User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting (view source)
Revision as of 20:53, 21 July 2020
, 3 years ago→Dealing with last-place candidates
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=== Dealing with last-place candidates ===
It is not necessary to make any markings for a candidate a voter ranked as their last choice, because this means they wouldn't vote for that candidate in any matchups. One way of thinking about this is that if the voter hadn't ranked that candidate, then no marks would've been made to count them, and in effect the voter would still be treated as ranking them last.
This can save a great deal of work in some cases; if a voter ranks all of 10 candidates, and ranks 5 of them last (i.e. they are all ranked 6th), then 5*(5+1)=30 fewer marks need be made if not counting them (explanation for the math: there are 5 such candidates, and they are each ranked under 5 candidates, with 1 additional mark made to record that they were ranked by the voter). In fact, if not using this trick, negative counting can actually require more marks than regular counting in some cases.
==== Write-in candidates ====
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. This can be compared to the regular approach to dealing with write-ins at [[Pairwise counting#Dealing with write-in candidates]].
== Semi-negative counting procedure ==
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* With semi-negative counting, it only required '''6''' marks to count.
With semi-negative counting, it is possible to reduce the number of marks required to count a ballot by roughly half or greater, depending on which of the other two approaches it is compared to, and how many of the candidates are ranked by the voter. The positive and negative marks can either be stored as separate values, or they can be combined during the counting (i.e. 5 positive votes for A>B and 3 negative votes for A>B can be stored as 2 votes for A>B. This means incrementing and decrementing the same number during the count, so it could be confusing).
== Comparison to other vote-counting procedures ==
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This approach can be considered an [[Approval voting]]-based or [[cardinal]] approach, because when using the Approval-style approach for equal-rankings (explicit equal-rankings are counted as a vote for both candidates in the matchup), then each voter that votes Approval-style (i.e. explicitly ranks some candidates 1st and leaves all other unranked, which is implicitly treated as ranking them last) will have their ballot counted like an [[Approval ballot]] (i.e. the preference for each approved candidate on the ballot will be counted with one mark per candidate, and no marks will be used to count disapproved candidates). Further, in some implementations, it allows a voter to give support to both candidates in a matchup, just like in cardinal methods.
=== Using with strength of preference ===
Negative vote-counting can be used to count weak pairwise preferences (i.e. if a voter only wants to give 0.4 votes in a matchup, rather than 1 vote; see [[Rated pairwise preference ballot#Implementations]]) by counting only a "partial ballot" marking a candidate, and partial (i.e. weighted or fractional) negative votes in certain matchups. In other words, it is treated as if only a partial voter or ballot supported a candidate (see [[KP transform]]). Note that this is equivalent to using Score voting in a matchup, if using a scale of 0 to 1 rather than the more familiar 0 to 5 or 0 to 10 scales.
== Notes ==
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=== Independence of unranked candidates ===
The negative approach doesn't require additional marks to be made for a given ballot when candidates are added to the election that that ballot doesn't vote for. For example, at most 3 marks need be made for a voter whose ballot is A>B, regardless of whether there are 2 candidates in the election or 100.
=== Negative counting used for non-pairwise methods ===
Negative numbers can be used to count Approval voting, and can also be used in the context of most PR methods.
* For Approval, when a voter approved more than half of the candidates, they can be considered to disapprove fewer than half the candidates. That is, a ballot approving A, B, and C, but not D, can be counted as a ballot that approves everyone except D.
** Note that the same trick works for Score, but doesn't always speed the counting up there. For example, a voter who scores a candidate a 3 out of 5 can be thought of as giving them 5 positive points and -2 negative points as well.
* For sequential PR methods, some selection algorithm generally picks the a winner in a given round, then reweighting is applied to the votes, and this repeats. Because reweighting generally only alters some votes, it's often possible to treat the votes in one round as being the votes from a previous round, except some candidates have lost some support. [[SPAV]] is one such example. <ref>{{Cite web|url=https://forum.electionscience.org/t/possible-trick-for-counting-spav-and-cardinal-pr-faster/657|title=Possible trick for counting SPAV (and cardinal PR) faster|date=2020-05-26|website=The Center for Election Science|language=en-US|access-date=2020-07-21}}</ref>
== References ==
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