User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
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Revision as of 07:28, 21 May 2020
, 4 years ago→Formula for counting the required number of marks to be made
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== Comparison to other vote-counting procedures ==
It can also be useful to compare these results to the amount of vote-counting work that would be done in other voting methods.
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** 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.
* '''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.
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.
Example with a voter voting A>B=C>D with 6 candidates:
{| class="wikitable"
|+Negative counting values ''italicized'' and <small>smaller</small> (with optional negative counting values ''italicized'' but regular-size),
Regular approach values bolded and <big>enlargened</big>
!
!A
!B
!C
!D
!E
!F
|-
|A
|''<small>1 ballot</small>''
|<big>'''1'''</big>
|<big>'''1'''</big>
|<big>'''1'''</big>
|<big>'''1'''</big>
|<big>'''1'''</big>
|-
|B
|''<small>-1</small>''
|''<small>1 ballot</small>''
|''(1 equal-ranking)''
|<big>'''1'''</big>
|<big>'''1'''</big>
|<big>'''1'''</big>
|-
|C
|<small>''-1''</small>
|''(1 equal-ranking)''
|''<small>1 ballot</small>''
|<big>'''1'''</big>
|<big>'''1'''</big>
|<big>'''1'''</big>
|-
|D
|<small>''-1''</small>
|<small>''-1''</small>
|<small>''-1''</small>
|''<small>1 ballot</small>''
|<big>'''1'''</big>
|<big>'''1'''</big>
|-
|E
|
|
|
|
|
|
|-
|F
|
|
|
|
|
|
|}
The negative counting values can clearly be used to reproduce the values created by the regular approach (see the Math part of the [[#Description]]), whereas the regular approach leaves each of the cells used by the negative approach blank (i.e. with a value of 0). In either approach, the values in each cell can be added up per ballot; see the [[#Comprehensive example]] section.
The "(1 equal-ranking)" part indicates that one voter equally ranked B and C; this value is optional in the negative counting approach (and is never used in the regular approach), but can be included if it is desired to have traditional pairwise totals, by using it to give both B and C negative votes in the B vs C matchup (see the [[#Dealing with equal-ranking]] section).
==== Formula for counting the required number of marks to be made ====
| |||