Tragni's method: Difference between revisions
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Tragni's method is a
==Procedure==
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[[File:Formula Tragni's method.png|700px|frameless]]
With MAX = 5, the proportions range is [1/MAX, MAX] = [1/5, 5]. MAX indicates the highest value that can be used in the cardinal part of the vote.
''If of the two candidates in head-to-head only the order is known, and not the proportion (as in the rankings), then the lesser is placed at [worst] and the greater one at [best], but this is not the context.''
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Wins C, the candidate who has least 0 (defeats) on his row (or the one that has most 1).
===Example===
Given the following vote: A[worst] B[1] C[2] D[3] E[4] F[5] G[best] the respective complete P Table is obtained:
{| class="wikitable" style="text-align:center;"
|-
!
! A [worst]
! B [1]
! C [2]
! D [3]
! E [4]
! F [5]
! G [best]
|-
| A [worst]
| 1
| 1/5
| 1/5
| 1/5
| 1/5
| 1/5
| 1/5
|-
| B [1]
| 5
| 1
| 1/2
| 1/3
| 1/4
| 1/5
| 1/5
|-
| C [2]
| 5
| 2
| 1
| 2/3
| 2/4
| 2/5
| 1/5
|-
| D [3]
| 5
| 3
| 3/2
| 1
| 3/4
| 3/5
| 1/5
|-
| E [4]
| 5
| 4
| 4/2
| 4/3
| 1
| 4/5
| 1/5
|-
| F [5]
| 5
| 5
| 5/2
| 5/3
| 5/4
| 1
| 1/5
|-
| G [best]
| 5
| 5
| 5
| 5
| 5
| 5
| 1
|}
The propositions are all contained in [1/5, 5]. A [worst] always loses against everyone with 1/5, while G [best] always wins against everyone with 5. The voter will therefore be free to vote for his intermediate candidates without his vote changing the chances of victory of the [best] and [worst] candidates.
===Tie solutions===
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The candidate with the highest WP win.
* If some candidates remain in tie then, using
==Proportional head-to-head==
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'''[[Consistency criterion|Consistency]]''': if the two separate elections give the same winner, then the union of the two electorates will give the same winner (meets the criterion).
If in one of the two elections X is in tie with other candidates, while in the other X wins, then it's not said that with the union of the electorates X wins (
'''[[Reversal symmetry]]''': if the candidates were rated only with [worst] and [best] (which are then reversed), then this criterion is met. If the candidates are rated even with the cardinal scores in [1,5] then the vote cannot be completely reversed, and the criterion isn't applicable. When it's applicable, it's always satisfied.
'''[[Later-no-harm criterion|Later-no-harm]]''': if the more-preferred candidate is rated [best], then the criterion is met.
==Strategies resistance==
<!-- Color: (resistance) #00e800, #a5fa00, #ffff00, #ffff00, #ffc000, #ff8837, #ff0000 (no resistance) -->
{| class="wikitable" style="text-align:center"
|- style="font-size:80%;"
! style="width: 150px;" |[[Tactical voting#Definitions|Min-maxing (benefit)]]
! style="width: 150px;" |[[Tactical voting#Definitions|Min-maxing (disadvantage)]]
! style="width: 150px;" |[[Tactical voting#Pushover|Push-over]]
! style="width: 150px;" |[[Tactical voting#Voting_for_the_lesser_of_two_evils|Voting lesser of two evils]]
|- style="font-size:80%;"
|-
! style="background: #00e800; font-weight: inherit; height: 16px;" |
! style="background: #a5fa00; font-weight: inherit; height: 16px;" |
! style="background: #00e800; font-weight: inherit; height: 16px;" |
! style="background: #00e800; font-weight: inherit; height: 16px;" |
|}
'''[[Tactical voting#Definitions|Min-maxing (benefit)]]''': a voter gives maximal support to some candidates and no support to all other candidates, to benefit those with maximal support (becomes Bullet voting if only 1 candidate has maximal support).
In Tragni's method the voter can give maximal support to a candidate, rating him [best]. The ratings given to the other candidates will not reduce the chances of victory for the rated [best] candidates, therefore the voter is free to show his/her true interests regarding those candidates.
'''[[Tactical voting#Definitions|Min-maxing (disadvantage)]]''': a voter gives maximal support to some candidates and no support to all other candidates, to disadvantage those with no support. It also includes the problem of candidates little known by the voter, who would receive additional support.
In Tragni's method the voter can give minimal support to a candidate, rating him [worst]. The ratings given to the other candidates will not increase the chances of victory for the rated [worst] candidates, therefore the voter is free to show his/her true interests regarding those candidates.
Regarding little-known candidates: if they aren't evaluated, they automatically receive [worst]; if they are evaluated, they will receive the lowest rating, but higher than [worst], that is 1. With this rating, it's practically impossible for a little known candidate to win.
'''[[Tactical voting#Pushover|Push-over]]''': a voter rating an alternative lower in the hope of getting it elected, or rating an alternative higher in the hope of defeating it (concerns only methods that fail monotony).
'''[[Tactical voting#Voting_for_the_lesser_of_two_evils|Voting lesser of two evils]]''': given 2 front runners, a voter gives maximal support to the best one and no support to the worst one.
In Tragni's method, assuming that the 2 front runners have different ratings in the non-strategic vote, then if the worst of the 2 is rated [worst], or if the best is rated [best], or they are rated 1 and 5 respectively, then the vote doesn't change (no strategy); otherwise, the worst of the 2 will be rated [worst]. The one described is the worst case.
''If in the [[Tragni's method#Formula|formula]] to manage the proportions of [worst] and [best], a higher value had been used instead of MAX (like MAX + 1 or MAX * 2), then in the case with the two front runners rated 1 and 5, the worst would have been put to [worst], increasing the damage of this strategy, even if only slightly.''
==Systems Variations==
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* eliminate all other candidates, normalizing the votes with Min-Max Normalization.
* of the two remaining candidates, the one who wins in the P head-to-head wins the election.
===Extended Tragni's method (E-TM)===
It's Tragni's method in which [best] and [worst] are divided into 3 semi-cardinal symbols and MAX = 4. The range options are:
[ 1w | 2w | 3w ] | 1 | 2 | 3 | 4 | [ 1b | 2b | 3b ]
The #w values will always be worst than the others. The #b values will always be best than the others. If two #w or #b values are to be considered, then they will be treated as cardinal values to make the proportion.
It offers a better representation of interests than Tragni's method, but it's more complex to understand how symbols work.
E-TM meets all the criteria satisfied by Tragni's method, replacing [worst] and [best] with the #w and #b values respectively.
It resists even more to the min-maxing tactic, because candidates who in the Tragni's method would all be put equally [worst] or [best], in E-TM can receive more precise ratings through the #w and #b values.
==Systems Comparison==
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