Pairwise counting: Difference between revisions

[[File:Pairwise counting procedure.png|thumb|The procedure for pairwise counting with various ballot formats and examples.]]One potentially useful trick is to, for each voter who has only one 1st choice, report who their 1st choice is, and then skip the pairwise counting for all matchups involving that candidate. So for example, if 3 voters vote A>B>C, then only the fact that there are 3 1st choices for A and 3 voters who prefer B>C need be recorded; this is because a voter prefers their 1st choice to all others, so it can be inferred that 3 unique 1st choices for A means 3 votes for both A>B and A>C. This can be used to save a lot of time for vote-counting in elections where most voters only report a few of their top preferences. It is possible to do this even for voters who equally rank multiple candidates 1st; someone who votes A=B>C>D could either be considered to support (A, B) or be considered two separate voters voting A and B each as their 1st choice. Note that the latter approach, while it won't change the margin in the matchup between A and B, and thus won't change who wins in their matchup, will make the vote totals inaccurate. For example, if there was a matchup of 2 to 1 in favor of A>B, and then 100 A=B voters are added to the election, then the matchup would become 102 to 101, which maintains the margin but changes the ratio from 66.66% in favor of A to just over 50%. So to balance this out, it's possible to record a negative vote in the A vs. B matchup to counter the fake positive vote added by treating the indifferent voter as separate voters i.e. 100 votes would be subtracted from both A>B and B>A.