Distributed Voting
Distributed Voting (DV) is a Single-Winner and Multi-Winner Cumulative voting system.
Procedure
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.
- In each individual vote, the points of the eliminated candidate are removed and the vote is normalized, so that it has 100 points again.
By repeating the process from the beginning, a candidate is eliminate each time.
The remaining candidates are the winners.
Procedure specification
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]
Normalization formula
e := value of the candidate eliminated from a vote.
v0 := old value of candidate X.
v1 := new value of candidate X.
Failed to parse (unknown function "\begin{equation}"): {\displaystyle \begin{equation} v1=\frac{v0}{1-\frac{e}{100}} \end{equation}}
It’s possible to divide by 100 all the points present in the initial votes, and use the following simplified formula throughout the counting process:
Failed to parse (unknown function "\begin{equation}"): {\displaystyle \begin{equation} v1=\frac{v0}{1-e} \end{equation}}
Vote without 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 forms that the vote can take:
- honest form: A[80] B[20]
- tactical form: A[100] B[0]
It's recommended to use the honest form, also because the vote from the beginning may not have candidates with 0 points.
Vote with only 0 points
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:
- The vote is excluded from the count: A[0] B[0].
- The points are divided equally between the remaining candidates with 0 points: A[50] B[50].
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-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
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]
In this case, the worst candidate is both C and D so you have to eliminate them simultaneously. The amount of points to be redistributed will be the sum of the points that had C and D (40 in the example).
Other properties
Tactical vote resistance
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].
- 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.
- 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.
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.
Equality
By "Equality" means "one person, one vote (100 points)".
- 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.
There is no passage in the Distributed Voting where Equality doesn’t met.
Free Riding
Given an honest vote of this type A[50] B[30] C[15] D[5], Free Riding can have the following consequences:
- 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.
Using the Surplus Handling, in addition to increasing the complexity of the counting, 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. The Surplus Handling in the Distributed Voting would also cancel the Equality in some steps of the count. For these reasons it's better to avoid using Surplus Handling in Distributed Voting.
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 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.
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.
Eg: 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.
Eg: 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/votes to distribute.
Vote writing
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.
Before the counting process, the grades will be normalized to 100-point grades, where the Xs are considered as equal weight values.
Examples of how a vote can be written by the voter and subsequently, in the counting, converted into 100 points:
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
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.
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 comparison
IRV
Examples where the 100 points are distributed exponentially:
100 → it's like IRV 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
By distributing points between 3 or more candidates, the Distributed Voting becomes increasingly different from the IRV, because of normalization in the counting.
Cardinal Voting
Given a Cardinal vote like A[10] B[4] C[2] (range [0,10]), candidate A is eliminated, because he is considered to be the worst candidate overall.
- If the vote takes the form B[4] C[2] (leaving the vote unchanged), then a voting system equivalent to the Score Voting is obtained in which the single winner is from the beginning the candidate with the highest sum.
- If the vote takes the form B[10] C[5] or B[8] C[4] or B[6] C[4] or B[2] C[1], then a different voting system will be obtained.
The problem is that all the forms of voting listed respect the relative interests of the voter, but at the same time, they can ultimately return a different single winner. The Cardinal voting systems solves this ambiguity by making an arbitrary choice, not decided by the voters.
The problem described is avoided by Distributed Voting, because by removing a candidate, there is only one and unique way to proportionally redistribute the 100 points of the voter, respecting his relative interests.
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.