Distributed Multi-Voting

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

This voting method consists of evaluating all possible elections (subset of candidates) to find out which candidate loses the most and then eliminate him, and repeat the process.

Procedure

DMV procedure

Each voter has 100 points to distribute among the candidates according to his preferences. All candidates in the vote have 0 points by default.

For each single vote, get the normalized votes on all subsets conteining at least 2 candidates. Add up the points for each candidate of the normalized votes, obtaining the converted original vote.
After obtaining all the converted original votes, the candidate with the lowest sum, of the converted votes, loses.
Eliminate the loser from all the original votes. Repeat the whole process from the beginning, leaving as many winner as you like.

% of victory: got the winners, eliminate the losers from all the original votes and normalize. The % of victory are obtained from the sum of the points for each candidate.

Normalization

Given a vote like this: A[60], B[30], C[10], D[0] to normalize it to the subset of candidates A,B,C you have to:

set the candidate (s) with the lowest score between A,B,C to 0.
apply the following formula on the other candidates:

S = sum of the points of the candidates.
v0 = value of candidate X, before normalization
v1 = value of candidate X, after normalization.
v1 = (v0/S)*100

In normalization for the % of victory, use the same formula without setting the candidate with the lowest score to 0.

If the candidates of the subset, in a certain vote, all have the same score different from 0 then, before normalization, don’t set the lowest score to 0.