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 04:18, 20 May 2020
, 4 years ago→Comparison to the regular approach
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It is perhaps possible to make a special marking for a last-choice candidate that indicates they are not preferred over any of the on-ballot 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.
== Comparison to
It can also be useful to compare these results to the amount of vote-counting work that would be done in other voting methods.
* With [[Score voting]], the number of candidates that a ballot gives an above-minimum score to is the number of marks that are made for that ballot.▼
** Note that this will generally be strictly greater than with [[Approval voting]], because a voter is likely to score more candidates than they would approve; the general trend is that the more gradations/allowed scores there are, the more likely a voter is to score more candidates.▼
** It isn't possible to know for certain how voters would score the candidates when provided only ranked data. However, it is possible to guess; for example, if there were certain candidates known to be frontrunners, then strategic voters would likely do [[min-max voting]] among those frontrunners, and adjust their scores for candidates they preferred more or less than their preferred frontrunner(s) accordingly. In addition, it can be assumed some voters would do [[normalization]].
* With [[RCV]], there is some additional work involved in transporting the ballots to a centralized location, and in doing multiple rounds of counting, rather than one; ignoring that, however, at least one mark must be made per ballot (to indicate 1st choices), and then in each sequential round where votes are transferred, the number of transferred votes is the number of additional marks that must be made in that round.▼
=== Comparison to the regular pairwise counting approach ===
Verbal comparison between the regular approach and negative counting:
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=== Election example comparisons ===
It is possible to compare the number of marks that must be made in either approach for certain elections, because their full ballot set has been published. Any election using ranked or rated ballots can be used for this purpose. The calculations and numbers used in this section may be slightly off for some examples, though general conclusions (should) still hold; because of this, it is suggested that the reader apply a ~10% margin of error or more when considering how superior one pairwise counting approach is to another.
Note that when equal-ranking isn't allowed, only the number of voters who ranked a certain number of candidates needs to be known.
▲It can also be useful to compare these results to the amount of vote-counting work that would be done in other voting methods.
▲* For [[FPTP]], one mark is made per ballot.
▲* With [[Score voting]], the number of candidates that a ballot gives an above-minimum score to is the number of marks that are made for that ballot.
▲** Note that this will generally be strictly greater than with [[Approval voting]], because a voter is likely to score more candidates than they would approve; the general trend is that the more gradations/allowed scores there are, the more likely a voter is to score more candidates.
▲** It isn't possible to know for certain how voters would score the candidates when provided only ranked data. However, it is possible to guess; for example, if there were certain candidates known to be frontrunners, then strategic voters would likely do [[min-max voting]] among those frontrunners, and adjust their scores for candidates they preferred more or less than their preferred frontrunner(s) accordingly. In addition, it can be assumed some voters would do [[normalization]].
▲* With [[RCV]], there is some additional work involved in transporting the ballots to a centralized location, and in doing multiple rounds of counting, rather than one; ignoring that, however, at least one mark must be made per ballot (to indicate 1st choices), and then in each sequential round where votes are transferred, the number of transferred votes is the number of additional marks that must be made in that round.
==== Burlington 2009 mayoral election ====
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** The calculation is (1*1481 + 3*1912 + 6*1799 + 10*873 + 10*2944).
* The regular approach would require at least '''73,669''' marks.
** This is if
** Calculation: (4*1481 + 7*1912 + 9*1799 + 10*873 + 10*2944). (This is with number of candidates, N, being 5.)
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== Connection to cardinal methods ==
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]]).
== Notes ==
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
=== Dealing with truncation ===
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