Distributed Voting: Difference between revisions

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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]].

This system is a specific type of [[Instant Runoff Normalized Ratings]] (L1 norm), which also deals with the [[Multi-Member System|Multi-Winner System]] and which doesn't accept the case of negative ratings.

==Procedure==

[[File:DV Procedure.svg|alt=DV procedure|350px|thumb|DV procedure]]

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[[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])]]

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[[File:Digital ballot DV.gif|320px|thumb|DV digital ballot (cumulative 100 points)]]

Voter ~~has 100 points to distribute among the~~ candidates (range [0,10] ~~can~~ ~~also~~ be ~~used~~).

Voter score candidates with range [0,10]. The vote is then converted to 100 points (normalization).

# The worst candidate, with the lowest sum of points, is eliminated.

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==Ballot==

===Digital ballot===

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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:

In the paper ballot is used the ranges, that are easier to understand for a voter. Ballots using ranges will be normalized to 100-point votes, and then apply the Distributed Voting procedure. 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)

===~~Real~~ ballot===

===Digital ballot===

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By using self-resizing sliders it's possible to obtain simple ballot that use the cumulative vote, with 100 points to distribute. However, it's better to use range [0,10] also in digital ballot.

The way to vote in Distribute Voting is, in theory, to assign 1 point to the least preferred candidate, and then assign points to the other candidates proportionally to the appreciation towards the less preferred candidate. Non-preferred (or unknown) candidates will remain with 0 points.

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==Procedure specification==

A vote like this: A[1] B[2] C[4] D[0] means that voter likes B 2 times A, and likes C 4 times A (or 2 times B). Vote like this: A[1] B[0] C[0] D[0] means that the voter likes only A. Both votes are then normalized to 100 points so that they have the same power.

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===Normalization formula===

This way of voting has no restrictions on the rating, therefore it offers the best representation of interests, but it's the most complex to understand and subject to tactical votes (in which certain candidates are awarded more points than necessary). To avoid such complexity and tactical votes, it's best to use range [0,10], by accepting a reduction in interest representation.

P = 100 (can also be set to 1).

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==Procedure specification==

S = points sum of the candidates remaining in the vote.

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V = old value of candidate X.

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newV = new value of candidate X.

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<math>\begin{equation}

newV=\frac{V}{S} \cdot P

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\end{equation}</math>

===Normalization example===

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A[0] B[25] C[75]

A[0] B[100]

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===Normalization formula===

e = value of the candidate eliminated from a vote.

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v0 = old value of candidate X.

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v1 = new value of candidate X.

P = 100 (total points used in a normalized vote)

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<math>\begin{equation}

v1=\frac{v0}{1-\frac{e}{P}}

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\end{equation}</math>

===No 0 points===

If the only candidate C with 0 points is eliminated from a vote like this A[80] B[20] C[0], there are 2 procedures you can use:

# A[100] B[0] : set the candidate with the least points to 0.

# A[80] B[20] : having eliminated C (0 points), there aren't points to redistribute.

Eg. given the following 2 votes to count: V1-A[55] B[45] C[0] and V2-A[0] B[100] C[0] then:

*using procedure 1, a tie is obtained between A and B.

*using procedure 2, B would win.

V1 likes A and B almost in the same way, so the victory of B would make both V1 and V2 happy. For this reason it's recommended to use procedure 2, which keeps the voter's initial interests even in the counting.

===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 ~~the standard~~ Distributed Voting it's not used~~, also~~ in [[Multi-Member System|multi-winner]]).

* [[Surplus Handling]] (in Distributed Voting it's not used in the [[Multi-Member System|multi-winner]] context).

* 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~~. The more seats and districts increase, the more the error can increase~~.

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 (~~which~~ ~~isn't~~ ~~the~~ ~~same~~ ~~for~~ ~~everyone~~).

* 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 (P = weight, in the normalization formula).

* 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.

* 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.

===[[Independence of Worst Alternatives|IWA]] example===

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~~]

Head-to-head: A beats C beats B beats A. Distributed Voting in the first step eliminates candidate B, considered the worst, and between A and C, wins A.

Distributed Voting satisfies the [[Independence of Worst Alternatives|IWA]], so if candidate B (the worst) is added to the AvsC context (with A winner), it makes sense that A continues to be the winner.

===[[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.

~~Using the~~ [[Surplus Handling]]:

The [[Surplus Handling]]:

* cancel the ~~[[Distributed Voting#~~Equality~~|Equality]]~~ in some steps of the count.

* cancel the Equality in some steps of the count.

* 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 ~~power~~.

* 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 satisfaction (he's already 99% satisfied with the victory of A).

* isn't appropriate to manage seats with different weights.

For these reasons it's better to avoid using Surplus Handling in Distributed Voting.

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.

* 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:

~~100~~ → it's like [[IRV]]

99,1 → it's like [[IRV]]

99,1 → it's ~~like~~ [[IRV]]

90,9,1 → it's a bit different from [[IRV]]

90,9,1 → it's a ~~bit~~ different from [[IRV]]

70,24,5,1 → it's different from [[IRV]]

60,27,9,3,1 → it's very different from [[IRV]]

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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]]

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10,5,1 → 63,31,6 → it's very 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

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61: A[10] B[6] C[0]

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39: A[0] B[6] C[10]

Eliminated in order C,A.

B wins.

IRNR and Distributed Voting are equivalent in this case.

Range [-5,+5] with IRNR

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61: A[+5] B[+1] C[-5]

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39: A[-5] B[+1] C[+5]

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.

By distributing points between 3 or more candidates, the Distributed Voting becomes increasingly different from the [[IRV]], because of normalization in the counting.

==Related Systems ==