Talk:Pairwise counting: Difference between revisions
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== Ways of speeding up pairwise counting ==
[[User:Kristomun]], I wanted to discuss your edit https://electowiki.org/w/index.php?title=Pairwise_counting&diff=next&oldid=9855. I later generalized the point that I was making, which you removed, so let me explain my generalization: if there are, say, 5 candidates A through E, and a voter bullet votes A, there is no need to record A's victory in all 4 matchups, because you can just say "A gets a vote in every match-up" and move on from that. This information can be stored in the cell comparing A to themselves. Likewise, if someone ranked A>B, you only need to record in addition "B gets a vote against everyone except A" which can be shown with a negative vote in the B>A column. In other words, instead of recording 4+3 matchups (A beats B through E and B beats C through E), the work can be shortened to recording 2+1=3 (2 votes for A and B in every matchup, and 1 negative vote for B>A) things. If there are a lot of candidates, this can create quite a lot of time savings. I should note that someone who votes A>B=C would need a negative vote for both B>C and C>B with this approach to preserve the accurate winning votes total in the B vs C matchup (though the margin will be accurate either way), so that's the only time it might require more markings than the regular approach. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 03:24, 12 April 2020 (UTC)
: It doesn't seem to gain you much. Suppose you're using a method like minmax. You need to determine the strength of each candidate's weakest pairwise showing (or the closest to a landslide in favor of the other candidate). If you've used a shortcut/speedup when noting the pairwise matrix, you still have to unpack that speedup, i.e. "decompress" the Condorcet matrix in order to determine the relevant pairwise contest for each candidate. And if you're doing that, you could just as well decompress the matrix as part of the counting procedure itself.
: In other words, suppose you happen upon a voter who bullet-votes for A. You can either indirectly mark that he bullet-votes for A by using negative counts, or you can just increment the entire A vs everybody row without looking at the ballot more than once. It seems to me that the latter is easier to do and less messy: that the benefit you get by speedup isn't as great as it seems because you have to translate into a canonical representation at some point anyway.
: 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]])
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