Distributed Voting

Distributed Voting (DV) is a Single-Winner and Multi-Winner Cumulative voting system.

Procedure

DV procedure

Voting

Each voter has 100 points to distribute among the candidates according to his preferences.

All candidates in the vote have 0 points by default.

Counting the votes

1. The point for each candidate are summed and the one with the lowest sum is eliminated.
2. 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. The sum of the points of the remaining candidates indicates the % of victory.

Procedure specification

Example normalization of a single vote

Given an initial vote of this type, with candidates A,B,C,D,E:

A[0] B[1] C[3] D[6] E[90] : E is removed

A[0] B[10] C[30] D[60] : D is removed

A[0] B[25] C[75] : C is removed

A[0] B[100]

Normalization of the vote

e := value of the candidate eliminated from the 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}}

In an electronic system 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}}

During counting, points can be represented in decimal form.

Managing votes 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:

1. honest form: A[80] B[20]
2. 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.

Managing votes with 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:

1. The vote is excluded from the count: A[0] B[0].
2. 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.

Managing tie during the count

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

Simplified voting 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 DV from becoming like IRV).

About Equal Vote

By "equal vote" or "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.

Forum Debate

• "Sequential Elimination systems". The Center for Election Science. 2020-01-27. Retrieved 2020-02-19.
• "Best single-winner Voting System (in full honest context)". The Center for Election Science. 2020-01-29. Retrieved 2020-02-19.
• "Distributed Voting (DV) vs Range Voting (RV)". The Center for Election Science. 2020-05-12. Retrieved 2020-05-15.