# Committee Selection with Attribute Level Preferences

## TL;DR

This paper introduces a novel approach to committee selection based on attribute preferences, proposing new properties and algorithms, and proving certain optimal solutions are NP-complete.

## Contribution

It formalizes attribute-based committee selection, defines new fairness properties, and analyzes the computational complexity of related aggregation and selection problems.

## Key findings

- Existing approval rules do not satisfy the new properties.
- A greedy algorithm satisfies some properties but not all.
- Optimal committee selection with certain fairness criteria is NP-complete.

## Abstract

We consider the problem of committee selection from a fixed set of candidates where each candidate has multiple quantifiable attributes. To select the best possible committee, instead of voting for a candidate, a voter is allowed to approve the preferred attributes of a given candidate. Though attribute based preference is addressed in several contexts, committee selection problem with attribute approval of voters has not been attempted earlier. A committee formed on attribute preferences is more likely to be a better representative of the qualities desired by the voters and is less likely to be susceptible to collusion or manipulation. In this work, we provide a formal study of the different aspects of this problem and define properties of weak unanimity, strong unanimity, simple justified representations and compound justified representation, that are required to be satisfied by the selected committee. We show that none of the existing vote/approval aggregation rules satisfy these new properties for attribute aggregation. We describe a greedy approach for attribute aggregation that satisfies the first three properties, but not the fourth, i.e., compound justified representation, which we prove to be NP-complete. Furthermore, we prove that finding a committee with justified representation and the highest approval voting score is NP-complete.