Tragni's method
Tragni's method is a Single-Winner, invented by Aldo Tragni.
The peculiarity of this method is the use of some non-cardinal values, and the use of multiplication to make the aggregation of votes.
Procedure
Voter score candidates using value {[worst],1,...,5,[best]}.
- Make all head-to-heads, in which the candidate who is proportionally worse than the other loses (see Formula to calculate the proportionality).
- The candidate who loses least times in head-to-head, wins the election.
Ballot
This method use ranges with values shown below:
[worst] | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 | [best]
or
[worst] | 1 | 2 | 3 | 4 | 5 | [best]
The absence of evaluation is considered [worst]. The cardinal part of the vote is always included in the range [1,MAX] (positive, without 0). In this case MAX = 5. Different MAX values can generate different results.
Formula
Given the head-to-head [A-B], make for each vote and then multiply all the fractions between them. If the result is > 1 then wins A, if < 1 then wins B, if = 1 then both win (tie isn't a defeat).
Below is a more rigorous description, given the head-to-head [A-B]:
MAX indicates the highest value that can be used in the cardinal part of the vote.
P Table (boolean)
P Table contains all the P values, obtained with the Formula indicated above. Boolean P Table is a simplified version.
Boolean P Table initially has all values = 0. Put 1 in the candidates who win, and leave 0 in those who lose, for each head-to-head.
[A,B] → B loses [A,C] → A loses [A,D] → tie (no one loses) [B,C] → B loses [B,D] → D loses [C,D] → D loses
| A | B | C | D | |
|---|---|---|---|---|
| A | 1 | 0 | 1 | |
| B | 0 | 0 | 1 | |
| C | 1 | 1 | 1 | |
| D | 1 | 0 | 0 |
Wins C, the candidate who has least 0 (defeats) on his row (or the one that has most 1).