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Political Science
Comparative Politics

Committee Scoring Rules: Axiomatic Characterization and Hierarchy

Profile image of Arkadii SlinkoArkadii Slinko

2018, arXiv (Cornell University)

Abstract

Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-kcounting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k-Approval Chamberlin-Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.

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Arkadii Slinko

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We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the singlewinner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-k-counting rule to satisfy the fixed-majority criterion. We find that, for most of the rules in our new class, the complexity of winner determination is high (that is, the problem of computing the winners is NP-hard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.

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Social Choice and Welfare, 2018

We characterize the class of committee scoring rules that satisfy the fixedmajority criterion. We argue that rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed-majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-kcounting rule to satisfy the fixed-majority criterion. We show that, for many top-kcounting rules, the complexity of winner determination is high (formally, we show that the problem of deciding if there exists a committee with at least a given score is NPhard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.

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Egalitarian Committee Scoring Rules
Aismyfirstname Wuffle

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

We introduce and study the class of egalitarian variants of committee scoring rules, where instead of summing up the scores that voters assign to committees---as is done in the utilitarian variants---the score of a committee is taken to be the lowest score assigned to it by any voter. We focus on five rules, which are egalitarian analogues of SNTV, the k-Borda rule, the Chamberlin--Courant rule, the Bloc rule, and the Pessimist rule. We establish their computational complexity, provide their initial axiomatic study, and perform experiments to represent the action of these rules graphically.

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Voting with Rank Dependent Scoring Rules
Judy Goldsmith

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Positional scoring rules in voting compute the score of an alternative by summing the scores for the alternative induced by every vote. This summation principle ensures that all votes contribute equally to the score of an alternative. We relax this assumption and, instead, aggregate scores by taking into account the rank of a score in the ordered list of scores obtained from the votes. This defines a new family of voting rules, rank-dependent scoring rules (RDSRs), based on ordered weighted average (OWA) operators, which, include all scoring rules, and many others, most of which of new. We study some properties of these rules, and show, empirically, that certain RDSRs are less manipulable than Borda voting, across a variety of statistical cultures.

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Recovering non-monotonicity problems of voting rules
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Social Choice and Welfare, 2020

A social choice rule (SCR) is monotonic if raising a single alternative in voters' preferences while leaving the rankings otherwise unchanged is never detrimental to the prospects for winning of the raised alternative. Monotonicity is rather weak but well-known to discriminate against scoring elimination rules, such as plurality with a run o and single transferable vote. We dene the minimal monotonic extension of an SCR as its unique monotonic supercorrespondence that is minimal with respect to set inclusion. After showing the existence of the concept, we characterize, for every non-monotonic SCR, the alternatives that its minimal monotonic extension must contain. As minimal monotonic extensions can entail coarse SCRs, we address the possibility of rening them without violating monotonicity provided that this renement does not diverge from the original SCR more than the divergence prescribed by the minimal monotonic extension itself. We call these renements monotonic adjustments and identify conditions over SCRs that ensure unique monotonic adjustments that are minimal with respect to set inclusion. As an application of our general ndings, we consider plurality with a runo, characterize its minimal monotonic extension as well as its (unique) minimal monotonic adjustment. Interestingly, this adjustment is not coarser than plurality with a runo itself, hence we suggest it as a monotonic substitute to plurality with a runo. JEL Classications: D71, D79.

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The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: The Prior Successor Paradox and the Leaving Member Paradox which occur when a member of an elected committee leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.

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committee election problem is to choose from a finite set S of candidates a nonempty subset of committee members as the consequence of an election in which each voter expresses a preference for a candidate in S. We use ideas of vote concentration to formulate families of committee election rules, which may exhibit several natural, intuitively appealing properties. One concept of vote concentration, a typification of committee strength, ensures that the associated committee election rule is strategy-proof and so is not subject to voter manipulation. (~

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In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins of victory or loss between candidates, then the voting rule yields the same outcome in both elections. Although this is a mathematically natural invariance property to consider, whether it should be regarded as a normative axiom on voting rules is less clear. In this paper, we address this question for voting rules with any kind of output, whether a set of candidates, a ranking, a probability distribution, etc. We prove that a voting rule is margin-based if and only if it satisfies some axioms with clearer normative content. A key axiom is what we call Preferential Equality, stating that if two voters both rank a candidate x immediately above a candidate y, then either voter switching to rank y immediately above x will have the same effect on the election outcome as if the other voter made the switch, so each voter's preference for y over x is treated equally.

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Scoring rules: an alternative parameterization
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This note presents an alternative parameterization of any scoring rule that satisfies the score-expansion property. This parameterization is based on the vector that specifies, for every number of alternatives k, k≥3, the minimal size of a coalition that can veto an alternative which is preferred by everybody outside the coalition. Our result sheds new light on the commonly used plurality and Borda rules, as well as the inverse plurality rule and any "vote for t alternatives rule".

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Analysing Irresolute Multiwinner Voting Rules with Approval Ballots via SAT Solving
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2020

Suppose you want to design a voting rule that can be used to elect a committee or parliament by asking each voter to approve of a subset of the candidates standing. There are several properties you may want that rule to satisfy. First, voters should enjoy some form of proportional representation. Second, voters should not have an incentive to misrepresent their preferences. Third, outcomes should be Pareto efficient. We show that it is impossible to design a voting rule that satisfies all three properties. We also explore what possibilities there are when we weaken our requirements. Of special interest is the methodology we use, as a significant part of the proof is outsourced to a SAT solver. While prior work has considered similar questions for the special case of resolute voting rules, which do not allow for ties between outcomes, we focus on the fact that, in practice, most voting rules allow for the possibility of such ties.

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References (86)

  1. K. Arrow. Social Choice and Individual Values. John Wiley and Sons, 1951 (revised editon, 1963).
  2. H. Aziz, M. Brill, V. Conitzer, E. Elkind, R. Freeman, and T. Walsh. Justified representation in approval-based committee voting. Social Choice and Welfare, 48(2):461-485, 2017.
  3. H. Aziz, E. Elkind, P. Faliszewski, M. Lackner, and P. Skowron. The Condorcet principle for multiwinner elections: From shortlisting to proportionality. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, pages 84-90, 2017.
  4. H. Aziz, E. Elkind, S. Huang, M. Lackner, L. Sanchez-Fernandez, and P. Skowron. On the complexity of extended and proportional justified representation. In Proceedings of the 32nd AAAI Conference on Artificial Intelligence, 2018. To appear.
  5. H. Aziz, S. Gaspers, J. Gudmundsson, S. Mackenzie, N. Mattei, and T. Walsh. Computational aspects of multi-winner approval voting. In Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems, pages 107-115, 2015.
  6. M. Balinski and H. P. Young. Fair Representation: Meeting the Ideal of One Man, One Vote. Yale University Press, 1982. (2nd Edition [with identical pagination], Brookings Institution Press, 2001).
  7. S. Barberà and D. Coelho. How to choose a non-controversial list with k names. Social Choice and Welfare, 31(1):79-96, 2008.
  8. S. Barber and B. Dutta. Implementability via protective equilibria. Journal of Mathematical Economics, 10(1):49-65, 1982.
  9. N. Betzler, A. Slinko, and J. Uhlmann. On the computation of fully proportional representa- tion. Journal of Artificial Intelligence Research, 47:475-519, 2013.
  10. S. Brams, M. Kilgour, and R. Sanver. A minimax procedure for electing committees. Public Choice, 132(3-4):401-420, 2007.
  11. R. Bredereck, P. Faliszewski, A. Igarashi, M. Lackner, and P. Skowron. Multiwinner elec- tions with diversity constraints. In Proceedings of the 32nd AAAI Conference on Artificial Intelligence, 2018. To appear.
  12. R. Bredereck, P. Faliszewski, A. Kaczmarczyk, R. Niedermeier, P. Skowron, and N. Talmon. Robustness among multiwinner voting rules. In Proceedings of the 10th International Sympo- sium on Algorithmic Game Theory, pages 80-92, 2017.
  13. M. Brill, R. Freeman, S. Janson, and M. Lackner. Phragmén's voting methods and justified representation. In Proceedings of the 31st AAAI Conference on Artificial Intelligence, pages 406-413, 2017.
  14. M. Brill, J.-F. Laslier, and P. Skowron. Multiwinner approval rules as apportionment methods. In Proceedings of the 31st AAAI Conference on Artificial Intelligence, pages 414-420, 2017.
  15. J. Byrka, P. Skowron, and K. Sornat. Proportional approval voting, harmonic k-median, and negative association. Technical Report arXiv:1704.02183 [cs.DS], arXiv.org, June 2017.
  16. L. Celis, L. Huang, and N. Vishnoi. Group fairness in multiwinner voting. Technical Report arXiv:1710.10057 [cs.CY], arXiv.org, Oct. 2017.
  17. B. Chamberlin and P. Courant. Representative deliberations and representative decisions: Proportional representation and the Borda rule. American Political Science Review, 77(3):718- 733, 1983.
  18. P. Chebotarev and E. Shamis. Characterizations of scoring methods for preference aggregation. Annals of Operations Research, 80:299-332, 1998.
  19. S. Ching. A simple characterization of plurality rule. Journal of Economic Theory, 71(1):298- 302, 1996.
  20. D. Cornaz, L. Galand, and O. Spanjaard. Bounded single-peaked width and proportional representation. In Proceedings of the 20th European Conference on Artificial Intelligence, pages 270-275, Aug. 2012.
  21. A. Darmann. How hard is it to tell which is a Condorcet committee? Mathematical Social Sciences, 66(3):282-292, 2013.
  22. B. Debord. An axiomatic characterization of Borda's k-choice function. Social Choice and Welfare, 9(4):337-343, 1992.
  23. M. Dummett. Voting Procedures. Oxford University Press, 1984.
  24. E. Elkind, P. Faliszewski, J. F. Laslier, P. Skowron, A. Slinko, and N. Talmon. What do multiwinner voting rules do? an experiment over the two-dimensional euclidean domain. In Proceedings of the 31st AAAI Conference on Artificial Intelligence, pages 494-501, 2017.
  25. E. Elkind, P. Faliszewski, P. Skowron, and A. Slinko. Properties of multiwinner voting rules. Social Choice and Welfare, 48(3):599-632, 2017.
  26. E. Elkind and A. Ismaili. OWA-based extensions of the Chamberlin-Courant rule. In Pro- ceedings of the 4th International Conference on Algorithmic Decision Theory, pages 486-502, 2015.
  27. E. Elkind, J. Lang, and A. Saffidine. Condorcet winning sets. Social Choice and Welfare, 44(3):493-517, 2015.
  28. P. Faliszewski, M. Lackner, D. Peters, and N. Talmon. Effective heuristics for committee scoring rules. In Proceedings of the 32nd AAAI Conference on Artificial Intelligence, 2018. To appear.
  29. P. Faliszewski, J. Sawicki, R. Schaefer, and M. Smolka. Multiwinner voting in genetic algo- rithms. IEEE Intelligent Systems, 32(1):40-48, 2016.
  30. P. Faliszewski, P. Skowron, A. Slinko, and N. Talmon. Committee scoring rules: Axiomatic classification and hierarchy. In Proceedings of the 25th International Joint Conference on Artificial Intelligence, pages 250-256, 2016.
  31. P. Faliszewski, P. Skowron, A. Slinko, and N. Talmon. Multiwinner analogues of the plurality rule: Axiomatic and algorithmic views. In Proceedings of the 30th AAAI Conference on Artificial Intelligence, pages 482-488, 2016.
  32. P. Faliszewski, P. Skowron, A. Slinko, and N. Talmon. Multiwinner rules on paths from k- Borda to Chamberlin-Courant. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, pages 192-198, 2017.
  33. P. Faliszewski, P. Skowron, A. Slinko, and N. Talmon. Multiwinner voting: A new challenge for social choice theory. In U. Endriss, editor, Trends in Computational Social Choice, pages 27-47. AI Access, 2017.
  34. P. Faliszewski, A. Slinko, K. Stahl, and N. Talmon. Achieving fully proportional representation by clustering voters. In Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems, pages 296-304, 2016.
  35. D. Felsenthal and Z. Maoz. Normative properties of four single-stage multi-winner electoral procedures. Behavioral Science, 37:109-127, 1992.
  36. P. Fishburn. An analysis of simple voting systems for electing committees. SIAM Journal on Applied Mathematics, 41(3):499-502, 1981.
  37. P. Fishburn. Majority committees. Journal of Economic Theory, 25(2):255-268, 1981.
  38. P. Fishburn and W. Gehrlein. Borda's rule, positional voting, and Condorcet's simple majority principle. Public Choice, 28(1):79-88, 1976.
  39. P. Gärdenfors. Positionalist voting functions. Theory and Decision, 4(1):1-24, 1973.
  40. W. Gehrlein. The condorcet criterion and committee selection. Mathematical Social Sciences, 10(3):199-209, 1985.
  41. J. Goldsmith, J. Lang, N. Mattei, and P. Perny. Voting with rank dependent scoring rules. In Proceedings of the 28th AAAI Conference on Artificial Intelligence, pages 698-704. AAAI Press, 2014.
  42. B. Hansson and H. Sahlquist. A proof technique for social choice with variable electorate. Journal of Economic Theory, 13:193-200, 1976.
  43. R. Izsak, G. Woeginger, and N. Talmon. Committee selection with interclass and intraclass synergies. In Proceedings of the 32st AAAI Conference on Artificial Intelligence, 2018.
  44. S. Janson. Phragmén's and Thiele's election methods. Technical Report arXiv:1611.08826 [math.HO], arXiv.org, 2016.
  45. J. Kacprzyk, H. Nurmi, and S. Zadrozny. The role of the OWA operators as a unification tool for the representation of collective choice sets. In Recent Developments in the Ordered Weighted Averaging Operators, pages 149-166. Springer, 2011.
  46. M. Kilgour. Approval balloting for multi-winner elections. In J.-F. Laslier and R. Sanver, editors, Handbook on Approval Voting, pages 105-124. Springer, 2010.
  47. M. Kilgour and E. Marshall. Approval balloting for fixed-size committees. In Electoral Systems, Studies in Choice and Welfare, volume 12, pages 305-326, 2012.
  48. M. Lackner and D. Peters. Preferences single-peaked on a circle. In Proceedings of the 31st AAAI Conference on Artificial Intelligence, pages 649-655, 2017.
  49. M. Lackner and P. Skowron. Consistent approval-based multi-winner rules. Technical Report arXiv:1704.02453 [cs.GT], arXiv.org, Apr. 2017.
  50. A. Lijphart and B. Grofman. Choosing an Electoral System: Issues and Alternatives. Praeger, New York, 1984.
  51. T. Lu and C. Boutilier. Budgeted social choice: From consensus to personalized decision making. In Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pages 280-286, 2011.
  52. T. Lu and C. Boutilier. Value-directed compression of large-scale assignment problems. In Proceedings of the 29th AAAI Conference on Artificial Intelligence, pages 1182-1190, 2015.
  53. E. Maskin. Nash equilibrium and welfare optimality. The Review of Economic Studies, 66(1):23-38, 1999.
  54. K. May. A set of independent necessary and sufficient conditions for simple majority decision. Econometrica, 20(4):680-684, 1952.
  55. V. Merlin. The axiomatic characterization of majority voting and scoring rules. Mathematical Social Sciences, 41(161):87-109, 2003.
  56. B. Monroe. Fully proportional representation. American Political Science Review, 89(4):925- 940, 1995.
  57. R. Myerson. Axiomatic derivation of scoring rules without the ordering assumption. Social Choice and Welfare, 12(1):59-74, 1995.
  58. G. Nemhauser, L. Wolsey, and M. Fisher. An analysis of approximations for maximizing submodular set functions. Mathematical Programming, 14(1):265-294, 1978.
  59. D. Peters. Single-peakedness and total unimodularity: Efficiently solve voting problems with- out even trying. Technical Report arXiv:1609.03537 [cs.GT], arXiv.org, Sept. 2016.
  60. D. Peters and E. Elkind. Preferences single-peaked on nice trees. In Proceedings of the 30th AAAI Conference on Artificial Intelligence, pages 594-600, 2016.
  61. E. Phragmén. Sur une méthode nouvelle pour réaliser, dans les élections, la représentation proportionnelle des partis. Öfversigt af Kongliga Vetenskaps-Akademiens Förhandlingar, 51(3):133-137, 1894.
  62. E. Phragmén. Proportionella val. En valteknisk studie. Svenska spörsmål 25. Lars Hökersbergs förlag, Stockholm, 1895.
  63. E. Phragmén. Sur la théorie des élections multiples. Öfversigt af Kongliga Vetenskaps- Akademiens Förhandlingar, 53:181-191, 1896.
  64. M. Pivato. Variable-population voting rules. Journal of Mathematical Economics, 49(3):210- 221, 2013.
  65. A. Procaccia, J. Rosenschein, and A. Zohar. On the complexity of achieving proportional representation. Social Choice and Welfare, 30(3):353-362, 2008.
  66. F. Pukelsheim. Proportional Representation: Apportionment Methods and Their Applications. Springer, 2014.
  67. T. Ratliff. Some startling inconsistencies when electing committees. Social Choice and Welfare, 21(3):433-454, 2003.
  68. T. Ratliff and D. Saari. Complexities of electing diverse committees. Social Choice and Welfare, 43(1):55-71, 2014.
  69. J. Richelson. A characterization result for the plurality rule. Journal of Economic Theory, 19(2):548-550, 1978.
  70. L. Sánchez-Fernández and J. Fisteus. Monotonicity axioms in approval-based multi-winner voting rules. Technical Report arXiv:1710.04246 [cs.GT], arXiv.org, Oct. 2017.
  71. S. Sekar, S. Sikdar, and L. Xia. Condorcet consistent bundling with social choice. In Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems, pages 33-41, 2017.
  72. P. Skowron. FPT approximation schemes for maximizing submodular functions. Information and Computation, 257:65-78, 2017.
  73. P. Skowron and P. Faliszewski. Chamberlin-courant rule with approval ballots: Approximating the maxcover problem with bounded frequencies in fpt time. Journal of Artificial Intelligence Research, 60:687-716, 2017.
  74. P. Skowron, P. Faliszewski, and J. Lang. Finding a collective set of items: From proportional multirepresentation to group recommendation. Artificial Intelligence, 241:191-216, 2016.
  75. P. Skowron, P. Faliszewski, and A. Slinko. Achieving fully proportional representation: Ap- proximability result. Artificial Intelligence, 222:67-103, 2015.
  76. P. Skowron, P. Faliszewski, and A. Slinko. Axiomatic characterization of committee scoring rules. Technical Report arXiv:1604.01529 [cs.GT], arXiv.org, Apr. 2016.
  77. P. Skowron, M. Lackner, and M. B. D. P. E. Elkind. Proportional rankings. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, pages 409-415, 2017.
  78. P. Skowron, L. Yu, P. Faliszewski, and E. Elkind. The complexity of fully proportional repre- sentation for single-crossing electorates. Theoretical Computer Science, 569:43-57, 2015.
  79. J. Smith. Aggregation of preferences with variable electorate. Econometrica, 41(6):1027-1041, 1973.
  80. T. Thiele. Om flerfoldsvalg. In Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger, pages 415-441. 1895.
  81. N. Tideman and D. Richardson. Better voting methods through technology: The refinement- manageability trade-off in the Single Transferable Vote. Public Choice, 103(1-2):13-34, 2000.
  82. R. Yager. On ordered weighted averaging aggregation operators in multicriteria decisionmak- ing. IEEE Transactions on Systems, Man and Cybernetics, 18(1):183-190, 1988.
  83. H. Young. An axiomatization of Borda's rule. Journal of Economic Theory, 9(1):43-52, 1974.
  84. H. Young. Social choice scoring functions. SIAM Journal on Applied Mathematics, 28(4):824- 838, 1975.
  85. L. Yu, H. Chan, and E. Elkind. Multiwinner elections under preferences that are single-peaked on a tree. In Proceedings of the 23rd International Joint Conference on Artificial Intelligence, pages 425-431, 2013.
  86. F. Zanjirani and M. Hekmatfar, editors. Facility Location: Concepts, Models, and Case Studies. Springer, 2009.

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We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWA-based, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin-Courant, as the only rules in certain intersections of these classes. We introduce decomposable rules, describe some of their applications, and show that the class of decomposable rules strictly contains the class of OWA-based rules.

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Committee scoring voting rules are multiwinner analogues of positional scoring rules, which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top- k -counting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k -Approval Chamberlin--Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.

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Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such as a parliament, or a set of locations for a set of public facilities. In the spirit of celebrated Young's characterization result that axiomatizes single-winner scoring rules, we provide an axiomatic characterization of multiwinner committee scoring rules. We show that committee scoring rules-despite forming a remarkably general class of rules-are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by one axiom specific to multiwinner rules which we call committee dominance. In the course of our proof, we develop several new notions and techniques. In particular, we introduce and axiomatically characterize multiwinner decision scoring rules, a class of rules that broadly generalizes the well-known majority relation.

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We present and advertise the class of committee scoring rules, recently introduced as multiwinner analogues of single-winner scoring rules. We present a hierarchy of committee scoring rules (which includes all previously studied subclasses of committee scoring rules, as well as two new subclasses) and discuss their axiomatic properties (while focusing on fixed-majority consistency and monotonicity) as well as their computational properties (with a special focus on positive results).

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