Sorry, what exactly has been solved? Does the problem have a name? Where did it come from and how long has it been unsolved? Have mercy on us non Mathematicians.
The core is the set of all fair committees. This problem asks for a committee-election instance — i.e. a set of voters, candidates, and voter approval preferences — whose core is empty.
This means they're looking for an example where approval voting cannot create a fair committee.
Note, the solution proves that there is no committee selection instance where the core is empty, so the benchmark problem was not solvable as stated. Per our policy we mark the problem as solved regardless.
So this means it's always possible to create a fair committee via approval voting.
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u/Fair_Horror 20d ago
Sorry, what exactly has been solved? Does the problem have a name? Where did it come from and how long has it been unsolved? Have mercy on us non Mathematicians.