an early version of this paper). The above-mentioned election system proposed by Ramon Llull in the thirteenth century is in this notation Copeland 1 , where tied candidates are awarded one point ea... |

76 |
A Theorem on the Construction of Voting Paradoxes
- McGarvey
- 1953
(Show Context)
Citation Context ... graphs in the proofs of resistance for candidate control. In effect, Copeland α candidate-control problems often can be viewed (with some care regarding ties) as graph-theoretic problems. Lemma 4.6 (=-=McGarvey, 1953-=-) There is a polynomial-time algorithm that given as input an antisymmetric directed graph G outputs an election E such that G = G(E). Proof. For the sake of completeness, we give the algorithm. Let G... |

65 | Elections can be manipulated often - Friedgut, Kalai, et al. |

65 | Generalized scoring rules and the Frequency of Coalitional Manipulability
- Xia, Conitzer
- 2008
(Show Context)
Citation Context ... Hemaspaandra, Rothe, and Spakowski (2007) and Homan and Hemaspaandra (to appear) provide discussions of some of these issues. Regarding the recent work of Friedgut, Kalai, and Nisan (2008) (see also =-=Xia and Conitzer, 2008-=-a, 2008b), that very interesting work is not on control, and the lower bounds proven there do not show that one can manipulate most of the time, but rather that work provides lower bounds that unfortu... |

60 | Voting for movies: The anatomy of a recommender system - Ghosh, Mundhe, et al. - 1999 |

60 | Dichotomy for Voting Systems
- Hemaspaandra, Hemaspaandra
- 2007
(Show Context)
Citation Context ...ds for other rules, we suspect that the dream-case path would be to find broad results that in one stroke reveal the control-resistance patterns of whole classes of election systems. For example, see =-=Hemaspaandra and Hemaspaandra 2007-=-, which does essentially that for manipulation of scoring systems. 3. Procaccia et al. (2008) independently of our work in Faliszewski et al. 2007 used a similar technique in their work regarding the ... |

56 | A heuristic technique for multiagent planning - Ephrati, Rosenschein - 1997 |

48 | Copeland voting: ties matter
- Faliszewski, Hemaspaandra, et al.
- 2008
(Show Context)
Citation Context ... When we henceforward say “irrational voters,” we mean that the voters may have irrational preferences, not that they each must.) We study the issues of bribery and control and we point the reader to =-=Faliszewski et al. 2008-=- for work on manipulation. (Very briefly summarized, the work of Faliszewski et al., 2008, on manipulation of Copeland α elections 279FALISZEWSKI, HEMASPAANDRA, HEMASPAANDRA, & ROTHE shows that for a... |

45 | Strategic manipulability without resoluteness or shared beliefs: Gibbard-satterthwaite generalized - Duggan, Schwartz |

45 | A sufficient condition for voting rules to be frequently manipulable
- Xia, Conitzer
- 2008
(Show Context)
Citation Context ... Hemaspaandra, Rothe, and Spakowski (2007) and Homan and Hemaspaandra (to appear) provide discussions of some of these issues. Regarding the recent work of Friedgut, Kalai, and Nisan (2008) (see also =-=Xia and Conitzer, 2008-=-a, 2008b), that very interesting work is not on control, and the lower bounds proven there do not show that one can manipulate most of the time, but rather that work provides lower bounds that unfortu... |

43 | The complexity of bribery in elections
- Faliszewski, Hemaspaandra, et al.
- 2006
(Show Context)
Citation Context ...meter algorithms— has, for example, also been used (although somewhat tacitly—see the coming discussion in the second paragraph of Footnote 17) within the study of bribery (Faliszewski et al., 2006a; =-=Faliszewski, Hemaspaandra, & Hemaspaandra, 2006-=-b). To the best of our knowledge, this bounded-case approach to finding the limits of resistance results has not been previously used to study control problems. In this section we do precisely that. I... |

41 | A richer understanding of the complexity of election systems - Faliszewski, Hemaspaandra, et al. - 2009 |

40 |
Positive Political Theory I: Collective Preference
- Austen-Smith, Banks
- 2000
(Show Context)
Citation Context ...s ci to c j}‖ − ‖{v ∈ V | v prefers c j to ci}‖ otherwise. 4. In this paper, we take “linear order” to mean a strict total order. This is a common convention within voting theory, see, e.g., the book =-=Austen-Smith and Banks 2000-=-. However, we mention that in the field of mathematics the term “linear order” is typically taken to allow nonstrictness, i.e., to allow ties. 283FALISZEWSKI, HEMASPAANDRA, HEMASPAANDRA, & ROTHE So, ... |

40 | Parameterized complexity for the skeptic - Downey - 2003 |

33 | Hybrid elections broaden complexity-theoretic resistance to control
- Hemaspaandra, Hemaspaandra, et al.
- 2007
(Show Context)
Citation Context ..., 2005; Hemaspaandra & Hemaspaandra, 2007; Procaccia & Rosenschein, 2007; Meir, Procaccia, Rosenschein, & Zohar, 2008) and of controlling elections via procedural changes (Hemaspaandra et al., 2007a; =-=Hemaspaandra, Hemaspaandra, & Rothe, 2007-=-b; Meir et al., 2008; Erdélyi, Nowak, & Rothe, 2008b). Recently, Faliszewski, Hemaspaandra, and Hemaspaandra (2006a) introduced the study of the complexity of bribery in elections. Bribery shares some... |

30 | Sincere-strategy preference-based approval voting fully resists constructive control and broadly resists destructive control. Mathematical Logic Quarterly 55(4):425–443
- Erdélyi, Nowak, et al.
- 2009
(Show Context)
Citation Context ...ein, 2007; Meir, Procaccia, Rosenschein, & Zohar, 2008) and of controlling elections via procedural changes (Hemaspaandra et al., 2007a; Hemaspaandra, Hemaspaandra, & Rothe, 2007b; Meir et al., 2008; =-=Erdélyi, Nowak, & Rothe, 2008-=-b). Recently, Faliszewski, Hemaspaandra, and Hemaspaandra (2006a) introduced the study of the complexity of bribery in elections. Bribery shares some features of manipulation and some features of cont... |

29 | Parameterized computational complexity of Dodgson and Young elections
- Betzler, Guo, et al.
(Show Context)
Citation Context ...odgson winner/score work of Bartholdi et al., 1989b, is known to be about FPT algorithms—due to the proof of Bartholdi et al., 1989b, itself, see the discussion in Faliszewski et al., 2006a, see also =-=Betzler, Guo, and Niedermeier, 2008-=-. Although the paper of Bartholdi et al., 1989b, doesn’t address the succinct input model, Faliszewski et al., 2006a, notes that their approach works fine even in the succinct cases of the winner prob... |

27 |
An introduction to vote-counting schemes
- Levin, Nalebuff
- 1995
(Show Context)
Citation Context ... mention that a probabilistic variant of Copeland voting (known as the Jech method) was defined already in 1929 by Zermelo (1929) and later on was reintroduced by several other researches (see, e.g., =-=Levin and Nalebuff, 1995-=-, for further references and a description of the Jech method). We note in passing that the Jech method is applicable even when it is fed incomplete information. In the present paper, however, we do n... |

26 | Introduction to Algorithms. The MIT press and McGraw-Hill bock company, sixteenth edition - Cormen, Leiserson, et al. - 1996 |

25 | Small coalitions cannot manipulate voting
- Elkind, Lipmaa
- 2005
(Show Context)
Citation Context ...dy of computational properties of election systems. Some topics that have received much attention are the complexity of manipulating elections (Conitzer & Sandholm, 2003, 2006; Conitzer et al., 2007; =-=Elkind & Lipmaa, 2005-=-; Hemaspaandra & Hemaspaandra, 2007; Procaccia & Rosenschein, 2007; Meir, Procaccia, Rosenschein, & Zohar, 2008) and of controlling elections via procedural changes (Hemaspaandra et al., 2007a; Hemasp... |

25 | Llull and Copeland voting broadly resist bribery and control
- Faliszewski, Hemaspaandra, et al.
- 2007
(Show Context)
Citation Context ...sses of election systems. For example, see Hemaspaandra and Hemaspaandra 2007, which does essentially that for manipulation of scoring systems. 3. Procaccia et al. (2008) independently of our work in =-=Faliszewski et al. 2007-=- used a similar technique in their work regarding the complexity of achieving proportional representation. 281FALISZEWSKI, HEMASPAANDRA, HEMASPAANDRA, & ROTHE control problem, namely control by parti... |

25 | The complexity of strategic behavior in multi-winner elections
- Meir, Procaccia, et al.
(Show Context)
Citation Context ...ttention are the complexity of manipulating elections (Conitzer & Sandholm, 2003, 2006; Conitzer et al., 2007; Elkind & Lipmaa, 2005; Hemaspaandra & Hemaspaandra, 2007; Procaccia & Rosenschein, 2007; =-=Meir, Procaccia, Rosenschein, & Zohar, 2008-=-) and of controlling elections via procedural changes (Hemaspaandra et al., 2007a; Hemaspaandra, Hemaspaandra, & Rothe, 2007b; Meir et al., 2008; Erdélyi, Nowak, & Rothe, 2008b). Recently, Faliszewski... |

24 | The voting problem - Stearns - 1959 |

23 | Critical Strategies Under Approval Voting, Who Gets Ruled In and Ruled Out, Working Paper, forthcoming in electoral studies - Brams, Sanver - 2005 |

23 |
On the complexity of achieving proportional representation
- Procaccia, Rosenschein, et al.
(Show Context)
Citation Context ...on are the complexity of manipulating elections (Conitzer & Sandholm, 2003, 2006; Conitzer et al., 2007; Elkind & Lipmaa, 2005; Hemaspaandra & Hemaspaandra, 2007; Procaccia & Rosenschein, 2007; Meir, =-=Procaccia, Rosenschein, & Zohar, 2008-=-) and of controlling elections via procedural changes (Hemaspaandra et al., 2007a; Hemaspaandra, Hemaspaandra, & Rothe, 2007b; Meir et al., 2008; Erdélyi, Nowak, & Rothe, 2008b). Recently, Faliszewski... |

22 | An Axiomatic Approach to Personalized Ranking Systems
- Altman, Tennenholtz
- 2007
(Show Context)
Citation Context ...or election systems. (However, we note in passing that there do exist some modern papers in which the voter and candidate sets are taken to be identical, see for example the work of and references in =-=Altman and Tennenholtz, 2007-=-.) 277FALISZEWSKI, HEMASPAANDRA, HEMASPAANDRA, & ROTHE 1.2 Computational Social Choice In general it is impossible to design a perfect election system. Arrow (1963) famously showed that there is no s... |

20 | 2009. Guarantees for the success frequency of an algorithm for finding Dodgson election winners - Homan, Hemaspaandra |

18 | Multi-winner elections: Complexity of manipulation, control and winner-determination - Procaccia, Rosenschein, et al. - 2007 |

17 | Parameterized complexity of candidate control in elections and related digraph problems
- Betzler, Uhlmann
(Show Context)
Citation Context ...on systems for which a comprehensive analysis has been conducted previously are plurality, Condorcet, and (variants of) approval voting (see Bartholdi et al., 1992; Hemaspaandra et al., 2007a, 2007b; =-=Betzler and Uhlmann, 2008-=-; Erdélyi et al., 2008b; see also Meir et al., 2008, for some results on (variants of) approval voting, single nontransferable vote, and cumulative voting with respect to constructive control via addi... |

17 |
A ‘reasonable’ social welfare function, mimeographed
- Copeland
- 1951
(Show Context)
Citation Context ...ach delegate votes for whichever alternative a majority of his or her constituents prefers among that pair. Llull’s election system is remarkably similar to what is now known as “Copeland elections” (=-=Copeland, 1951-=-), a more than half-century old voting procedure that is based on pairwise comparisons of candidates: The winner (by a majority of votes—in this paper “majority” always, as is standard, means strict m... |

17 | Approximability of Dodgson’s rule - McCabe-Dansted, Pritchard, et al. - 2008 |

16 | On approximating optimal weighted lobbying, and frequency of correctness versus average-case polynomial time - Erdélyi, Hemaspaandra, et al. - 2007 |

13 | On the robustness of preference aggregation in noisy environments
- Procaccia, Rosenschein, et al.
- 2007
(Show Context)
Citation Context ...olm, & Lang, 2007, can be scaled to be equivalent to Copeland 0.5 ). Copeland 0 , where tied candidates come away empty-handed, has sometimes also been referred to as “Copeland elections” (see, e.g., =-=Procaccia, Rosenschein, and Kaminka, 2007-=-, and Faliszewski, Hemaspaandra, Hemaspaandra, and Rothe, 2007, an early version of this paper). The above-mentioned election system proposed by Ramon Llull in the thirteenth century is in this notati... |

10 |
voting fully resists constructive control
- Faliszewski, Hemaspaandra, et al.
- 2008
(Show Context)
Citation Context ... When we henceforward say “irrational voters,” we mean that the voters may have irrational preferences, not that they each must.) We study the issues of bribery and control and we point the reader to =-=Faliszewski et al. 2008-=- for work on manipulation. (Very briefly summarized, the work of Faliszewski et al., 2008, on manipulation of Copeland α elections 279FALISZEWSKI, HEMASPAANDRA, HEMASPAANDRA, & ROTHE shows that for a... |

9 | The Copeland method II: Manipulation, monotonicity and paradoxes
- Merlin, Saari
- 1997
(Show Context)
Citation Context ... receive α points. So the system widely referred to in the literature as “Copeland elections” is Copeland 0.5 , where tied candidates receive half a point each (see, e.g., Saari and Merlin, 1996, and =-=Merlin and Saari, 1997-=-; the definition used by Conitzer, Sandholm, & Lang, 2007, can be scaled to be equivalent to Copeland 0.5 ). Copeland 0 , where tied candidates come away empty-handed, has sometimes also been referred... |

8 |
Invitation to fixed-parameter algorithms. Habilitation thesis, Universität Tübingen
- Niedermeier
- 2002
(Show Context)
Citation Context ...to test—most importantly, they test that the subelections match the pairwise outcomes specified by j ′-COTs T1 and T2. Finally and crucially, by Lenstra’s (1983) algorithm (see also Downey, 2003, and =-=Niedermeier, 2002-=-, which are very clear regarding the “linear”s later in this sentence), since this integer linear programming constraint feasibility problem has a fixed number of constraints (and in our case in fact ... |

7 | Nonuniform bribery (short paper
- Faliszewski
- 2008
(Show Context)
Citation Context ...t of the election and, thus, as problems of finding coalitions, especially if one assigns prices to voters to measure the difficulty of convincing a particular voter to join the coalition (see, e.g., =-=Faliszewski, 2008-=-, for an example of a bribery problem where such an interpretation is very natural). It is quite natural to study control and bribery both in constructive settings (where we want to make our favorite ... |

7 |
The electoral writings of Ramon Llull
- Hägele, Pukelsheim
(Show Context)
Citation Context ...e. This understanding of history has been reconsidered during the past few decades, as it has been discovered that the study of elections was considered deeply as early as the thirteenth century (see =-=Hägele and Pukelsheim, 2001-=-, and the citations therein regarding Ramon Llull and the fifteenthcentury figure Cusanus, especially the citations that in Hägele and Pukelsheim, 2001, are numbered 3, 5, and 24–27). Ramon Llull (b. ... |

6 | The copeland method i; relationships and the dictionary,” Economic Theory
- Saari, Merlin
- 1996
(Show Context)
Citation Context ...ase of a tie both candidates receive α points. So the system widely referred to in the literature as “Copeland elections” is Copeland 0.5 , where tied candidates receive half a point each (see, e.g., =-=Saari and Merlin, 1996-=-, and Merlin and Saari, 1997; the definition used by Conitzer, Sandholm, & Lang, 2007, can be scaled to be equivalent to Copeland 0.5 ). Copeland 0 , where tied candidates come away empty-handed, has ... |

5 | The new FIFA rules are hard: complexity aspects of sport competitions - Kern, Paulusma |

2 | revised editon - Arrow - 1951 |

1 |
Introduction to Algorithms (second
- Downey
- 2003
(Show Context)
Citation Context ...they are supposed to test—most importantly, they test that the subelections match the pairwise outcomes specified by j ′-COTs T1 and T2. Finally and crucially, by Lenstra’s (1983) algorithm (see also =-=Downey, 2003-=-, and Niedermeier, 2002, which are very clear regarding the “linear”s later in this sentence), since this integer linear programming constraint feasibility problem has a fixed number of constraints (a... |

1 | Positive Political Theory I: Collective Preference. Univ. of Mich - Austen-Smith, Banks - 2000 |

1 | The voting problem. The American Mathematical Monthly, 66(9):761–763 - Stearns - 1959 |