Distributed Score Voting
Distributed Score Voting (DSV) is a Single-Winner and Multi-Winner Cardinal voting system.
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
W = sum of all the points in the original vote (100 for all voters, at the beginning).
1) All head-to-head matches are conducted between candidates. In head-to-head, the candidate who has more points in a vote than his opponent receives W points from the vote. The candidate who gets the most points wins the head-to-head.
Graphically, each candidate is a node; the head-to-head is represented by an arrow, leaving the winning candidate, entering the losing candidate. The tie is represented as a double arrow entering, that is both candidates are considered losers.
2) Find the smallest set X of nodes that don’t have incoming arrows, coming from outside the set.
Then remove all candidates not in X from the votes.
3) Convert the votes into a range form, assigning 0 points to the candidates with the lowest score and normalizing* the remaining candidates, using the following formula:
M = candidate with the highest score, before normalization.
v0 = current value of candidate C, to be normalized.
v1 = value of candidate C, after normalization.
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}{M} \cdot W \end{equation}}
4) Add up the points for each candidate of the range votes, and the candidate who has the highest sum, wins.
The choice of the single winner ends here.
5) If you want to have more winners, then remove the single-winner from all original votes, repeating the whole procedure from point 1.
The value W of each original vote is reduced by the points assigned to the removed candidate.
By repeating this process several times, you can get as many winners as you like, which will be those removed in point 5.
6) If you want to know the % of victory of the winning candidates then, in each original vote, you must remove all the candidates who haven’t won, and normalize* the vote with the formula used in point 3 (with W=100 fixed). The sum of points for each candidate will indicate the % of victory.
Head-to-head
In a head-to-head between candidates A and B, a vote like A[10], B[30], C[60], D[0] could be treated in 2 different forms:
1) A[25], B[75] or A[33] B[100]
This form is subject to some problems:
- in a context with only one winner and two candidates, the voter is unlikely to want to distribute his points in that way.
- greatly increase the tactical vote in which voters accumulate points on their preferred candidate.
- prevent the DSV to meet the following criteria: majority criterion, majority loser criterion, mutual majority criterion.
2) A[0], B[100] that is, 0 to the minor and maximum to the major
This form avoids all the problems mentioned above.
Simplified 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
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.