User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
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[[File:
== Description ==
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|-
|B
| -10 votes
|''15 ballots''
|}
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|-
|A
| ---
|10 (votes)
|-
|B
|5
| ---
|}
=== Dealing with equal-ranking ===
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5 A=B </blockquote>then either it can be marked that A wins against B by:
* 2 votes to 1
* 7 votes to 6
This is because the voters who equally ranked A and B can be considered to, in the A vs B matchup, either be voting for:
* Neither of them (similar to [[FPTP|choose-one FPTP voting]]; this is the traditional pairwise counting approach).
* Both of them (similar to [[Approval voting]]).
This is related to how, in [[Approval voting]], if A has 30 approvals and B 20, and no other information is supplied, then it is impossible to know whether any of the 20 voters who approved B also approved A or not.
This can change who wins in certain [[:
Note: Voters who don't rank either of the candidates in a matchup are generally considered to equally rank them, but no implementation of negative counting would consider them to vote for both candidates in the matchup. Only voters who have marked both candidates can be counted that way.
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Verbal comparison between the regular approach and negative counting:
*
** This can be slow, and also can make it difficult to accommodate write-in candidates (see [[Pairwise counting#Dealing with write-in candidates]]), since the vote-counters won't know ahead of time who those candidates are, and thus won't be able to indicate preferences in those matchups.
*
It's actually possible to visualize, in a pairwise counting matrix, what values have to be recorded for each approach; this is because the cells of the pairwise matrix used in each approach are disjoint.
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For example, a voter who votes A>B when there are 10 candidates can be assumed to vote for A and B in every matchup, except they don't prefer B>A:
* Usually, this would require manually marking each of those positive preferences, resulting in 9 marks to show A being preferred to all other candidates, and 8 marks to show B preferred to all candidates except A, for a total of 17 marks.
* But negative counting only requires 3 marks: 1 each for A and B to indicate they are preferred in every matchup, and 1 to indicate that this isn't the case for B>A.
=== Election example comparisons ===
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* Negative counting approach requires at least '''4482''' marks.
** Calculation: (48 + 3*35 + 6*22 + 10*39 + 15*25 + 21*16 + 28*10 + 36*6 + 45*4 + 55*4 + 55*40)
* Regular approach requires at least '''8223''' marks.
** Calculation: (10*48 + 19*35 + 27*22 + 34*39 + 40*25 + 45*16 + 49*10 + 52*6 + 54*4 + 55*4 + 55*40)
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===== Non-pairwise methods =====
*
== Connection to cardinal methods ==
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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).]]
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).
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