# Distributed Voting

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

DV promotes the Vote unitarity and the reduction of the deviation that the vote has from the true interests of a voter.

## 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.

1. The point for each candidate are summed.
2. The candidate with the lowest sum is eliminated.
3. In each individual vote, the points of the eliminated candidate are removed and the vote is normalized, so that it has 100 points again.

This process can be carried out several times, and ends when the remaining candidates are the number of winners requested by the election.

### Normalization of the vote

e := value of the candidate eliminated from the vote.

X := candidate, still present in the vote, whose new amount of points is to be calculated.

v0 := old value of candidate X.

v1 := new value of candidate X.

${\displaystyle $$v1=\frac{v0\cdot 100}{100-e}$$}$

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 in counting:

${\displaystyle $$v1=\frac{v0}{1-e}$$}$

During counting, points can be represented in decimal form.

### Example normalization of a 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 eliminated:

A[0], B[10], C[30], D[60]

D is eliminated:

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

C is eliminated:

A[0], B[100]

### Managing votes with 0 points

If the only candidate (C) with points is eliminated from a vote (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.

For the reasons indicated above, it’s strongly discouraged to use procedure 2.

Procedure 2 can be considered a variant used only to ensure total Vote unitarity.

### 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 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

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.