Distributed Voting: Difference between revisions
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[[File:DV Procedure.svg|alt=DV procedure|351px|thumb|DV procedure]]
Distributed Voting (DV) is a [[Single Member system|Single-Winner]] and [[Multi-Member System|Multi-Winner]], [[Cardinal voting systems]] proposed by [[User:Aldo Tragni|Aldo Tragni]].
==Procedure==
Voter score candidates with range [0,9]. The vote is then converted to 100 points (normalization).
# The worst candidate, with the lowest sum of points, is eliminated.
# The points of the eliminated candidate are proportionally redistributed in each vote (normalization).
By repeating processes 1 and 2,
==Extended procedure (single winner)==
It's the procedure indicated above in which:
* the votes are reversed and made negative before counting ''(subtracting 9 from the original ratings)''.
Original vote: A[9] B[7] C[5] D[3] E[1] F[0]
Reversed vote, made negative: A[0] B[-2] C[-4] D[-6] E[-8] F[-9]
''Reversing and making negative means that the voter's 100 points are used to disadvantage the worst from winning (points will be always negative in the counting). This procedure reduces the failure of monotony, for the single-winner case, and increases resistance to min-maxing strategies.''
==Ballot==
===Paper ballot===
Some examples of normalization:
Range [0,
[[File:Digital ballot DV.gif|320px|thumb|DV digital ballot (cumulative 100 points)]]
===Digital ballot===
By using self-resizing sliders it's possible to obtain a simple ballot that use the cumulative vote, with 100 points to distribute. However, it's better to use range [0,9] also in digital ballot.
==Procedure specification==
===Normalization formula===
P = 100 (can also be set to 1).
S = points sum of the candidates remaining in the vote, after an elimination.
V = old points value of candidate X.
newV = new points value of candidate X.
<math>\begin{equation}
newV=\frac{V}{S} \cdot P
\end{equation}</math>
If S=0 then all candidates remain at 0 points.
===Normalization example===
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A[0] B[25] C[75]
A[0] B[100]
===Tie during counting===
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* When the worst is eliminated, the candidates with the lowest score among those left in the vote must be set to 0, and then normalizes.
* [[Surplus Handling]] (in
* If the remaining candidates are contained in a [[Smith set]], then the candidates with the highest sum wins.
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Total difference: 5.3% + 3.2% + 8.3% + 6% = 22.8%
An average error of 5.7% each candidate
===Government===
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Procedure for choosing the prime minister (PM) and the leader of the opposition (LO):
* Parliamentarians elect, through Distributed Voting, the PM. Instead of being normalized to 100 points, the votes in this election are normalized to the weight that each individual parliamentary has (
* Once the PM is elected, only the votes that have assigned 0 points to the PM are taken and used to elect the LO, again through the Distributed Voting. Parliamentarians need to know in advance that giving 0 points to a candidate means being against them (opposites).
* Parliamentarians who gave 0 points to both the PM and the LO, can be considered neutral.
==Other properties==
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Each voter, based on his own interests, creates the following 2 sets of candidates:
* Winner Set = set containing a
* Loser Set = set containing the candidates who aren't part of the Winner Set.
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Satisfy the [[Honesty criterion]] (on hypotheses) only if, in a vote, are removed first all the candidates of the Winner Set or first all those of the Loser Set.
===[[Surplus Handling]]===
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Equality: Distributed Voting ensures that the power of the voters is always equal (100 points distributed) in all the counting steps, including the result.
* cancel the
* increase the complexity of the counting.
* isn't appropriate to manage seats with different weights.
For these reasons, it's better to avoid using Surplus Handling in Distributed Voting System.
===Suitable for Web===
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* Ex.1: a streamer wants to talk about 3 topics in a 4-hour live, chosen by his supporters through a poll. With Distributed Voting the 3 winning arguments A,B,C would also have associated the % of victory: A[50%] B[26%] C[24%]. These % indicate to the streamer that he must devote 2 hours to topic A, and 1 hour to topics B and C. Without these %, the streamer would have mistakenly spent 1 hour and 20 min for each of the topics.
* Ex.2: in an image contest, there is a cash prize to be awarded to the 3 best images. The prize will be divided appropriately according to the % of victory and not in a pre-established way before the contest.
==Systems Variations==
===Distributed Equal-Vote (DEV)===
Voter score candidates with range [-5,+5]. Each ballot is normalized by distributing -100 points between negative ratings, and 100 points between positive ratings (distribution of points uses the normalization of [[Distributed Voting]]).
The candidate with the lowest sum of points is eliminated, and ballots normalized.
By repeating the elimination process, the worst candidate is eliminated each time, and the remaining candidates are the winners.
''Equal-Vote because given a vote, there can always be an opposite one that cancels it.''
==Systems comparison==
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Examples where the 100 points are distributed exponentially:
Using range [0,9] completely eliminates the similarity:
range[0,9] → 100 points
9,1 → 90,10 → it's a bit different from [[IRV]]
9,5,1 → 60,33,7 → it's very different from [[IRV]]
Range [0,9] was chosen to better balance the simplicity of writing, the representation of interests, and the correctness of the count. Normalization applied to a range too small as [0,5], alters the voter's interests too much in the count.
===[[IRNR]]===
[[IRNR]] (L1 norm) is applied also on ranges with negative values such as [-5,+5] but this makes it subject to ambiguity.
Range [0,10] with IRNR
61: A[10] B[6] C[0]
39: A[0] B[6] C[10]
Eliminated in order C,A.
B wins.
Range [-5,+5] with IRNR
61: A[+5] B[+1] C[-5]
39: A[-5] B[+1] C[+5]
Eliminated in order C,B.
A wins.
In IRNR only by moving the range in negative value (leaving the interests of the voters and the size of the range unchanged), the winner changes. Distributed Voting instead avoid this ambiguity by imposing 0 as the minimum value in the range.
IRNR is a [[Single Member system|Single-Winner system]] which also, unlike Distributed Voting, doesn't reverse and make negative the vote before the count.
==Related Systems ==
* [[Instant Runoff Normalized Ratings]] (ratings also negative, and it doesn't reverse and make negative the vote)
* [[Baldwin's method]] (Borda, and variant with different normalization)
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