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).
- 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.
- 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.
- Convert the marks 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}}
- 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.
- 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, I can get as many winners as I like, which will be those removed in point 5.
- 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.