Distributed Voting: Difference between revisions
Added section about IRNR
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Distributed Voting (DV) is a [[Single Member system|Single-Winner]] and [[Multi-Member System|Multi-Winner]], [[Cardinal voting systems]].
This system, in the [[Single Member system|Single-Winner]] context, avoids the ambiguity of the [[IRNR]] (L1 norm). More information in the dedicated [[Distributed Voting#IRNR|section]].
==Procedure==
[[File:DV Procedure.svg|alt=DV procedure|350px|thumb|DV procedure]]
[[File:Digital ballot DV.gif|320px|thumb|DV digital ballot (cumulative 100 points)]]▼
[[File:DV paper ballot.svg|320px|thumb|DV paper ballot (range [0,10])]]
▲[[File:Digital ballot DV.gif|320px|thumb|DV digital ballot (cumulative 100 points)]]
Voter
# The worst candidate, with the lowest sum of points, is eliminated.
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==Ballot==
By using self-resizing sliders it's possible to obtain simple ballot that use the cumulative vote, with 100 points to distribute. However, the ranges [0,10] can also be used for digital ballot, as described below.▼
===Paper ballot===
Some examples of normalization:
Range [0,10] → Normalized in 100 points
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10,6,3,1 → 50,30,15,5 (note: there isn't 0 in the lowest score)
===
▲By using self-resizing sliders it's possible to obtain simple ballot that use the cumulative vote, with 100 points to distribute. However,
==Procedure specification==▼
===Normalization formula===▼
P = 100 (can also be set to 1).
▲==Procedure specification==
S = points sum of the candidates remaining in the vote.
<math>\begin{equation}▼
newV=\frac{V}{S} \cdot P
===Normalization example===
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A[0] B[25] C[75]
A[0] B[100]
▲===Normalization formula===
▲ v0 = old value of candidate X.
▲ v1 = new value of candidate X.
▲ <math>\begin{equation}
▲ \end{equation}</math>
===All 0 points===
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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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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.
35 A[0] B[1] C[99]▼
33 A[99] B[0] C[1]▼
32 A[1] B[99] C[0]▼
Sum A[3299] B[3203] C[3498]▼
===[[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.
* if a voter votes A[99] B[1] C[0], in case A wins by getting double the threshold, the voter would be very satisfied with A's victory, then move half the points from A to B would mean giving the voter extra unjustified
* 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: on a crowdfunding platform, fans can have a different weight in the vote, based on how much money they have donated. In Distributed Voting you can manage directly this difference in power by assigning fans different amounts of points to distribute, through the cumulative vote.
* Ex.3: 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.
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Examples where the 100 points are distributed exponentially:
60,27,9,3,1 → it's very different from [[IRV]]▼
Using range [0,10] completely eliminates the similarity:
range[0,10] → 100 points
10,1 → 91,9 → it's a bit different from [[IRV]]
Range [0,10] 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 on rating ballots, also on ranges with negative values such as [-5,+5]. Distributed Voting, in the [[Single Member system|Single-Winner]] context, is a subcategory of IRNR, which binds the minimum value of the rating ballots to 0 (doesn't accept ratings with negative values). This constraint is important because it avoids the ambiguity of the IRNR:
Range [0,10] with IRNR and Distributed Voting
Eliminated in order C,A.
B wins.
IRNR and Distributed Voting are equivalent in this case.
Range [-5,+5] with IRNR
Eliminated in order C,B.
A wins.
In IRNR only by changing the range, 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 rating.
==Related Systems ==
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