Multi-member system: Difference between revisions

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Multi member systems, also called multi winner systems, are systems which elect multiple people in one election. In the context of multi-member systems, they are defined to be proportional if the [[Hare Quota Criterion]] is satisfied. This is not meant to imply anything about [[Proportional representation]]. It is common for several of these systems to be combined into a [[Regional System]].
Multi member voting methods, also called multi winner methods, are voting methods which elect multiple people in one election. In the context of multi-member methods, they are defined to be proportional if the [[Hare Quota Criterion]] is satisfied. This is not meant to imply anything about [[Proportional representation|Proportional Representation]]. It is common for several of these voting methods to be combined into a [[Regional System]].


==[[Block voting | Bloc Systems]]==
==[[Block voting | Bloc Voting Methods]]==


Bloc Systems elect all members at once under the same metric which would be used in a [[Single Member system]].
Bloc methods find the candidate set with the most support or the most votes overall using the same metric which would be used in a [https://electowiki.org/wiki/Single_Member_system single member system]. The number of seats up for election is determined and the top candidates are elected to fill those seats.


Common examples:
Common examples:
* Bloc Approval Voting: Each voter chooses (no ranking) as many candidates as desired. Only one vote is allowed per candidate. Voters may not vote more than once for any one candidate. Add all the votes. Elect the candidates with the most votes until all positions are filled.
*'''Bloc Approval Voting''': Each voter chooses (no ranking) as many candidates as desired. Only one vote is allowed per candidate. Voters may not vote more than once for any one candidate. Add all the votes. Elect the candidates with the most votes until all positions are filled.
* Bloc Plurality Voting: Each voter chooses as many candidates as there are seats to be elected. Add all the votes. Elect the candidates with the most votes until all positions are filled.
*'''Bloc Score Voting''': Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable. Add all the scores. Elect the candidates with the highest total score until all positions are filled.
* Bloc Score Voting: Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable. Add all the votes. Elect the candidates with the highest scores until all positions are filled.
*'''Bloc STAR Voting''': Each voter scores all the candidates on a scale from 0-5. All the scores are added and the two highest scoring candidates advance to an automatic runoff. The finalist who was preferred by (scored higher by) more voters wins the first seat. The next two highest scoring candidates then runoff, with the finalist preferred by more voters winning the next seat. This process continues until all positions are filled.
*'''[https://electowiki.org/wiki/Cumulative_voting Cumulative Voting:]''' In this system, a voter facing multiple choices is given X number of ''points''. The voter can then assign his points to one or more of the choices, thus enabling one to weight one's vote if desired. This could be achieved through a normalized [[Ratings ballot|ratings ballot]], or through multiple [[Plurality ballot|plurality ballots]], one per each point allocated. Typically, each voter will have as many votes as there are winners to be selected.
* [[Cumulative voting]]


==Sequential Systems==
==Sequential [[Proportional representation|Proportional]] Methods==
Sequential Cardinal Methods elect winners one at a time in sequence using a candidate selection method and a reweighting mechanism. The single-winner version of the selection is applied to find the first winner, then a reweighting is applied before the selection of the next and subsequent winners. A reweighting is applied to either the ballot or the scores for the ballot itself. The purpose of the reweighting phase is to ensure that the [[Proportional representation|Hare Quota Criterion]] is met to ensure proportional election outcomes.

Sequential systems elect winners via a repeated two step process of selection and ballot reweighting. The purpose of the reweighting is to fulfill Hare Quota Criterion.


Common examples:
Common examples:
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* [[Single non-transferable vote]]
* [[Single non-transferable vote]]


==Optimal Systems==
==Optimal Methods==


Optimal systems elect all members by the optimization of a quality function.
Optimal methods elect all members by the optimization of a quality function.


Common examples:
Common examples:

Revision as of 02:43, 15 December 2019

Multi member voting methods, also called multi winner methods, are voting methods which elect multiple people in one election. In the context of multi-member methods, they are defined to be proportional if the Hare Quota Criterion is satisfied. This is not meant to imply anything about Proportional Representation. It is common for several of these voting methods to be combined into a Regional System.

Bloc Voting Methods

Bloc methods find the candidate set with the most support or the most votes overall using the same metric which would be used in a single member system. The number of seats up for election is determined and the top candidates are elected to fill those seats.

Common examples:

  • Bloc Approval Voting: Each voter chooses (no ranking) as many candidates as desired. Only one vote is allowed per candidate. Voters may not vote more than once for any one candidate. Add all the votes. Elect the candidates with the most votes until all positions are filled.
  • Bloc Score Voting: Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable. Add all the scores. Elect the candidates with the highest total score until all positions are filled.
  • Bloc STAR Voting: Each voter scores all the candidates on a scale from 0-5. All the scores are added and the two highest scoring candidates advance to an automatic runoff. The finalist who was preferred by (scored higher by) more voters wins the first seat. The next two highest scoring candidates then runoff, with the finalist preferred by more voters winning the next seat. This process continues until all positions are filled.
  • Cumulative Voting: In this system, a voter facing multiple choices is given X number of points. The voter can then assign his points to one or more of the choices, thus enabling one to weight one's vote if desired. This could be achieved through a normalized ratings ballot, or through multiple plurality ballots, one per each point allocated. Typically, each voter will have as many votes as there are winners to be selected.

Sequential Proportional Methods

Sequential Cardinal Methods elect winners one at a time in sequence using a candidate selection method and a reweighting mechanism. The single-winner version of the selection is applied to find the first winner, then a reweighting is applied before the selection of the next and subsequent winners. A reweighting is applied to either the ballot or the scores for the ballot itself. The purpose of the reweighting phase is to ensure that the Hare Quota Criterion is met to ensure proportional election outcomes.

Common examples:

Optimal Methods

Optimal methods elect all members by the optimization of a quality function.

Common examples:

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