User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
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Revision as of 05:59, 21 May 2020
, 4 years ago→Comparison to the regular pairwise counting approach
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* '''Negative counting approach''': The vote-counters mark a candidate as being ranked on a ballot, assume the voter who ranked them prefers that candidate in every matchup, and then show which matchups this is not true for.
==== Formula for counting the required number of marks to be made ====
The formula
* In negative counting, the series starts at 0 when 0 candidates are ranked, and then the formula is that the number of marks that must be made for a given number of candidates that were ranked on a ballot is the value in the series for a ballot that had ranked one less candidate than that given number, plus the number of candidates ranked on the ballot.
** This is because for each additional candidate added (ranked below all candidates already on a ballot), one mark is made to indicate that they were ranked, and [number of candidates already on ballot] marks are made to indicate the voter's preference for all of those already-ranked candidates over the newly ranked candidate.
* In the regular approach, take whatever number of marks would be produced in negative counting for a given number of ranked candidates on a ballot (see above bullet point), and then subtract it from the number of candidates that are ranked on a ballot multiplied by the number of non-write-in candidates in the election.
**This is because, if the negative counting approach is thought of as "count the number of times a candidate is "preferred to themselves" (i.e. the number of ballots they're ranked on) and the number of ballots that prefer them less than each other candidate", then the regular approach doesn't require counting either of those pieces of information, but does require counting the number of times a candidate is preferred over each of the other candidates
***For example, with 10 candidates, for a ballot with one 1st choice that doesn't rank any of the other candidates, the negative counting approach only requires counting the fact that the 1st choice is "preferred to themselves", whereas the regular approach requires counting that the 1st choice is preferred over each of the other 9 candidates; so there are either 1 or 9 (10-1) marks to be made.
****If this ballot also ranked a 2nd choice, the negative approach requires indicating that the 2nd choice is also "preferred to themselves", and preferred less than the 1st choice, while the regular approach requires indicating that the 2nd choice is preferred over each of 8 candidates i.e. all of the 10 candidates that aren't the 1st choice or 2nd choice.
Here are some examples for the first numbers in each series:
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