Katana VentraIP

Multiwinner voting

Multiwinner,[1] at-large, or committee[2][3] voting refers to electoral systems that elect several candidates at once. Such methods can be used to elect parliaments or committees.

(MNTV): the weight vector is (1,1,...,1). It is also called plurality-at-large approval-voting.

Multiple non-transferable vote

Approval-Chamberlin-Courant (ACC): the weight vector is (1,0,...,0). That is, each voter gives 1 point to a committee, if and only if it contains one of his approved candidates.

(PAV): the weight vector is the Harmonic progression (1, 1/2, 1/3, ..., 1/k).

Proportional approval voting

Sequential rules: using any single-winner voting rule, pick a single candidate and add it to the committee. Repeat the process k times.

[18]

Best-k rules: using any scoring rule, assign a score to each candidate. Pick the k candidates with the highest scores.

[1]

Excellence means that the committee should contain the "best" candidates. Excellence-based voting rules are often called screening rules.[18] They are often used as a first step in a selection of a single best candidate, that is, a method for creating a shortlist. A basic property that should be satisfied by such a rule is committee monotonicity (also called house monotonicity, a variant of resource monotonicity): if some k candidates are elected by a rule, and then the committee size increases to k+1 and the rule is re-applied, then the first k candidates should still be elected. Some families of committee-monotone rules are:


The property of committee monotonicity is incompatible with the property of stability (a particular adaptation of Condorcet's criterion): there exists a single voting profile that admits a unique Condorcet set of size 2, and a unique Condorcet set of size 3, and they are disjoint (the set of size 2 is not contained in the set of size 3).[18]


On the other hand, there exists a family of positional scoring rules - the separable positional scoring rules - that are committee-monotone. These rules are also computable in polynomial time (if their underlying single-winner scoring functions are).[1] For example, k-Borda is separable while multiple non-transferable vote is not.

Narrow-top criterion: if there exists a committee of size k containing the top-ranked candidate of every voter, then it should be elected.

[1]

Top-member monotonicity: if a committee is elected, and some voter shifts upwards the rank of his most-preferred winner, then the same committee should be elected.

[22]

Diversity means that the committee should contain the top-ranked candidates of as many voters as possible. Formally, the following axioms are reasonable for diversity-centered applications:

—can be seen as a generalization of multiwinner voting where candidates have different costs

Participatory budgeting