Ranked preference approval voting: Difference between revisions
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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. |
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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=== Ballot format === |
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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. |
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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. |
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==== Top Three Tournament ==== |
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{| class="wikitable" |
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RPAV-T3: Ranked preference approval ballot (score 5 = Most Approved, score 4 = Approved, score 3 = Slightly Approved, score 2 = Slightly Disapproved Compromise, score 1 = Disapproved Compromise, score 0 = Strongly Disapproved and Rejected [or blank]). |
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|+ |
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!Tier |
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!Approved |
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!Description |
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|1 |
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|Yes |
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|Most/Strongly approved |
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|2 |
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|Yes |
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|Approved |
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|- |
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|3 |
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|Yes |
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|Slightly/Barely approved |
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|- |
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|4 |
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|No |
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|Slightly/Barely disapproved |
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|- |
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|5 |
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|No |
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|Disapproved |
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|6 |
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|No |
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|Most/Strongly Disapproved; Rejected; Unknown |
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|} |
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===Single Winner RPAV methods === |
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Count candidate scores of 3-5 as approved, 0-2 as disapproved. Sort the candidates in descending order of approval, and take the top three approved candidates. Use rankings inferred from ratings to form a pairwise matrix for those three candidates. The pairwise winner of the highest approved candidate versus the pairwise winner between the second and third most approved candidates wins the election. |
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====Top Three Tournament==== |
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RPAV-T3: |
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* Use a 6-tier approval ballot as above. |
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* 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) |
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* Use rankings to form a pairwise matrix for those three candidates. |
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** If a ballot rates candidate X higher than candidate Y, X receives a vote in the pairwise X-Y contest, and visa-versa. |
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* 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)) |
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====Smith//Approval==== |
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RPAV-Smith-Approval: |
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* Same ballot as RPAV-T3. |
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* Find Smith Set: |
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** Compute Pairwise matrix |
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** Initialize Smith Set as empty set |
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** Find candidate(s) with the smallest number of pairwise losses, add them to Smith Set |
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** For each untested Smith Set candidate, add in any candidates not already in Smith Set who defeat that candidate. |
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⚫ |
Revision as of 20:57, 17 May 2023
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.
Ballot format
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.
Tier | Approved | Description |
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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 Three Tournament
RPAV-T3:
- 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.
- 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.