User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting (view source)
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This advice is less relevant when write-ins are allowed, however, because even if a voter ranks a candidate last among the candidates named on their ballot, they are still implicitly ranking that candidate above all of the write-in candidates they didn't rank on their ballot. So if last-ranked candidates aren't counted, then it may be necessary to modify how the calculation is done, or otherwise mention caveats in the final result, to avoid giving the impression that the vote totals are accurate for the matchups involving write-in candidates (however, the totals will only be off by the number of voters that rank a non-write-in candidate last and don't rank the write-in candidate for a given matchup between such candidates).
It is possible to make a special marking for a last-choice candidate that indicates they are not preferred over any of the on-ballot (regular) candidates, but that they are preferred over all write-in candidates. It would then only be necessary to record negative votes for matchups involving write-in candidates who are ranked above the last-choice candidate on some ballots. This would mean making at most two additional marks for every last-ranked candidate on a ballot, because in practice, in most elections, voters are only allowed to write in at most one candidate.<ref name=":0">{{Cite web|url=https://forum.electionscience.org/t/negative-vote-counting-approach-for-pairwise-counting/644|title=Negative vote-counting approach for pairwise counting|date=2020-04-27|website=The Center for Election Science|language=en-US|access-date=2020-09-15}}</ref> This can be compared to the regular approach to dealing with write-ins at [[Pairwise counting#Dealing with write-in candidates]].
=== Regular pairwise counting but done by counting first choices separately ===
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== Notes==
[[File:Negative vote-counting approach to pairwise counting.png|thumb|1114x1114px|Negative vote-counting approach for pairwise counting (Note: Regular approach may be better in some use cases; see cited discussions in text to the left).Here is a discussion clarifying some confusion that may arise from seeing the above picture: <ref name=":1">{{Cite web|url=https://www.reddit.com/r/EndFPTP/comments/gh7fix/new_pairwise_counting_approach_based_on_approval/|title=r/EndFPTP - New pairwise counting approach based on Approval voting|website=reddit|language=en-US|access-date=2020-09-15}}</ref>]]
In practice, to make pairwise counting easier, voters could be provided with two or fewer ranks than the number of candidates, with equal-ranking being allowed so that voters could do [[preference compression]]. This way, a voter who would usually indicate a preference that would have to be counted between two candidates would have to indicate no preference between them instead.
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===Alternative ways to frame negative pairwise counting===
An alternative way to do the negative approach, which is more similar to the regular approach, is to, when candidate B is explicitly ranked below A on a ballot, instead of counting -1 votes for B>A, count 1 vote for A>B, and later on, when the math is done, the number of votes for B>A is the number of ballots ranking B minus the number of votes for A>B. In other words, a part of the regular pairwise counting approach is used, but only in matchups where both candidates are explicitly ranked by the voter (i.e. a voter who voted A>B and left C unranked would have their vote for A>B counted, but not their vote for A>C, because later on it will be inferred that they must have preferred A to C by virtue of having ranked A but not C).
===Inspiration===▼
[[Approval voting]] can be thought of as a [[Smith-efficient]] [[Condorcet method]] where, when a voter approves a candidate, they are assumed to vote for them in every head-to-head matchup (see [[Self-referential Smith-efficient Condorcet method]]). Further, approving a candidate can be thought of as ranking them 1st, while disapproving a candidate can be thought of as ranking them last. Given that connection, and that in Approval voting, the vote-counting is done by counting the number of ballots that approve/mark a candidate, rather than by harder [[pairwise counting]], it is clear that a similar counting procedure could be applied to pairwise counting itself. The only complexity is that when voters rank candidates, they are allowed to express that they don't prefer certain candidates in certain matchups; thus, negative votes are necessary to communicate that lack of preference for specific matchups. ▼
This has the advantage of, when every voter does [[bullet voting]], being counted exactly like an [[FPTP]] election (one mark per ballot for the candidate it marked), which also shows that FPTP can be thought of as a constrained form of Approval. ▼
===Comprehensive example===
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|-
|C
| -1 vote
|
|''1 ballot''
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|-
|D
| -1 vote
| -1 vote
| -1 vote
|''1 ballot''
|
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|''(Ranked on) 1 ballot''
|
| -1 vote
| -1 vote
| -1 vote
|
|-
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|
|
| -1 vote
|''1 ballot''
|
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|
|
| -1 vote
|
|''1 ballot''
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|''(Ranked on) 2 ballots''
|
| -1 vote
| -1 vote
| -1 vote
|
|-
| B
| -1 vote
|''1 ballot''
|
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|-
|C
| -1 vote
|
|''2 ballots''
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|-
| D
| -1 vote
| -1 vote
| -2 votes
|''2 ballots''
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== History ==
[[User:BetterVotingAdvocacy]] created this vote-counting method around May 2020. It was discussed on the [[CES Forum]]<ref name=":0" />, Reddit's r/EndFPTP<ref name=":1" />, and Electowiki<ref>{{Cite web|url=https://electowiki.org/wiki/Talk:Pairwise_counting|title=Pairwise counting|date=2020-09-01|website=Electowiki|language=en|access-date=2020-12-02}}</ref>.
▲===Inspiration===
▲[[Approval voting]] can be thought of as a [[Smith-efficient]] [[Condorcet method]] where, when a voter approves a candidate, they are assumed to vote for them in every head-to-head matchup (see [[Self-referential Smith-efficient Condorcet method]]). Further, approving a candidate can be thought of as ranking them 1st, while disapproving a candidate can be thought of as ranking them last. Given that connection, and that in Approval voting, the vote-counting is done by counting the number of ballots that approve/mark a candidate, rather than by harder [[pairwise counting]], it is clear that a similar counting procedure could be applied to pairwise counting itself. The only complexity is that when voters rank candidates, they are allowed to express that they don't prefer certain candidates in certain matchups; thus, negative votes are necessary to communicate that lack of preference for specific matchups.
▲This has the advantage of, when every voter does [[bullet voting]], being counted exactly like an [[FPTP]] election (one mark per ballot for the candidate it marked), which also shows that FPTP can be thought of as a constrained form of Approval.
== See also ==
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