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Proportional Subset Voting: Difference between revisions

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Proportional Subset Voting (view source)

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Proportional Subset Voting (PSV) is a [[Single Member system|Single-Winner]] and [[Multi-Member System|Multi-Winner]], [[Cardinal voting systems]] developedproposed by [[User:Aldo Tragni|Aldo Tragni]].
 
==Procedure==
 
Ballot use range [0-MAX,MAX]. 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 1<math>\begin{equation}2^0\end{equation}</math>, the 2nd highest rating is divided by <math>\begin{equation}2^1\end{equation}</math>, ... , the N-th highest rating (which is the lowest) is divided by <math>\begin{equation}2^{N-1}\end{equation}</math>.
* after this division, the ratings are added to obtain the value S.
 
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N = 2 (winners)
Original vote, with range [0-4,54]:
A[54] B[0-4] C[20] D[42]
Subsets
A,B: 54/1 + 0-4/2 = 52
A,C: 54/1 + 20/2 = 64
A,D: 54/1 + 42/2 = 75
B,C: 2-4/1 + 0/2 = 2-4
B,D: -4/1 + 02/2 = 4-3
C,D: 40/1 + 2/2 = 51
Converted vote:
A,D[75] A,C[64] A,B[52] C,D[51] B,D[4-3] B,C[2-4]
 
The following example shows how the sums for each subset are obtained, given the converted votes:
 
3 converted votes:
A,D[75] A,C[64] A,B[52] C,D[51] B,D[4-3] B,C[2-4]
A,D[52] A,C[64] A,B[2-4] C,D[7] B,D[4-3] B,C[51]
A,D[64] A,C[75] A,B[51] C,D[52] B,D[2-4] B,C[4-3]
Sums for each subset:
A,D[1811] A,C[1913] A,B[12-1] C,D[1710] B,D[-10] B,C[11-6]
The winner is {A,C}
 
===Name derivation===
 
Proportional Subset Voting (PSV):
 
* "Proportional" (P): describes how the scores S are calculated from the vote (reference to [[Proportional approval voting|PAV]]).
* "Subset" (S): because the initial vote is converted into a cardinal vote in which the options evaluated are the subsets (instead of the individual candidates), on which [[Range Voting]] is then applied.
* "[[Range Voting]]" (V): for each candidate, the sum of the values ​​obtained in the votes is calculated, and the highest one wins.
 
==Subset Voting (category)==
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Considering one vote, a score S is obtained for each subset of N candidates. This procedure is applied to all votes and returns converted votes.
 
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.
 
''The way of calculating S and the [[Single Member system|Single-Winner system]] chosen, determines the variant of Subset Voting.''
 
===Thiele method===
 
Thiele method uses range [0,MAX] and 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 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]]
[[Category:Multi-winner voting methods]]
[[Category:Cardinal voting methods]]
Aldo Tragni
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