Electing a committee with dominance constraints
We consider the problem of electing a committee of k candidates, subject to constraints as to which committees are admissible for constitutional, conventional, or practical reasons. In our framework, the candidates are given labels as an abstraction of a politician’s religion, a film’s genre, a song...
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| Published in: | Annals of operations research Vol. 318; no. 2; pp. 985 - 1000 |
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| Format: | Journal Article |
| Language: | English |
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01.11.2022
Springer Springer Nature B.V |
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| ISSN: | 0254-5330, 1572-9338 |
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| Abstract | We consider the problem of electing a committee of
k
candidates, subject to constraints as to which committees are admissible for constitutional, conventional, or practical reasons. In our framework, the candidates are given labels as an abstraction of a politician’s religion, a film’s genre, a song’s language, or other attribute, and the election outcome is constrained by interval constraints (constraints of the form “Between 3 and 5 candidates with label X”) and dominance constraints (“At least as many candidates with label X as with label Y”). The goal is to select a committee that is as good as possible among those that satisfy the constraints. The difficulty is that in the standard social choice framework we do not have a quantifiable notion of “goodness”, only a voting rule that tells us which committee is the best. In this paper we argue how the logic underlying separable and best-
k
rules can be extended into an ordering of committees from best to worst, and study the question of how to select the best valid committee with respect to this order. The problem is
NP
-hard, but we show the existence of a polynomial time solution in the case of tree-like constraints, and a fixed-parameter tractable algorithm for the general case. |
|---|---|
| AbstractList | We consider the problem of electing a committee of k candidates, subject to constraints as to which committees are admissible for constitutional, conventional, or practical reasons. In our framework, the candidates are given labels as an abstraction of a politician’s religion, a film’s genre, a song’s language, or other attribute, and the election outcome is constrained by interval constraints (constraints of the form “Between 3 and 5 candidates with label X”) and dominance constraints (“At least as many candidates with label X as with label Y”). The goal is to select a committee that is as good as possible among those that satisfy the constraints. The difficulty is that in the standard social choice framework we do not have a quantifiable notion of “goodness”, only a voting rule that tells us which committee is the best. In this paper we argue how the logic underlying separable and best-k rules can be extended into an ordering of committees from best to worst, and study the question of how to select the best valid committee with respect to this order. The problem is NP-hard, but we show the existence of a polynomial time solution in the case of tree-like constraints, and a fixed-parameter tractable algorithm for the general case. We consider the problem of electing a committee of k candidates, subject to constraints as to which committees are admissible for constitutional, conventional, or practical reasons. In our framework, the candidates are given labels as an abstraction of a politician’s religion, a film’s genre, a song’s language, or other attribute, and the election outcome is constrained by interval constraints (constraints of the form “Between 3 and 5 candidates with label X”) and dominance constraints (“At least as many candidates with label X as with label Y”). The goal is to select a committee that is as good as possible among those that satisfy the constraints. The difficulty is that in the standard social choice framework we do not have a quantifiable notion of “goodness”, only a voting rule that tells us which committee is the best. In this paper we argue how the logic underlying separable and best- k rules can be extended into an ordering of committees from best to worst, and study the question of how to select the best valid committee with respect to this order. The problem is NP -hard, but we show the existence of a polynomial time solution in the case of tree-like constraints, and a fixed-parameter tractable algorithm for the general case. We consider the problem of electing a committee of k candidates, subject to constraints as to which committees are admissible for constitutional, conventional, or practical reasons. In our framework, the candidates are given labels as an abstraction of a politician's religion, a film's genre, a song's language, or other attribute, and the election outcome is constrained by interval constraints (constraints of the form "Between 3 and 5 candidates with label X") and dominance constraints ("At least as many candidates with label X as with label Y"). The goal is to select a committee that is as good as possible among those that satisfy the constraints. The difficulty is that in the standard social choice framework we do not have a quantifiable notion of "goodness", only a voting rule that tells us which committee is the best. In this paper we argue how the logic underlying separable and best-k rules can be extended into an ordering of committees from best to worst, and study the question of how to select the best valid committee with respect to this order. The problem is [Formula omitted]-hard, but we show the existence of a polynomial time solution in the case of tree-like constraints, and a fixed-parameter tractable algorithm for the general case. |
| Audience | Academic |
| Author | Ianovski, Egor |
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| CitedBy_id | crossref_primary_10_1016_j_jcss_2025_103702 crossref_primary_10_1007_s11127_024_01163_3 crossref_primary_10_1007_s10479_022_04764_7 crossref_primary_10_1007_s10726_025_09928_x crossref_primary_10_1016_j_jmateco_2024_103077 crossref_primary_10_3917_redp_351_0169 crossref_primary_10_1016_j_ejor_2025_06_013 |
| Cites_doi | 10.2307/1957270 10.1287/moor.8.1.1 10.1007/978-3-642-02839-7_6 10.1007/s00355-017-1026-z 10.1007/978-3-642-20441-8_12 10.1007/s00355-003-0209-y 10.1007/BF00182574 10.1007/3-540-35605-3_6 10.1007/s11127-007-9165-x 10.2307/2082518 10.1016/j.artint.2018.07.005 10.1016/0022-0531(81)90005-3 10.1016/0165-4896(85)90043-5 10.1007/s10726-019-09634-5 10.1016/j.jmateco.2017.01.008 10.1016/j.jmateco.2015.08.008 10.1287/inte.20.5.67 10.1287/moor.8.4.538 10.1007/s00355-007-0268-6 10.1007/978-1-4020-7964-1_4 10.1007/BF01082056 10.1002/bs.3830370203 10.1007/s00355-018-1126-4 10.1007/s11127-019-00692-6 10.1137/0141041 10.24963/ijcai.2018/20 10.1609/aaai.v32i1.11457 10.1609/aaai.v28i1.8827 10.24963/ijcai.2018/80 10.2139/ssrn.3005958 |
| ContentType | Journal Article |
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k
candidates, subject to constraints as to which committees are admissible for constitutional, conventional,... We consider the problem of electing a committee of k candidates, subject to constraints as to which committees are admissible for constitutional, conventional,... |
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| SubjectTerms | Algorithms Analysis Business and Management Candidates Combinatorics Committees Constraints Elections Game theory Operations research Operations Research/Decision Theory Original Research Polynomials Preferences Social choice Theory of Computation Voting |
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| Title | Electing a committee with dominance constraints |
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