Part of the Politics and Economics series |
Electoral systems |
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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.
There are many scenarios in which multiwinner voting is useful. 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. These can be classified based on the voting type— approval voting vs. ranked voting.
Some election systems elect multiple members by competition held among individual candidates. Such systems are some variations of multiple non-transferable voting and single transferable voting.
In other systems, candidates are grouped in committees (slates) and voters cast votes for the committees (or slates).
Approval voting is a common method for single-winner elections and sometimes for multiwinner elections. In single-winner elections, each voter marks the candidate he approves, and the candidate with the most votes wins.
With multiwinner voting, there are many ways to decide which candidate should be elected. In some, each voter ranks the candidates; in others they cast X votes. As well, each voter may cast single or multiple votes.
Already in 1895, Thiele suggested a family of weight-based rules called Thiele's voting rules. [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). Each voter assigns, to each committee containing p candidates approved by the voter, a score equal to w1+...+wp. The committee with the highest total score is elected. Some common voting rules in Thiele's family are:
There are rules based on other principles, such as minimax approval voting [6] and its generalizations, [7] as well as Phragmen's voting rules [8] and the method of equal shares. [9] [10]
The complexity of determining the winners vary: MNTV winners can be found in polynomial time, while Chamberlin-Courant [11] and PAV are both NP-hard.
Positional scoring rules are common in rank-based single-winner voting. Each voter ranks the candidates from best to worst, a pre-specified function assigns a score to each candidate based on his rank, and the candidate with the highest total score is elected.
In multiwinner voting held using these systems, we need to assign scores to committees rather than to individual candidates. There are various ways to do this, for example: [1]
In single-winner voting, a Condorcet winner is a candidate who wins in every head-to-head election against each of the other candidates. A Condorcet method is a method that selects a Condorcet winner whenever it exists. There are several ways to adapt Condorcet's criterion to multiwinner voting:
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.
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:
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. Formally, if the committee is of size k, there are n voters, and some L*n/k voters rank the same L candidates at the top (or approve the same L candidates), then these L candidates should be elected. This principle is easy to implement when the voters vote for parties (in party-list systems), but it can also be adapted to approval voting or ranked voting; see justified representation and proportionality for solid coalitions.
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: CS1 maint: multiple names: authors list (
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Part of the Politics and Economics series |
Electoral systems |
---|
Politics portal Economics portal |
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.
There are many scenarios in which multiwinner voting is useful. 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. These can be classified based on the voting type— approval voting vs. ranked voting.
Some election systems elect multiple members by competition held among individual candidates. Such systems are some variations of multiple non-transferable voting and single transferable voting.
In other systems, candidates are grouped in committees (slates) and voters cast votes for the committees (or slates).
Approval voting is a common method for single-winner elections and sometimes for multiwinner elections. In single-winner elections, each voter marks the candidate he approves, and the candidate with the most votes wins.
With multiwinner voting, there are many ways to decide which candidate should be elected. In some, each voter ranks the candidates; in others they cast X votes. As well, each voter may cast single or multiple votes.
Already in 1895, Thiele suggested a family of weight-based rules called Thiele's voting rules. [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). Each voter assigns, to each committee containing p candidates approved by the voter, a score equal to w1+...+wp. The committee with the highest total score is elected. Some common voting rules in Thiele's family are:
There are rules based on other principles, such as minimax approval voting [6] and its generalizations, [7] as well as Phragmen's voting rules [8] and the method of equal shares. [9] [10]
The complexity of determining the winners vary: MNTV winners can be found in polynomial time, while Chamberlin-Courant [11] and PAV are both NP-hard.
Positional scoring rules are common in rank-based single-winner voting. Each voter ranks the candidates from best to worst, a pre-specified function assigns a score to each candidate based on his rank, and the candidate with the highest total score is elected.
In multiwinner voting held using these systems, we need to assign scores to committees rather than to individual candidates. There are various ways to do this, for example: [1]
In single-winner voting, a Condorcet winner is a candidate who wins in every head-to-head election against each of the other candidates. A Condorcet method is a method that selects a Condorcet winner whenever it exists. There are several ways to adapt Condorcet's criterion to multiwinner voting:
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.
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:
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. Formally, if the committee is of size k, there are n voters, and some L*n/k voters rank the same L candidates at the top (or approve the same L candidates), then these L candidates should be elected. This principle is easy to implement when the voters vote for parties (in party-list systems), but it can also be adapted to approval voting or ranked voting; see justified representation and proportionality for solid coalitions.
{{
cite book}}
: CS1 maint: multiple names: authors list (
link)