User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
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==== Write-in candidates ====
[[File:Approaches for handling write-in candidates in pairwise counting.png|thumb|837x837px|A non-comprehensive description of how write-in candidates can be counted in both regular and negative pairwise counting approaches.]]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]].
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=== Regular pairwise counting but done by counting first choices separately ===
Note that regular pairwise counting can have its required number of marks reduced, without using any negative numbers, by counting 1st choices separately from all other ranks; see the section above [[Pairwise counting#Uses for first choice information]]. This is essentially equivalent to doing semi-negative pairwise counting with negative counting only applied to 1st choices and regular pairwise counting applied to all other candidates.
Example for a voter ranking A>B=C>D (with candidates E and F unranked):
{| class="wikitable"
|+Modified regular approach values '''bolded''', regular approach values ''italicized''
!
!A
!B
!C
!D
!E
!F
|-
|A
|'''1 ballot'''
|''1''
|''1''
|''1''
|''1''
|''1''
|-
|B
|
|
|
|'''''1'''''
|'''''1'''''
|'''''1'''''
|-
|C
|
|
|
|'''''1'''''
|'''''1'''''
|'''''1'''''
|-
|D
|
|
|
|
|'''''1'''''
|'''''1'''''
|-
|E
|
|
|
|
|
|
|-
|F
|
|
|
|
|
|
|}
* In this example, only one mark is done in the modified approach for tallying the voter's preference for Candidate A, while five marks are done in the regular approach for that candidate. For all other candidates, both approaches require the same number of tally marks.
The regular approach requires [(number of candidates)-2] less marks if using this modification i.e. a voter who ranks 2 candidates sequentially when there are 10 candidates only requires ''1''+8=9 marks rather than ''9''+8=17 marks to have their ballot counted, a [(10)-2=] 8-mark difference.
* The 1st choice information allows one to determine the [[FPTP]] winner (so long as no voters equally ranked any candidates 1st), and the [[IRV]] winner in cases where some candidate is the [[Condorcet winner]] and has over 1/3rd of 1st choices (see [[Dominant mutual third]]).
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