  In this paper, we study some multiagent variants of the knapsack problem.
Fluschnik et al. [AAAI 2019] considered the model in which every agent assigns
some utility to every item. They studied three preference aggregation rules for
finding a subset (knapsack) of items: individually best, diverse, and
Nash-welfare-based. Informally, diversity is achieved by satisfying as many
voters as possible. Motivated by the application of aggregation operators in
multiwinner elections, we extend the study from diverse aggregation rule to
Median and Best scoring functions. We study the computational and parameterized
complexity of the problem with respect to some natural parameters, namely, the
number of voters, the number of items, and the distance from an easy instance.
We also study the complexity of the problem under domain restrictions.
Furthermore, we present significantly faster parameterized algorithms with
respect to the number of voters for the diverse aggregation rule.
