Proportional Subset Voting: Difference between revisions
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Proportional Subset Voting (PSV) is a [[Single Member system|Single-Winner]] and [[Multi-Member System|Multi-Winner]], [[Cardinal voting systems]]
==Procedure==
Ballot
For each vote, and for each subset of <math>N</math> candidates
* create a list of <math>G_i</math> groups, 1 for each percentage, multiple of <math>\frac{100\%}{N}</math> ''(eg for N = 4 the groups are 0%, 25%, 50%, 75%, 100%)''.
* for each <math>G_i</math>, the voters with a total approval <math>=G_i</math> are counted getting <math>C_i</math> <math>(\ \mathrm{ total\ approval\ of\ the\ N\ candidates}=\frac{\mathrm{ratings\ sum}}{N}\ )</math>. Each <math>C_i</math> is then divided by the number of voters.
* find the group with the lowest percentage <math>G_{min}</math> containing <math>C_{min}>0</math>, and associate <math>S_{min}=\{G_{min},C_{min}\}</math> to the subset.
* find the group with the highest percentage <math>G_{max}</math> containing <math>C_{max}>0</math>, and associate <math>S_{max}=\{G_{max},C_{max}\}</math> to the subset.
===Example===▼
Sort the subsets from major to minor based on the <math>S_{min}</math> value; if there are tied subsets then sort them from minor to major based on the <math>S_{max}</math> value. The subset that is first after sorting wins.
If there are any tied subsets, <math>P</math> is calculated which is the sum of the products between <math>G_i</math> and <math>C_i</math>. The subset that has highest <math>P</math> wins.
===Procedure with range===
The ratings of the range have values between [0%,100%]. For example, if it has 5 ratings {0,1,2,3,4} then the respective values will be {0%,25%,50%,75%,100%}.
The only difference with the procedure that uses multiple-choice ballots is that:
* the total approval of a voter for N candidates must be somehow rounded up to a multiple of <math>\frac{100\%}{N}</math>, in order to be counted in the list of <math>G_i</math> groups.
Ballot uses 2 ratings, that is: {0,1} = {0%, 100%}. There are 6 winners and the following votes:
A[1] B[1] C[1] D[1] E[1] F[1] G[0] ...
A[1] B[1] C[1] D[1] E[1] F[1] G[0] ...
A[1] B[1] C[1] D[0] E[0] F[0] G[1] ...
The list of groups associated with the subset of 6 candidates is:
0%[] 16%[] 33%[] 50%[] 66%[] 83%[] 100%[]
The total approval of the 3 voters is calculated for the following subsets:
ABCDEF: [100%, 100%, 50%]
ABCDEG: [83%, 83%, 66%]
Total approvals are counted for each subset, and then divided by the number of voters (3 in this case):
ABCDEF
Count: 0%[] 16%[] 33%[] 50%['''1'''] 66%[] 83%[] 100%['''2''']
Division: 0%[] 16%[] 33%[] 50%['''33%'''] 66%[] 83%[] 100%['''66%''']
Short: 50%['''33%'''] 100%['''66%''']
ABCDEG
Count: 0%[] 16%[] 33%[] 50%[] 66%['''1'''] 83%['''2'''] 100%[]
Division: 0%[] 16%[] 33%[] 50%[] 66%['''33%'''] 83%['''66%'''] 100%[]
Short: 66%['''33%'''] 83%['''66%''']
Find <math>\{S_{min},S_{max}\}</math> and sort:
ABCDEG: {33%,83%}
ABCDEF: {33%,100%}
ABCDEG wins.
Calculate P, just to show how this is done:
ABCDEF: 50%[33%] 100%[66%] --> 50%*33% + 100%*66% = 0,825
ABCDEG: 66%[33%] 83%[66%] --> 66%*33% + 83%*66% = 0,765
==Subset Voting (category)==
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N is the number of winners.
''The size of the range, procedure p1, and procedure p2 chosen, determine the variant of Subset Voting.''
▲Considering the subsets as single candidates, a [[Single Member system|Single-Winner system]] applicable on the converted votes, is used to obtain the winning subset.
[[Category:Single-winner voting methods]]
[[Category:Multi-winner voting methods]]
[[Category:Cardinal voting methods]]
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