Talk:Pairwise counting: Difference between revisions
→Ways of speeding up pairwise counting
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: Perhaps it could be used as a sort of shorthand if lots of voters bullet-vote or only rank a few candidates each, out of very many candidates. But even so, the point remains that when you're done counting, you have to e.g. add 2917 to every A>X pairwise matrix cell if you recorded 2917 bullet votes for A. So this would make sense if adding 2917 to every one is significantly less expensive than adding 1 to every one, 2917 times, as part of the count. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 23:57, 14 April 2020 (UTC)
:: In the example in your second paragraph, we don't need negative counts to indicate a bullet voter; we can just say "A is marked on 1 ballot", and then we are done processing that ballot. The key thing I think you missed is that the unpacking happens at the central counting place using this approach, rather than in the precincts. So, for example, if there are 5 candidates, instead of the vote-counter marking A>B, A>C, A>D, A>E, the central counting place gets the information "A is marked on 1 ballot" and then they can unpack this by saying "OK so A must have gotten 1 vote in A>B, A>C, A>D, and A>E." Thus, the unpacking doesn't actually take any significant amount of work to do. Another thing that may have been misinterpreted is the negative count approach; you only need negative counts when a voter ranks one candidate above or equal to another candidate. So, for example, someone voting A>B only needs a negative vote recorded in B>A in order for us to figure out which matchups they don't prefer B in, because in all other matchups we know they prefer B, therefore we can just record that "B is marked on 1 ballot" and this one negative vote, which allows us to collectively say "B is preferred in every matchup except against A". Thus, it still only requires looking at the ballot once per candidate. Regarding your point in your third paragraph, it seems to me that it would always be significantly easier to record a bullet vote with only 1 marking rather than several? I made an example of this at https://www.reddit.com/r/EndFPTP/comments/fylh2p/how_are_elections_run_under_condorcet_reported/fn75b3g/ if it helps. A broader point I should mention is that, ignoring equal-rankings, this approach will always require at most a few more markings than the regular approach (at most it's the number of markings in the regular approach plus the number of candidates), and often will require far fewer. I'll show this for the 4-candidate case: if someone votes A>B>C>D, then in the usual approach, we do 3 markings for A's matchups, 2 for B's, and 1 for C's. With this approach, we do 4 markings, one for each candidate to indicate that they were ranked by the voter, and then we do 3 negative votes for D, 2 negatives for C, and 1 for B. Now, if this voter had only ranked A>B, then in the usual approach that's 3+2=5, whereas with this approach, it's 2+1=3. As the number of on-ballot candidates increase, the time-savings starts to possibly become worth it. Anyways, I think one thing we can probably agree on is that even if you're using the regular pairwise counting approach, it's smart to, for every voter who has only one 1st choice candidate, report the bullet votes for that candidate and skip counting that candidate's matchups, while still manually counting the matchups of all lower-ranked candidates. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 01:07, 15 April 2020 (UTC)
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