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 23:52, 18 July 2020
, 3 years ago→Formula for counting the required number of marks to be made
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****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 (with the upper bound bolded):
{| class="wikitable"
|+Number of marks required in each vote-counting approach ''when equal-ranking isn't allowed'' ("N" refers to total number of non-write-in candidates in election)
!Number of candidates ranked ("R")
!Regular approach
!Negative counting
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|3N-6 [3, '''6+''']
|[3, '''6''']
|[2, 4, 5, '''6]'''
|-
|4
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Notes:
* For regular counting, a lower bound has been provided (
* For both negative and semi-negative counting, the numbers provided are a series that include both lower and upper bounds on the number of marks that have to be made, depending on
** For counting last-ranked candidates, see [[#Dealing with last-place candidates]]. If no marks are made for them, then a ballot that ranks all candidates requires the same number of marks as a ballot that ranks at least one less candidate i.e. all candidates except the last-ranked candidate(s). For example, a ballot that ranks 5 candidates when there are 5 candidates total can be thought of as ranking the top 4 candidates, and leaving the 5th candidate unranked.
** Semi-negative counting's performance is always better than or equal to negative counting's performance when the same number of candidates run and the same number of candidates are ranked in both approaches. As an example for a voter who ranks 2 candidates:
*** When only those 2 candidates run, then in both approaches, at least '''1''' mark needs to be made (to count the 1st choice; the 2nd choice can be skipped because they are ranked last).
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* 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.
==== 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]]. The regular approach requires [(number of candidates)-2] less marks if using this modification
However, when voters equally rank multiple candidates 1st, then whether or not the modification is still applied can make a significant difference in overall number of marks.
=== Election example comparisons ===
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