# 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; by repeating the procedure several times, 1 or more winners (candidates left) are obtained.

## 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.

1. For each single vote, get the normalized votes on all subsets containing at least 2 candidates. Add up the points for each candidate of the normalized votes, obtaining the converted original vote.
2. After obtaining all the converted original votes, the candidate with the lowest sum, of the converted votes, loses.
3. Eliminate the loser from all the original votes, and setting the candidate with the lowest score in each vote to 0. 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,B,C,D 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 points of the candidates in the subset.
v0 = value of candidate X, before normalization
v1 = value of candidate X, after normalization.
$\begin{equation} v1=\frac{v0}{S} \cdot 100 \end{equation}$ 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.

## Criteria

Majority Maj. loser Mutual maj. Condorcet Cond. loser Smith IIA Clone proof Monotone Consistency Participation Later-no
Help
Later-no
Harm
Favorite
betrayal
DMV No* No* No* No* No* No* No* No* No* No* No* No* No* No*
A B C D
 original vote 100 0 0 0
converted vote 700 0 0 0
 original vote 99 1 0 0
converted vote 697 303 0 0
 original vote 96 4 1 0
converted vote 686 292 122 0
 original vote 51 49 0 0
converted vote 553 447 0 0
 original vote 75 20 5 0
converted vote 627 342 131 0
 original vote 35 33 32 0
converted vote 490 381 229 0

No* = the DMV can fail all the criteria but the cases in which they fail are extremely rare.

The original vote of the voter through point 1 of the procedure is converted, and the vote obtained is in part of the type:

• ranking (Borda), because the points tend to be distributed linearly in the converted vote (see all cases).
• range (Score), because by distributing the points in quite different quantities, the candidates tend to keep their score in the converted vote (see A,B,C in cases , , ,  ).
• cumulative, because the points distributed in the converted votes are however limited and fixed (700 in the case , 1000 in the cases  and , 1100 in the cases , ,  based the number of candidates evaluated).

The DMV in any case meets the IWA.