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==
[[File:DVS counting.jpg|alt=|thumb|DSV counting]]▼
===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.
===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:
Then remove all candidates not in X from the votes.▼
M = highest score among the candidates in the vote, before normalization.
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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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The value W of each original vote changes according to the following formula:
M = highest score among the candidates in the vote (before removing the candidate).
e = candidate's score eliminated.
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<math>
\begin{equation}
W1=\frac{W0
\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.
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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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! 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]]
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|-
! [[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
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! 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: #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]].
All the criteria not met are linked to the fact that, through tactical votes, it's possible add / remove a candidate from the [[Smith set]].
- 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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