Multi-member 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. 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.
• Single non-transferable vote: Each voter casts one vote for one candidate in a multi-candidate race for multiple offices
• 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.

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:

• Sequential Proportional Approval Voting
• Reweighted Range Voting
• Sequential Monroe
• Allocated Score
• Sequentially Subtracted Score
• Single transferable vote

Optimal Proportional Methods

Optimal Systems select all winners at once by optimizing a specific desirable metric for proportionality. First a "quality function" or desired outcome is determined, and then an algorithm is used to determine the winner set that best maximizes that outcome. In most systems this is done by permuting to all possible winner sets not a maximization algorithm. This makes such systems computationally expensive. Since ranks do not allow for the arithmatic operations to do such calculations. As such there are no optimal Ordinal voting systems but only optimal Cardinal voting systems

Common examples:

• Harmonic Voting
• Proportional approval voting
• Phragmén's Method
• Monroe's Method
• PAMSAC