Risk aversion in one-sided matching Article Swipe
Inspired by real-world applications such as the assignment of pupils to schools or the allocation of social housing, the one-sided matching problem studies how a set of agents can be assigned to a set of objects when the agents have preferences over the objects, but not vice versa. For fairness reasons, most mechanisms use randomness, and therefore result in a probabilistic assignment. We study the problem of decomposing these probabilistic assignments into a weighted sum of ex-post (Pareto-)efficient matchings, while maximizing the worst-case number of assigned agents. This decomposition preserves all the assignments' desirable properties, most notably strategy-proofness. For a specific class of probabilistic assignments, including the assignment by the Probabilistic Serial mechanism, we propose a polynomial-time algorithm for this problem that obtains a decomposition in which all matchings assign at least the expected number of assigned agents by the probabilistic assignment, rounded down, thus achieving the theoretically best possible guarantee. For general probabilistic assignments, the problem becomes NP-hard. For the Random Serial Dictatorship (RSD) mechanism, we show that the worst-case number of assigned agents by RSD is at least half of the optimal, and that this bound is asymptotically tight. Lastly, we propose a column generation framework for the introduced problem, which we evaluate both on randomly generated data, and on real-world school choice data from the Belgian cities Antwerp and Ghent.
Related Topics
Concepts
Probabilistic logic
Matching (statistics)
Randomized algorithm
Computer science
Set (abstract data type)
Decomposition
Time complexity
Mathematical optimization
Randomness
Class (philosophy)
Probabilistic analysis of algorithms
Mathematics
Theoretical computer science
Algorithm
Artificial intelligence
Statistics
Biology
Ecology
Programming language
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://biblio.ugent.be/publication/8716699
- OA Status
- green
- References
- 15
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3119362701
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W3119362701Canonical identifier for this work in OpenAlex
- Title
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Risk aversion in one-sided matchingWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
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2021-01-03Full publication date if available
- Authors
-
Tom Demeulemeester, Dries Goossens, Ben Hermans, Roel LeusList of authors in order
- Landing page
-
https://biblio.ugent.be/publication/8716699Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2101.00579.pdfDirect OA link when available
- Concepts
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Probabilistic logic, Matching (statistics), Randomized algorithm, Computer science, Set (abstract data type), Decomposition, Time complexity, Mathematical optimization, Randomness, Class (philosophy), Probabilistic analysis of algorithms, Mathematics, Theoretical computer science, Algorithm, Artificial intelligence, Statistics, Biology, Ecology, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
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15Number of works referenced by this work
- Related works (count)
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.data | 215 |
| abstract_inverted_index.from | 216 |
| abstract_inverted_index.half | 180 |
| abstract_inverted_index.have | 39 |
| abstract_inverted_index.into | 71 |
| abstract_inverted_index.most | 51, 95 |
| abstract_inverted_index.over | 41 |
| abstract_inverted_index.show | 167 |
| abstract_inverted_index.such | 4 |
| abstract_inverted_index.that | 121, 168, 185 |
| abstract_inverted_index.this | 119, 186 |
| abstract_inverted_index.thus | 144 |
| abstract_inverted_index.vice | 46 |
| abstract_inverted_index.when | 36 |
| abstract_inverted_index.(RSD) | 164 |
| abstract_inverted_index.bound | 187 |
| abstract_inverted_index.class | 101 |
| abstract_inverted_index.data, | 209 |
| abstract_inverted_index.down, | 143 |
| abstract_inverted_index.least | 131, 179 |
| abstract_inverted_index.study | 63 |
| abstract_inverted_index.these | 68 |
| abstract_inverted_index.which | 126, 202 |
| abstract_inverted_index.while | 79 |
| abstract_inverted_index.Ghent. | 222 |
| abstract_inverted_index.Random | 161 |
| abstract_inverted_index.Serial | 111, 162 |
| abstract_inverted_index.agents | 27, 38, 137, 174 |
| abstract_inverted_index.assign | 129 |
| abstract_inverted_index.choice | 214 |
| abstract_inverted_index.cities | 219 |
| abstract_inverted_index.column | 195 |
| abstract_inverted_index.number | 83, 134, 171 |
| abstract_inverted_index.pupils | 9 |
| abstract_inverted_index.result | 57 |
| abstract_inverted_index.school | 213 |
| abstract_inverted_index.social | 16 |
| abstract_inverted_index.tight. | 190 |
| abstract_inverted_index.versa. | 47 |
| abstract_inverted_index.Antwerp | 220 |
| abstract_inverted_index.Belgian | 218 |
| abstract_inverted_index.Lastly, | 191 |
| abstract_inverted_index.agents. | 86 |
| abstract_inverted_index.becomes | 157 |
| abstract_inverted_index.ex-post | 76 |
| abstract_inverted_index.general | 152 |
| abstract_inverted_index.notably | 96 |
| abstract_inverted_index.objects | 35 |
| abstract_inverted_index.obtains | 122 |
| abstract_inverted_index.problem | 21, 65, 120, 156 |
| abstract_inverted_index.propose | 114, 193 |
| abstract_inverted_index.rounded | 142 |
| abstract_inverted_index.schools | 11 |
| abstract_inverted_index.studies | 22 |
| abstract_inverted_index.Inspired | 0 |
| abstract_inverted_index.NP-hard. | 158 |
| abstract_inverted_index.assigned | 30, 85, 136, 173 |
| abstract_inverted_index.evaluate | 204 |
| abstract_inverted_index.expected | 133 |
| abstract_inverted_index.fairness | 49 |
| abstract_inverted_index.housing, | 17 |
| abstract_inverted_index.matching | 20 |
| abstract_inverted_index.objects, | 43 |
| abstract_inverted_index.optimal, | 183 |
| abstract_inverted_index.possible | 149 |
| abstract_inverted_index.problem, | 201 |
| abstract_inverted_index.randomly | 207 |
| abstract_inverted_index.reasons, | 50 |
| abstract_inverted_index.specific | 100 |
| abstract_inverted_index.weighted | 73 |
| abstract_inverted_index.achieving | 145 |
| abstract_inverted_index.algorithm | 117 |
| abstract_inverted_index.desirable | 93 |
| abstract_inverted_index.framework | 197 |
| abstract_inverted_index.generated | 208 |
| abstract_inverted_index.including | 105 |
| abstract_inverted_index.matchings | 128 |
| abstract_inverted_index.one-sided | 19 |
| abstract_inverted_index.preserves | 89 |
| abstract_inverted_index.therefore | 56 |
| abstract_inverted_index.allocation | 14 |
| abstract_inverted_index.assignment | 7, 107 |
| abstract_inverted_index.generation | 196 |
| abstract_inverted_index.guarantee. | 150 |
| abstract_inverted_index.introduced | 200 |
| abstract_inverted_index.matchings, | 78 |
| abstract_inverted_index.maximizing | 80 |
| abstract_inverted_index.mechanism, | 112, 165 |
| abstract_inverted_index.mechanisms | 52 |
| abstract_inverted_index.real-world | 2, 212 |
| abstract_inverted_index.worst-case | 82, 170 |
| abstract_inverted_index.assignment, | 141 |
| abstract_inverted_index.assignment. | 61 |
| abstract_inverted_index.assignments | 70 |
| abstract_inverted_index.decomposing | 67 |
| abstract_inverted_index.preferences | 40 |
| abstract_inverted_index.properties, | 94 |
| abstract_inverted_index.randomness, | 54 |
| abstract_inverted_index.Dictatorship | 163 |
| abstract_inverted_index.applications | 3 |
| abstract_inverted_index.assignments' | 92 |
| abstract_inverted_index.assignments, | 104, 154 |
| abstract_inverted_index.Probabilistic | 110 |
| abstract_inverted_index.decomposition | 88, 124 |
| abstract_inverted_index.probabilistic | 60, 69, 103, 140, 153 |
| abstract_inverted_index.theoretically | 147 |
| abstract_inverted_index.asymptotically | 189 |
| abstract_inverted_index.polynomial-time | 116 |
| abstract_inverted_index.(Pareto-)efficient | 77 |
| abstract_inverted_index.strategy-proofness. | 97 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/11 |
| sustainable_development_goals[0].score | 0.8199999928474426 |
| sustainable_development_goals[0].display_name | Sustainable cities and communities |
| citation_normalized_percentile |