Ranked preference approval voting: Difference between revisions
Formalized tier ballot
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Ranked Preference Approval Voting (RPAV) is a general term used to describe voting methods with approval inferred from a ranked ballot (equal ranking and ranking-gaps allowed), but is used specifically for two different single-winner methods and one multiwinner [[proportional representation]] method.
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The goal of RPAV is to emulate a general ranking with an explicit approval cutoff via a fixed ranking format with constant approval cutoff level. If you want to emulate the effect of being able to put an explicit approval cutoff somewhere in an M-level ranking, then you need 2*M ranks, with the top M ranks approved. This lets you rank M candidates as approved, or up to M-1 candidates disapproved but not last.
To de-emphasize *rating*, even though it could be considered equivalent to a score ballot, the RPAV ballot is set up as N ranked *tiers*. The terminology *tier* is chosen because a rank level is not exclusive --- more than one candidate can be ranked on a tier level --- and it is not necessary to rank a candidate on each tier. The default number of tiers is 6, which lets voters put an explicit approval cutoff somewhere in 3 ranking levels, an adequate level of resolution for most public elections.
{| class="wikitable"
|+
!Tier
!Approved
!Description
|-
|1
|Yes
|Most/Strongly approved
|-
|2
|Yes
|Approved
|-
|3
|Yes
|Slightly/Barely approved
|-
|4
|No
|Slightly/Barely disapproved
|-
|5
|No
|Disapproved
|-
|6
|No
|Most/Strongly Disapproved; Rejected; Unknown
|}
===Single Winner RPAV methods ===
====Top
RPAV-T3:
RPAV-Smith-Approval: Same ballot as RPAV-T3. Winner is the highest approved member of the Smith set. For three candidates, the winner of RPAV-T3 is the same as the winner of RPAV-Smith-Approval.▼
* Use a 6-tier approval ballot as above.
* Sort the candidates in descending order of approval, and take the top three approved candidates. (A = approval winner, B = approval runner-up, C = approval third place)
* Use rankings to form a pairwise matrix for those three candidates.
** If a ballot rates candidate X higher than candidate Y, X receives a vote in the pairwise X-Y contest, and visa-versa.
* The winner is the pairwise winner of the highest approved candidate versus the pairwise winner between the second and third most approved candidates wins the election. In other words, T3-winner = PW(A, PW(B,C))
====Smith//Approval====
RPAV-Smith-Approval:
* Same ballot as RPAV-T3.
* Find Smith Set:
** Compute Pairwise matrix
** Initialize Smith Set as empty set
** Find candidate(s) with the smallest number of pairwise losses, add them to Smith Set
** For each untested Smith Set candidate, add in any candidates not already in Smith Set who defeat that candidate.
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