Concept in the field of computational social choice
An agreeable subset is a subset of items that is considered, by all people in a certain group, to be at least as good as its complement. Finding a small agreeable subset is a problem in computational social choice.[1][2]
An example situation in which this problem arises is when a family goes on a trip and has to decide which items to take. Since their car is limited in size, they cannot pick all items, so they have to agree on a subset of items which are most important. If they manage to find a subset of items such that all family members agree that it is at least as good as the subset of items remaining at home, then this subset is called agreeable.
Another use case is when the citizens in some city want to elect a committee from a given pool of candidates, such that all citizens agree that the subset of elected candidates is at least as good as the subset of non-elected ones. Subject to that, the committee size should be as small as possible.
^Suksompong, Warut (2016-07-09). "Assigning a small agreeable set of indivisible items to multiple players". Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence. IJCAI'16. New York, New York, USA: AAAI Press: 489–495. arXiv:1606.08077. doi:10.1016/j.artint.2018.10.001. ISBN 978-1-57735-770-4.
^Manurangsi, Pasin; Suksompong, Warut (2019-03-01). "Computing a small agreeable set of indivisible items". Artificial Intelligence. 268: 96–114. arXiv:1606.08077. doi:10.1016/j.artint.2018.10.001. ISSN 0004-3702. S2CID 124836295.
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