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


Voter score candidates with range [0,9]. The vote is then converted to 100 points (normalization).
Each voter has 100 points to distribute among the candidates according to his preferences.


# The point for each candidate are summed and the one with the lowest sum is eliminated.
# The worst candidate, with the lowest sum of points, is eliminated.
# In each individual vote, the points of the eliminated candidate are removed and the vote is normalized, so that it has 100 points again.
# The points of the eliminated candidate are proportionally redistributed in each vote (normalization).


By repeating the process from the beginning, a candidate is eliminate each time.
By repeating processes 1 and 2, the worst candidate is eliminated each time, and the remaining candidates are the winners.


==Extended procedure (single winner)==
The remaining candidates are the winners.


It's the procedure indicated above in which:
==Procedure specification==
* 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]
===Normalization example===
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.''
Given an initial vote of this type, with candidates A,B,C,D,E, are removed in order E,D,C, and 100 points proportionally redistributed each time:


==Ballot==
A[0] B[1] C[3] D[6] E[90]
A[0] B[10] C[30] D[60]
A[0] B[25] C[75]
A[0] B[100]


===Normalization formula===
===Paper ballot===


Some examples of normalization:
e := value of the candidate eliminated from a vote.


Range [0,9] → Normalized in 100 points
v0 := old value of candidate X.
9,0,0,0     →   100,0,0,0
9,9,0,0  →   50,50,0,0
9,6,4,1     →   45,30,20,5 (note: there isn't 0 in the lowest score)


[[File:Digital ballot DV.gif|320px|thumb|DV digital ballot (cumulative 100 points)]]
v1 := new value of candidate X.
===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.
P := 100 (total points used in a vote)


==Procedure specification==
<math>\begin{equation}
v1=\frac{v0}{1-\frac{e}{P}}
\end{equation}</math>


===Normalization formula===
===Vote without 0 points===


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


# A[100] B[0] : set the candidate with the least points to 0.
If S=0 then all candidates remain at 0 points.
# A[80] B[20] : having eliminated C (0 points), there aren't points to redistribute.


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


Given an initial vote of this type, with candidates A,B,C,D,E, are removed in order E,D,C, and 100 points proportionally redistributed each time:
*using procedure 1, a tie is obtained between A and B.
*using procedure 2, B would win.


A[0] B[1] C[3] D[6] E[90]
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 honest interests even in the counting.
A[0] B[10] C[30] D[60]

A[0] B[25] C[75]
===Vote with only 0 points===
A[0] B[100]

If the only candidate C with points is eliminated from a vote like this A[0] B[0] C[100], you can proceed in 2 ways:

# A[0] B[0] : the vote is excluded from the count.
# A[50] B[50] : the points are divided equally between the remaining candidates with 0 points.

Using procedure 2 you get a vote that:

* cannot affect the victory of candidates who received the same points.
* reduces the distance between the candidates present in it, and this can affect a possible process of assigning seats.
* it can be considered not in accordance with the interests of the voter who, to those remaining candidates, had not awarded points.

The two procedures return the same winners, but in the [[Multi-Member System|multi-winner]] case the winners can have different % of victory; in this case it's better to use procedure 1 for the reasons indicated above.


===Tie during counting===
===Tie during counting===
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The tie can be managed in various ways:
The tie can be managed in various ways:


*delete C first, obtaining a result. Delete D first, getting another result. Check that the two results return the same winners.
*delete C first, getting a result. Delete D first, getting another result. Check that the two results return the same winners.
*delete C and D at the same time.
*delete C and D at the same time.
*randomly delete C or D.
*randomly delete C or D.
Line 84: Line 78:


===Procedure variant (discouraged)===
===Procedure variant (discouraged)===

One or more of the following steps are used:


* 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.
* 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 Distributed Voting it's not used for [[Multi-Member System|multi-winner]] context).
* If the remaining candidates are contained in a [[Smith set]], then the candidates with the highest sum wins.


==Seats allocation==
* Surplus Handling is used in the case of [[Multi-Member System|Multi-Winner]].


The Distributed Voting indicates the method for obtaining single or multiple winners. The Distributed Voting System also describes how seats should be handled.
==Other properties==


===Parliament===
===Tactical vote resistance===


Procedure for electing parliamentarians:
In the Distributed Voting, given an honest vote with this distribution of points [50 30 15 5 0], a tactical vote generally takes the following form [90 6 3 1 0].


* The state is divided into districts (at least 2, and possibly of similar size).
* If the first candidate to be eliminated were the first (the one with the most points), the two votes would both become like this [60 30 10 0], so the tactical vote would disappear.
* Each district must have at least 2 seats (at least 3, for a good representation). To satisfy this constraint you can increase the number of total seats or join the districts into groups.
* In each district, the DV is used to obtain a number of winners equal to the number of seats in the district. The sum of the points for each winning candidate will indicate the % of victory of the candidates.
* If P is the power assigned to the district, then the weight of each seat will be: P • "% of victory of the candidate".


Example - 2 districts, 6 seats
* If instead the second and third candidates were eliminated, the two votes would become [91 9 0] (honest) and [99 1 0] (tactical). They are different but they are very similar, comparing them to their initial state.
Districts: d1{70%} d2{30%}
Seats: d1{3} d2{3}
Result: d1{ A1[40%] B1[35%] C1[25%] } d2{ B2[40%] C2[35%] D2[25%] }
Seat weights: d1{ A1[0.28] B1[0.245] C1[0.175] } d2{ B2[0.12] C2[0.105] D2[0.075] }
Total power: A[28%] B[36.5%] C[25%] D[6%]


If I had unit seats:
In the Distributed Vote it's valid that, during the counting, the more points are redistributed after the elimination of the worst candidate, the more the votes become honest.
Seats: d1{4} d2{2}
Result: d1{ A1[2] B1[1] C1[1] } d2{ B2[1] C2[1] }
Total power: A[33.3%] B[33.3%] C[33.3%] D[0]


Total difference: 5.3% + 3.2% + 8.3% + 6% = 22.8%
===Equality===
An average error of 5.7% each candidate.


===Government===
By "Equality" means "equal power (100 points) to each person".


Procedure for choosing the prime minister (PM) and the leader of the opposition (LO):
* In the Distributed Voting the voters at the beginning all have 100 points to distribute according to their preferences, therefore Equality is satisfied.
* During all the counting steps, through the use of normalization, it ensures that all voters continue to have 100 points each, always distributed according to their interests, therefore Equality is satisfied.
* The result is one of the counting steps, in which Equality continues to be satisfied.


* 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).
There is no passage in the Distributed Voting where Equality doesn’t met.
* 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.


===[[Free Riding]]===
==Other properties==


===Tactical vote resistance===
Given an honest vote of this type A[50] B[30] C[15] D[5], [[Free Riding]] can have the following consequences:


'''Hypotheses'''
#increase the points given to the most preferred candidates who probably lose. The vote becomes similar to A[90] B[6] C[3] D[1].
#decrease the points given to candidates who probably win. The vote, with a decreasing probability of candidates' victory from left to right, becomes similar to A[25] B[25] C[35] D[15].
#the candidates' chances of winning aren't known enough. In this case, [[Free Riding]] doesn't occur and the voter tends to vote honestly.


Each voter, based on his own interests, creates the following 2 sets of candidates:
Using the [[Surplus Handling]]:


* Winner Set = set containing a number of favorite candidates equal to or less than the number of winners.
* reduces the tactic number 2 and greatly increases the tactic number 1, to the point that this would be used even when the voters don't know enough the chances of victory of the candidates.
* Loser Set = set containing the candidates who aren't part of the Winner Set.
* cancel the [[Distributed Voting#Equality|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.


Given an honest vote, the tactical vote is obtained by minimizing the points of the Loser Set, maximizing the points of the Winner Set, and maintaining the proportions of honest interests within the two sets.
For these reasons it's better to avoid using Surplus Handling in Distributed Voting.


Example
===[[Independence of Worst Alternatives|IWA]] example===
Candidates: [A B C D E]
Honest vote: [50 30 15 5 0]
Tactical vote (1 winner): [90 6 3 1 0]
Tactical vote (2 winners): [60 36 3 1 0]


'''Single winner'''
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]


Meets the [[Honesty criterion]] (on hypotheses) because:
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.


* at each [[Honesty criterion|Update Steps]] of the count, in which a candidate with points is removed, the tactical vote decreases the deviation from the honest one (the deviation is the sum of the absolute differences of the points for each candidate, between tactical and honest vote).
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.
* the [[Honesty criterion|Honesty Step]] occurs when the candidate in the Winner Set is removed or when all the candidates in the Loser Set are removed. In the best case, the [[Honesty criterion|Honesty Step]] can occur in the first [[Honesty criterion|Update Steps]].
* the [[Honesty criterion|Honesty Step]] is always present because in the single winner, during the counting, all candidates are always removed from at least one of the two Sets.


Example - 1 winner
===Suitable for Web===
Honest vote: [50 30 15 5 0]
Tactical vote: [90 6 3 1 0]
A is removed and the tactical vote becomes equal to the honest one, that is:
Vote: [60 30 10 0]


'''Multiple winner'''
If the seats had different fractional value, in addition to determining the winning candidates, Distributed Voting also determine their % of victory, which are already indicated by the sum of the points of the winning candidates, remaining at the end of the counting.


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.
Eg 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.


===[[Surplus Handling]]===
Eg 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.


Equality: Distributed Voting ensures that the power of the voters is always equal (100 points distributed) in all the counting steps, including the result.
Eg 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.


The [[Surplus Handling]]:
===Vote writing===


* cancel the Equality in some steps of the count.
To make the writing of the vote more comprehensible and simple, the voter can be left with almost complete freedom in the use of numerical values or only X.
* 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.
Before the counting process, the grades will be normalized to 100-point grades, where the Xs are considered as equal weight values.


===Suitable for Web===
Examples of how a vote can be written by the voter and subsequently, in the counting, converted into 100 points:


If the seats had different fractional value, in addition to determining the winning candidates, Distributed Voting also determine their % of victory, which are already indicated by the sum of the points of the winning candidates, remaining at the end of the counting.
X,0,0,0,0     →   100,0,0,0,0
X,X,X,X,0     →   25,25,25,25,0
4,3,2,1,0     →   40,30,20,10,0
40,6,3,1,0    →   80,12,6,2,0
101,0,0,0,0   →   100,0,0,0,0
999,99,9,1    →   89.17, 8.83, 1, 1


* 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.
The complexity in writing the vote adapts to the voter, and it’s also noted that, if 101 or 99 points are mistakenly distributed, the vote will still be valid.


* 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.
In the last example they are set to 1, the decimal values which should be less than 1, and the remaining points are divided proportionally among the other candidates (it serves to prevent Distributed Voting from becoming like [[IRV]]).

==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==
==Systems comparison==
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Examples where the 100 points are distributed exponentially:
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]]
70,24,5,1 → it's different from [[IRV]]
60,27,9,3,1 → it's very different from [[IRV]]

60,27,9,3,1 → it's very different from [[IRV]]
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 ==
By distributing points between 3 or more candidates, the Distributed Voting becomes increasingly different from the [[IRV]], because of normalization in the counting.
* [[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)


==Forum Debate==
==Forum Debate==

Latest revision as of 17:53, 30 March 2021

DV procedure
DV procedure

Distributed Voting (DV) is a Single-Winner and Multi-Winner, Cardinal voting systems proposed by Aldo Tragni.

Procedure

Voter score candidates with range [0,9]. The vote is then converted to 100 points (normalization).

  1. The worst candidate, with the lowest sum of points, is eliminated.
  2. The points of the eliminated candidate are proportionally redistributed in each vote (normalization).

By repeating processes 1 and 2, the worst candidate is eliminated each time, and the remaining candidates are the winners.

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 [0,9]  →   Normalized in 100 points
9,0,0,0      →   100,0,0,0
9,9,0,0      →   50,50,0,0
9,6,4,1      →   45,30,20,5    (note: there isn't 0 in the lowest score)
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.

Failed to parse (unknown function "\begin{equation}"): {\displaystyle \begin{equation}   newV=\frac{V}{S} \cdot P   \end{equation}}

If S=0 then all candidates remain at 0 points.

Normalization example

Given an initial vote of this type, with candidates A,B,C,D,E, are removed in order E,D,C, and 100 points proportionally redistributed each time: 

 A[0] B[1]  C[3]  D[6] E[90]
 A[0] B[10] C[30] D[60]
 A[0] B[25] C[75]
 A[0] B[100]

Tie during counting

Cases of parity can occur during counting, as in the following example: 

 Vote 1:       A[55]  B[25] C[10] D[10]
 Vote 2:       A[50]  B[30] C[10] D[10]
 Sum of votes: A[105] B[55] C[20] D[20]

The tie can be managed in various ways:

  • delete C first, getting a result. Delete D first, getting another result. Check that the two results return the same winners.
  • delete C and D at the same time.
  • randomly delete C or D.

This situation is extremely rare, and even when it occurs it's further rare that the order in which the candidates in the tie are eliminated affects the result. Random deletion is the easiest to use.

Procedure variant (discouraged)

One or more of the following steps are used:

  • 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 Distributed Voting it's not used for multi-winner context).
  • If the remaining candidates are contained in a Smith set, then the candidates with the highest sum wins.

Seats allocation

The Distributed Voting indicates the method for obtaining single or multiple winners. The Distributed Voting System also describes how seats should be handled.

Parliament

Procedure for electing parliamentarians:

  • The state is divided into districts (at least 2, and possibly of similar size).
  • Each district must have at least 2 seats (at least 3, for a good representation). To satisfy this constraint you can increase the number of total seats or join the districts into groups.
  • In each district, the DV is used to obtain a number of winners equal to the number of seats in the district. The sum of the points for each winning candidate will indicate the % of victory of the candidates.
  • If P is the power assigned to the district, then the weight of each seat will be: P • "% of victory of the candidate".
Example - 2 districts, 6 seats
Districts: d1{70%} d2{30%}
Seats:     d1{3}   d2{3}
Result:       d1{ A1[40%]  B1[35%]   C1[25%] }    d2{ B2[40%]  C2[35%]   D2[25%] }
Seat weights: d1{ A1[0.28] B1[0.245] C1[0.175] }  d2{ B2[0.12] C2[0.105] D2[0.075] }
Total power:  A[28%] B[36.5%] C[25%] D[6%]

If I had unit seats:
Seats:  d1{4} d2{2}
Result: d1{ A1[2] B1[1] C1[1] } d2{ B2[1] C2[1] }
Total power: A[33.3%] B[33.3%] C[33.3%] D[0]

Total difference: 5.3% + 3.2% + 8.3% + 6% = 22.8%
An average error of 5.7% each candidate.

Government

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 (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.

Other properties

Tactical vote resistance

Hypotheses

Each voter, based on his own interests, creates the following 2 sets of candidates:

  • Winner Set = set containing a number of favorite candidates equal to or less than the number of winners.
  • Loser Set = set containing the candidates who aren't part of the Winner Set.

Given an honest vote, the tactical vote is obtained by minimizing the points of the Loser Set, maximizing the points of the Winner Set, and maintaining the proportions of honest interests within the two sets. 

 Example
 Candidates:                [A  B  C  D E]
 Honest vote:               [50 30 15 5 0]
 Tactical vote (1 winner):  [90 6  3  1 0]
 Tactical vote (2 winners): [60 36 3  1 0]

Single winner

Meets the Honesty criterion (on hypotheses) because:

  • at each Update Steps of the count, in which a candidate with points is removed, the tactical vote decreases the deviation from the honest one (the deviation is the sum of the absolute differences of the points for each candidate, between tactical and honest vote).
  • the Honesty Step occurs when the candidate in the Winner Set is removed or when all the candidates in the Loser Set are removed. In the best case, the Honesty Step can occur in the first Update Steps.
  • the Honesty Step is always present because in the single winner, during the counting, all candidates are always removed from at least one of the two Sets.
 Example - 1 winner
 Honest vote:   [50 30 15 5  0]
 Tactical vote: [90 6  3  1  0]
   A is removed and the tactical vote becomes equal to the honest one, that is:
 Vote:             [60 30 10 0]

Multiple winner

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

Equality: Distributed Voting ensures that the power of the voters is always equal (100 points distributed) in all the counting steps, including the result.

The Surplus Handling:

  • cancel the Equality in some steps of the count.
  • 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

If the seats had different fractional value, in addition to determining the winning candidates, Distributed Voting also determine their % of victory, which are already indicated by the sum of the points of the winning candidates, remaining at the end of the counting.

  • 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

IRV

Examples where the 100 points are distributed exponentially: 

99,1        → it's like 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

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-Winner system which also, unlike Distributed Voting, doesn't reverse and make negative the vote before the count.


Related Systems

Forum Debate

  • "Distributed Voting (DV) vs Range Voting (RV)". The Center for Election Science. 2020-05-12. Retrieved 2020-05-15.
  • "Sequential Elimination systems". The Center for Election Science. 2020-01-27. Retrieved 2020-02-19.
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