Distributed Score Voting: Difference between revisions
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Distributed Score Voting (DSV) is a [[Single Member system|Single-Winner]] and [[Multi-Member System|Multi-Winner]] [[Cardinal voting systems| Cardinal voting system]].
In the [[Single Member system|Single-Winner]] part, it's similar to [[Smith//Score]]. In the [[Multi-Member System|Multi-Winner]] part, [[Distributed Multi-Voting]], the more preferred the winning candidate is in a vote, the more the weight of that vote is decreased in the choice of the next winner.
[[Category:Multi-winner voting methods]]
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==Procedure==
===Voting===
Each voter has 100 points to distribute among the candidates according to his preferences (it's also possible to write the vote even in a simpler form, with range from 0 to 5 points for each candidate).
All candidates in the vote have 0 points by default.
[[File:DSV procedure.jpg|alt=|thumb|DSV counting]]
===Counting the votes===
W =
1) All head-to-head matches are conducted between candidates. In head-to-head, the candidate who has more points in a vote than his opponent receives W points from the vote. The candidate who gets the most points wins the head-to-head.
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2) Find the smallest set X ([[Smith set]]) of nodes that don’t have incoming arrows, coming from outside the set.
3) Convert the votes using the following formula:
M =
v0 = current value of candidate C, to be normalized.
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v1=\frac{v0}{M} \cdot W
\end{equation}</math>
Then remove all candidates not in X from the votes.
4) Add up the points for each candidate of the range votes, and the candidate who has the highest sum, wins.
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5) If you want to have more winners, then remove the single-winner from all original votes, repeating the whole procedure from point 1.
The value W of each original vote
M = highest score among the candidates in the vote (before removing the candidate).
e = candidate's score eliminated.
W0 = previous value of W
W1 = new value of W
<math>
\begin{equation}
W1=\frac{W0}{\left( 1+\frac{e}{M}\right)}
\end{equation}</math>
By repeating this process several times, you can get as many winners as you like, which will be those removed in point 5.
6) If you want to know the % of victory of the winning candidates then, in each original vote, you must remove all the candidates who haven’t won, and normalize
S = sum of the points left in the vote.
v0 = current value of candidate C, to be normalized.
v1 = value of candidate C, after normalization.
<math>
\begin{equation}
v1=\frac{v0}{S} \cdot 100
\end{equation}</math>
The sum of points for each candidate will indicate the % of victory.
===Head-to-head===
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Before the counting process, the votes will be normalized to 100-point votes, where the Xs are considered as equal weight values.
Examples of how a vote can be written by the voter and subsequently,
X,0,0,0,0 → 100,0,0,0,0
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==Criteria==
{| class="wikitable" style="text-align:center"
<!-- criteria headers -->
|- style="font-size:80%;"
! rowspan=1 |
! rowspan=1 style="border-left: 2px solid #a0a0a0;" | [[Majority criterion|Majority]]
! rowspan=1 | [[Majority loser criterion|Maj. loser]]
! rowspan=1 | [[Mutual majority criterion|Mutual maj.]]
! rowspan=1 | [[Condorcet criterion|Condorcet]]
! rowspan=1 | [[Condorcet loser criterion|Cond. loser]]
! rowspan=1 | [[Smith criterion|Smith]]
! rowspan=1 | [[Pareto criterion|Pareto]]
! rowspan=1 | IIA*
! rowspan=1 | [[Independence of irrelevant alternatives|IIA]]
! rowspan=1 | [[w:Independence of clones criterion|Clone proof]]
! rowspan=1 style="border-left:2px solid #a0a0a0;" | [[Monotonicity criterion|Monotone]]
! rowspan=1 | [[Consistency criterion|Consistency]]
! rowspan=1 | [[Participation criterion|Participation]]
! rowspan=1 | [[w:Reversal symmetry|Reversal<br>symmetry]]
! rowspan=1 style="border-left:2px solid #a0a0a0;" | [[Later-no-help criterion|Later-no<br>Help]]
! rowspan=1 | [[Favorite betrayal criterion|Favorite<br>betrayal]]
|- style="font-size:80%;"
<!-- Methods -->
|-
! [[Distributed_Score_Voting|DSV<br>single-winner]]
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #fd8787; font-weight: inherit;" | No
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #fd8787; font-weight: inherit;" | No
! style="background: #fd8787; font-weight: inherit;" | No
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #fd8787; font-weight: inherit;" | No
! style="background: #fd8787; font-weight: inherit;" | No
|}
<b>IIA*</b>: X is a set containing all the preferred candidates over B. If I add C a less appreciated candidate (in head-to-head) than the candidates in X, then all candidates in X continue to be preferred over B.
This method also passes [[ISDA]].
- add one more candidate into the [[Smith set]] isn't a big problem because that additional candidate must then beat all the other candidates in point 4 of the procedure (and if he manages to beat them all it makes sense that he wins).
- removing a candidate from the [[Smith set]] is only possible when that candidate lose all the head-to-head with the candidates contained in the [[Smith set]]. This actually becomes a problem only if the excluded candidate is the one who really should have won.
Below is an example in which, through tactical votes, it's possible to bring out a candidate, who should have won, from the [[Smith set]] (making him lose).
===Tactical votes===
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* the new winner is actually a better candidate than the previous one (the new winner in the example could also be C).
* the voter has a fairly precise knowledge of the likely ballots result, without which this tactical vote would turn against him.
[[Category:Smith-efficient Condorcet methods]]
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