Proportional Subset Voting: Difference between revisions

Corrected the example.
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(Corrected the example.)
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==Procedure==
 
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:
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===Example===
 
The following example shows how scores S are obtained from aone vote:
 
N = 2 (winners)
Original vote, with range [-4,4]:
A[4] B[-4] C[0] D[2]
Subsets for N = '''2 winners'''
A,BAB: 4/1 + -4/2 = 2
A,CAC: 4/1 + 0/2 = 4
A,DAD: 4/1 + 2/2 = 5
B,CBC: -40/1 + 0-4/2 = -42
B,DBD: -42/1 + 2-4/2 = -30
C,DCD: 02/1 + 20/2 = 12
Converted vote:
A,DAD[5] A,CAC[4] A,BAB[2] C,DCD[12] B,DBD[-30] B,CBC[-42]
 
Original vote, with range [-4,4]:
A[4] B[-4] C[0] D[2]
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[5] ABD[4] ABC[3] BCD[1]
 
The following example shows how the sums for each subset are obtained, given the converted votes:
 
3 converted votes, with '''2 winners''':
A,DAD[5] A,CAC[4] A,BAB[2] C,DCD[12] B,DBD[-30] B,CBC[-42]
A,DAD[2] A,CAC[4] A,BAB[-42] C,DCD[7] B,DBD[-30] B,CBC[12]
A,DAD[4] A,CAC[5] A,BAB[12] C,DCD[2] B,DBD[-42] B,CBC[-30]
Sums for each subset:
A,DAD[11] A,CAC[13] A,BAB[-12] C,D CD[1011] B,DBD[-102] B,CBC[-60]
The winner is {A,C}AC.
 
==Subset Voting (category)==
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N is the number of winners.
 
ConsideringFor oneeach vote, a score S is obtainedand for each subset of N candidates., Thisa procedurescore S is appliedobtained tousing allprocedure votesp1, andfinally obtaining returnsthe converted votes.
 
ConsideringProcedure thep2 subsets(eg. asa single[[Single candidates, aMember system|Single-Winner system]]) applicableis used, on the converted votes, is used to obtain the winning subset.
 
''In the converted votes, subsets are considered as single candidates with a score.''
Considering the subsets as single candidates, a Single-Winner system applicable on the converted votes, is used to obtain the winning subset.
 
''The waysize of calculatingthe Srange, andprocedure thep1, [[Single Memberand system|Single-Winnerprocedure system]]p2 chosen, determinesdetermine the variant of Subset Voting.''
 
===Thiele method===
 
Thiele method uses range [0,MAX] and in p1 divides the values by <math>\begin{equation}i\end{equation}</math> with <math>\begin{equation}i=1,...,N\end{equation}</math>.
 
PSV uses range [-MAX,MAX] and in p1 divides the values by <math>\begin{equation}2^i\end{equation}</math> with <math>\begin{equation}i=0,...,N-1\end{equation}</math>.
 
[[Category:Single-winner voting methods]]
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