Distributed Multi-Voting: Difference between revisions
m
no edit summary
Aldo Tragni (talk | contribs) No edit summary |
Aldo Tragni (talk | contribs) mNo edit summary |
||
| (7 intermediate revisions by 2 users not shown) | |||
Line 6:
[[File:DMV procedure.jpg|thumb|DMV procedure]]
Each voter has 100 points to distribute among the candidates according to his preferences. All candidates in the vote have 0 points by default.
# For each single vote, get the normalized votes on all subsets
# After obtaining all the converted original votes, the candidate with the lowest sum, of the converted votes, loses.
# Eliminate the loser from all the original votes, and setting the candidate with the lowest score in each vote to 0. Repeat the whole process from the beginning, leaving as many winner as you like.
Line 15:
* set the candidate (s) with the lowest score between A,B,C to 0.
* apply the following formula on the other candidates:
S = sum of
v0 = value of candidate X, before normalization
v1 = value of candidate X, after normalization.
<math>\begin{equation}
In normalization for the % of victory, use the same formula without setting the candidate with the lowest score to 0.
Line 26:
If the candidates of the subset, in a certain vote, all have the same score different from 0 then, before normalization, don’t set the lowest score to 0.
==Tactical vote resistance==
The original vote of the voter through point 1 of the procedure is converted, and the vote obtained is in part of the type:
* ranking (Borda), because the points tend to be distributed linearly in the converted vote (see all cases).
* range (Score), because by distributing the points in quite different quantities, the candidates tend to keep their score in the converted vote (see A,B,C in cases [1], [2], [3], [5] ).
* cumulative, because the points distributed in the converted votes are however limited and fixed (700 in the case [1], 1000 in the cases [2] and [4], 1100 in the cases [3], [5], [6] based the number of candidates evaluated).
Meets [[Honesty criterion]] under the same assumptions as the [[Distributed Voting#Tactical vote resistance|Distributed Voting]].
Under the same assumptions as the [[Distributed Voting#Tactical vote resistance|DV]], this system also tries to satisfy the [[Honesty criterion|Perfect Honesty criterion]], by applying a conversion of the vote which serves to drastically reduce the deviation from the honest one.
Example
Candidates: [A B C D E]
Honest vote: [50 30 15 5 0]
Tactical vote: [90 6 3 1 0]
Honest converted vote: [1118 820 486 176 0]
Tactical coverted vote: [1434 622 390 153 0]
Error in %: [22% 24% 20% 13% 0] Avg error = 20%
633 out of 2600 is around 25%.
On average about 80% of the score, expressed in the tactical vote, is honest at the start of the counting, even if the voter used a tactical vote. A good representation of interests is also provided.
'''Other properties'''
In cases [1] and [2] it’s noted that the addition of 1 point on B, left the score of A practically unchanged in the converted vote, but in case [2] it obtained 303 points for B (same speech observing the case [3] or even [5] ); this means that the voter has an interest in expressing his preference towards B. At the same time, the voter doesn’t even have the interest of giving his limited points to candidates he doesn’t really support (reduced [[Vote splitting]]) .
==Systems variants (Multi-Voting method)==
In general, starting from a vote, all the votes are obtained for each subset of the candidates (some normalization is used), and then they are added together obtaining the converted vote. Subsequently, the count on the converted votes is applied.
===Score Multi-Voting (SMV)===
The following formula is used to normalize the votes:
[MIN, MAX] = ''[0,9]'' = range of the voting system.
[min, max] = ''[3,6]'' = lower and higher value among the candidates of the subset, in a vote.
Cnew = new value of the candidate, in a vote.
C = old value of the candidate, in a vote.
<math>\begin{equation}
C_{new} \ =\ MIN\ +\ ( C\ -\ min) \cdot \frac{MAX\ -\ MIN}{max\ -\ min}
\end{equation}</math>
If max = min, then Cnew = MAX
Example of normalized voting for a subset of candidates:
Original vote: A[9] B[6] C[5] D[3] F[0] G[1] H[1]
Subset {A,C,F}: A[9] C[5] F[0]
Subset {A,B,C}: A[9] B[2.25] C[0]
Subset {C,D,F}: C[9] D[5.4] F[0]
Subset {B,C,D}: B[9] C[6] D[0]
Subset {B,C,D,F}: B[9] C[7.5] D[4.5] F[0]
Subset {G,H}: G[9] H[9]
Subset...
By adding the converted votes, the candidate with the highest sum wins.
===STAR Multi-Voting (STAR-MV)===
The converted votes are calculated, as in the Score Multi-Voting, on which the STAR count is then applied.
[[Category:Cardinal voting methods]]
[[Category:Single-winner voting methods]]
[[Category:Multi-winner voting methods]]
| |||