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

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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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:

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.

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:

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.

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

Resistance to tactical votes

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.

Fractional seats - Suitable for Web

If the seats had fractional value (instead of unitary), in addition to determining the winning candidates, the voting method should also determine the % of victory of the winning candidates. In the Distributed Voting the % of victory 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 to distribute.

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 Distributed Voting from becoming like IRV).

About 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.

About 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.

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.