Proportional Subset Voting
Ballot use range [-MAX,MAX], also without 0. N is the number of winners.
For each vote, and for each subset of N candidates, the following procedure is applied, considering only the original ratings of the N candidates in the vote:
- the highest rating is divided by , the 2nd highest rating is divided by , ... , the N-th highest rating (which is the lowest) is divided by .
- after this division, the ratings are added to obtain the value S.
By applying this procedure, in the end, we obtain for each vote a list of scores S, one for each subset.
The scores S, for each subset, are added together and the subset with the highest sum contains the N winners.
The following example shows how scores S are obtained from one vote:
Original vote, with range [-4,4]: A B[-4] C D Subsets for N = 2 winners AB: 4/1 + -4/2 = 2 AC: 4/1 + 0/2 = 4 AD: 4/1 + 2/2 = 5 BC: 0/1 + -4/2 = -2 BD: 2/1 + -4/2 = 0 CD: 2/1 + 0/2 = 2 Converted vote: AD AC AB CD BD BC[-2]
Original vote, with range [-4,4]: A B[-4] C D Subsets for N = 3 winners ABC: 4/1 + 0/2 + -4/4 = 3 ACD: 4/1 + 2/2 + 0/4 = 5 ABD: 4/1 + 2/2 + -4/4 = 4 BCD: 2/1 + 0/2 + -4/4 = 1 Converted vote: ACD ABD ABC BCD
The following example shows how the sums for each subset are obtained, given the converted votes:
3 converted votes, with 2 winners: AD AC AB CD BD BC[-2] AD AC AB[-2] CD BD BC AD AC AB CD BD[-2] BC Sums for each subset: AD AC AB CD BD[-2] BC The winner is AC.
Subset Voting (category)
N is the number of winners.
For each vote, and for each subset of N candidates, a score S is obtained using procedure p1, finally obtaining the converted votes.
Procedure p2 (eg. a Single-Winner system) is used, on the converted votes, to obtain the winning subset.
In the converted votes, subsets are considered as single candidates with a score.
The size of the range, procedure p1, and procedure p2 chosen, determine the variant of Subset Voting.
Thiele method uses range [0,MAX] and in p1 divides the values by with .
PSV uses range [-MAX,MAX] and in p1 divides the values by with .