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.
- 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.
- 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, 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[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 points of the candidates in the subset.
v0 = value of candidate X, before normalization
v1 = value of candidate X, after normalization.
Failed to parse (unknown function "\begin{equation}"): {\displaystyle \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 | |
|---|---|---|---|---|
| [1] original vote | 100 | 0 | 0 | 0 |
| converted vote | 700 | 0 | 0 | 0 |
| [2] original vote | 99 | 1 | 0 | 0 |
| converted vote | 697 | 303 | 0 | 0 |
| [3] original vote | 96 | 4 | 1 | 0 |
| converted vote | 686 | 292 | 122 | 0 |
| [4] original vote | 51 | 49 | 0 | 0 |
| converted vote | 553 | 447 | 0 | 0 |
| [5] original vote | 75 | 20 | 5 | 0 |
| converted vote | 627 | 342 | 131 | 0 |
| [6] 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 (less frequent than many others voting systems that don't meet the same criteria).
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 [1], [2], [3], [5] ).
- cumulative, because the points distributed in the converted votes are however limited and fixed (700 in the case [1], 1000 in the cases [2] and [4], 1100 in the cases [3], [5], [6] based the number of candidates evaluated).
The DMV in any case meets the IWA.
Resistance to strategic votes
The DMV is extremely resistant to tactical votes, that ignore the election results.
The way in which the converted vote is obtained means that the voter doesn’t have a great interest in accumulating their points all on the same candidate. In cases [1] and [2] it’s noted that the addition of 1 point on B, left the score of A practically unchanged in the converted vote, but in case [2] it obtained 303 points for B (same speech observing the case [3] or even [5] ); this means that the voter has an interest in expressing his preference towards B. At the same time, the voter doesn’t even have the interest of giving his limited points to candidates he doesn’t really support (reduced dispersion of points) .
The DMV can be subject to tactical votes in which candidates change the order of their preferences based on the results of the elections; to use these tactical votes you must:
- are sufficiently aware of the expected results of an election (hard).
- fully understand the functioning of the DMV.
- be willing to take risks, because these tactical votes can backfire on the voter if they fail.
Overall in practical contexts it’s very difficult to create an effective strategic vote in the DMV.