Multiwinner voting

They can be broadly classified into three classes, based on the main objective in electing the committee:[4] A major challenge in the study of multiwinner voting is finding reasonable adaptations of concepts from single-winner voting.

[2][5] Each rule in the family is defined by a sequence of k weakly-positive weights, w1,...,wk (where k is the committee size).

Positional scoring rules are common in rank-based single-winner voting.

In multiwinner voting held using these systems, we need to assign scores to committees rather than to individual candidates.

There are several ways to adapt Condorcet's criterion to multiwinner voting: Excellence means that the committee should contain the "best" candidates.

These rules are also computable in polynomial time (if their underlying single-winner scoring functions are).

Formally, the following axioms are reasonable for diversity-centered applications: Proportionality means that each cohesive group of voters (that is: a group of voters with similar preferences) should be represented by a number of winners proportional to its size.