User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting (view source)
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[[Approval voting]] can be thought of as a [[Smith-efficient]] [[Condorcet method]] (i.e. one type of pairwise voting method) where, when a voter approves a candidate, they are assumed to vote for them in every head-to-head matchup against other candidates (see [[Self-referential Smith-efficient Condorcet method]]). Further, approving a candidate can be thought of as ranking them 1st, while disapproving a candidate can be thought of as ranking them last.
* 60 voters rank A=B (can be thought of in an Approval voting context as: 60 voters approve A and B)
This has the advantage of, when every voter does [[bullet voting]], being counted exactly like an [[FPTP]] election (one mark per ballot for the candidate it marked), which also shows that FPTP can be thought of as a constrained form of Approval. ▼
* 40 voters rank B=C (i.e. 40 voters approve B and C)
In both Approval voting and Condorcet systems, B is the winner. However, the traditional vote-counting procedure in Condorcet systems requires much more work and data storage than the vote-counting procedure used in Approval voting:
{| class="wikitable"
|+Condorcet (pairwise counting) values ''italicized'' (with pairwise winner of each matchup bolded), Approval voting values <u><big>underlined</big></u> (with the Approval voting winner bolded)
!
!A
!B
!C
!D
!E
|-
|A
|<u><big>60</big></u>
|''0''
|'''''60'''''
|'''''60'''''
|'''''60'''''
|-
|B
|'''''40'''''
|<u><big>'''100'''</big></u>
|'''''60'''''
|'''''100'''''
|'''''100'''''
|-
|C
|''40''
|''0''
|<u><big>40</big></u>
|'''''40'''''
|'''''40'''''
|-
|D
|''0''
|''0''
|''0''
|''0''
|''0''
|-
|E
|''0''
|''0''
|''0''
|''0''
|''0''
|}
* In this election, a total of 200 tally marks are made if counting the votes in an Approval voting-style (calculation: one has to count the 60 approvals for A + 100 approvals for B + 40 for C), but 600 tally marks need to be made if using regular pairwise counting (calculation: add up all the italicized values in the above table).
* The final election ranking of the candidates (as in, which candidate performed best, 2nd best, etc. in the election) is the same in both most Condorcet systems and in Approval voting: B>A>C>D=E.
Thus, it is clear that an Approval-voting-style vote-counting procedure could be applied in at least some election scenarios in order to obtain pairwise information from non-Approval-Voting ballots (at least, enough pairwise information to know the final election ranking/[[Smith set ranking]] for that election). However, a complexity arises in many election scenarios which makes the Approval voting vote-counting procedure unusable: when voters are allowed to rank candidates, they are allowed to express more than two levels of preference, which allows them to indicate that they don't prefer certain candidates in certain matchups, while still preferring those candidates in other matchups (i.e. a voter who ranks "A>B>C" can indicate that B is superior to C but inferior to A; this can't be done on an Approval voting-style ballot); thus, counting "negative votes" is necessary during the vote-counting procedure in order to record that lack of preference/dispreference for those middle-ranked candidates in matchups against higher- (or even equally-)ranked candidates.
▲
===Comprehensive example===
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