Brams-Sanver Preference Approval Voting (Simplification?)

[Brian Langstraat]

Brams-Sanver Preference Approval Voting (PAV) seems like a very good voting system for single-winner elections that combines Ranking (Preference/Condorcet) and Range simplified as Approval Voting (AV).

A detailed paper by Steven Brams and Remzi Sanver can be found at

http://www.nyu.edu/gsas/dept/politics/faculty/brams/approval_preference.pdf

A summary by Warren Smith is copied below from:

http://election-methods.electorama.narkive.com/J8pIq0gc/two-new-hybrid-approval-ranking-methods-by-brams-sanver

Preference-Approval-Voting:

0. The votes are full strict rank orderings

(no ballot truncation or equality-rankings allowed).

Also voters "approve" or "disapprove" or each candidate, in a manner that

has to be compatible with the rank order.

It is not illegal to approve everybody.

It is not illegal to disapprove everybody.

1. If no candidate, or exactly one candidate,

receives a majority of approval votes,

then the PAV winner is just the AV winner (i.e most-approved candidate).

2. If two or more candidates receive a majority of approval votes, then

(i) If one of these candidates is preferred by a majority to every other majority-approved

candidate, then he is the PAV winner (even if not the AV or Condorcet winner).

(ii) If there is a cycle among the majority-approved candidates, then the

AV winner among them is the PAV winner (even if not the AV or Condorcet winner).

PAV seemed to have the best performance of the voting systems when compared by Smith using Yee Pictures in:

http://www.rangevoting.org/IEVS/Pictures.html

Stating:

The Brams-Sanver "preference approval voting" method empirically also exhibits optimal performance in this case (honest voters using mean candidate utility as approval threshold). However one occasionally encounters 2D scenarios in which the Brams-Sanver picture and the Voronoi diagram do not completely coincide. 

Mean-based thresholding (defined as "The voter gives max to every candidate at least as good as the average value of all candidates, and gives min to the others.") is the best strategy here when the number of voters is sufficiently large as shown by Smith in:

http://www.rangevoting.org/RVstrat3.html

Simplification:

To force optimal performance by using mean-based thresholding, the voter's approval step is removed and the approval is assumed for the top-ranked half of candidates (rounded up).

Thus, voters only need to vote using full strict rank orderings and approval can be used during vote counting.

[Brian Olson]

If no candidate gets 50% approval, disqualify everyone on the ballot from running for 2 years and hold a special election in 4-6 weeks to try again.

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[Brian Langstraat]

Brian,

I appreciate your response, since it covers the weakest part of the original PAV.

1. If no candidate, or exactly one candidate,

receives a majority of approval votes,

then the PAV winner is just the AV winner (i.e most-approved candidate).

This allows a non-majority candidate to win.

When there is bullet voting with many candidates, a very low approval candidate or extremist could be the plurality winner.

Your suggestion is similar to None Of The Above (NOTA).

I think a good voting system should result in the number of winners needed to fill the electoral positions.

Special elections would be an necessary expense with probably less qualified or less interested candidates than the original election.

With the simplification that I suggested, at least one candidate would be guaranteed to get a majority unless all candidates were tied at 50%.

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[Brian Langstraat]

There are a few other changes that could be made to deal with issues that I see with the Brams-Sanver PAV.

When there is bullet voting with many candidates, a very low approval candidate or extremist could be the plurality winner.

This could be resolved by treating step 1 like step 2 such that "If one of these candidates is preferred by a majority to every other candidate, then he is the PAV winner."

Another issue where "exactly one candidate receives a majority" could result in a slim majority overriding a clear preference such as: 51% approve A and 49% approve B, but 98% prefer B to A.

I. 49 voters: B A | C

II. 49 voters: C | B A

III. 2 voters: A | B C

This could be resolved by removing the majority restriction between step 1 and step 2.

Thus, a super simplified PAV could result that is probably just a Condorcet method with cycles going to the Approval winner.

Super Simplified Preference-Approval-Voting:

0. The votes are full strict rank orderings

(no ballot truncation or equality-rankings allowed).

Approval is assumed for the top-ranked half (rounded up) of candidates.

For example, approval is assumed for the 3 top-ranked candidates out of 5 total candidates.

(i) If one of these candidates is most preferred to every other candidate, then he is the PAV winner (even if not the AV winner).

(ii) If there is a cycle among the most approved candidates, then the

AV winner among them is the PAV winner (even if not the AV or Condorcet winner).

[Brian Langstraat]

A further modification to "Super Simplified Preference-Approval-Voting" that incorporates Range Voting (RV) could be called Range-Preference-Voting (RPV).

Range-Preference-Voting:

0. The votes are scores in a range (blank,0-9) for each candidate (including write-ins) and "All Other Candidates"

(ballot truncation [blank score/No Opinion] and equal scores allowed).

It is not illegal to have equal scores for everybody.

It is not illegal to leave blank scores for everybody.

Each voter's scores are converted to a preference order, where the highest score(s) have the highest ranking, lower score(s) have progressively lower rankings, and blank score(s) have a ranking based on the voter's "All Other Candidates" score.

If "All Other Candidates" has a blank score, then each candidate with blank score is excluded from the voter's preference order and potential RV averaging.

1. If one of these candidates is most preferred to every other candidate, then he/she is the RPV winner (even if not the RV winner).

2. If there is a cycle among the most preferred candidates, then the RV (averaging, blanks allowed, "All Other Candidates" rule) winner among them is the RPV winner (even if not the RV or Condorcet winner).

3. If there is a rare tie between the top RV candidates, then (with the tied candidates) repeat Step 1, then Step 1 with "All Other Candidates" blanks = 0, then Step 2 with "All Other Candidates" blanks = 0, then Step 1 with "All Other Candidates" blanks = 0, then random winner to decide the RPV winner.

For comparison to the voting systems described in http://www.rangevoting.org/RuleD.html:

RPV (truncation allowed, unmentioned candidates treated as "All Other Candidates", averaging, blanks treated as "All Other Candidates")  ---  Unknown write-in candidates difficult to elect unless voters give unfavorable ratings to known, unfavorable candidates (e.g. Trump/Clinton). No bias against lesser-known (rather than lesser quality) candidates, provided they are well-enough known and favorable enough to outweigh voters' fear of the unknown. Great behavior.

[William Ti'iti'i Asiata Hunt]

Thanks for putting this thread here.

BS-PAV is my favorite voting method because as far as I can tell the justification for the winner(s) is as fair as could get in a voting system.

Also the concern for increased information needs from the constituency is I think more of a 20c mindset that can be more easily mitigated in the current era, what with the maturity of online user based social networks and the emergent field of data science and the very current topical theme of big data in today's advancing age of information and technological sophistication.

I actually mistakenly thought that I had invented/discovered PAV about 3 years ago whilst going through the motions of my own self-driven critique of voting systems and ideation of an ideal better alternative until I discovered this thread last Wednesday LOL!!!

But good to know that there is already real, well articulated academia available to support the meaningfulness of a BS-PAV voting system. As far as I am aware, this is the only paper that explores PAV (preference approval voting) in depth?? So not a lot of R&D exploring the real world ramifications of PAV yet...
And not to be confused with the other PAV proportional approval voting right?

Many thanks and warm regards

William

[William Waugh]

Does it meet the balance constraint? I mean, for every possible vote, is there another possible vote that would undo the effect of the first vote?

On Tuesday, May 9, 2017 at 4:06:00 PM UTC-4, Brian Langstraat wrote https://groups.google.com/d/msg/electionscience/enXR2zR1P9s/5SQDTJOnAQAJ

[Brian Langstraat]

William,

I think that Range-Preference-Voting (RPV) meets the balance constraint, since most forms of Condorcet and range should meet it .

For every score, there is opposite score such as a range of 0-9 has 0 vs 9 and 2 vs 7.

If all the scores for a vote are opposite all of the scores for another vote, then all of their converted preference orders should be opposite.

If a cycle is created by the opposing votes, then the opposing scores would be balanced.

Balanced tie-breakers would result in a random winner like I assume most voting systems meeting the balance constraint.

Perhaps, the weak spot is:

If "All Other Candidates" has a blank score, then each candidate with blank score is excluded from the voter's preference order and potential RV averaging.

If a candidate receives a blank score and "All Other Candidates" has a blank score for a vote resulting in an exclusion of the vote resulting in exclusion of the blank score, then an excluded score may not have an opposite.

If RPV needs to meet the balance constraint, then "All Other Candidates" could default to a score of 0.