Pairwise counting: Difference between revisions

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== AnotherExample exampleusing withrated numbers(score) ballots ==
 
Suppose there are five candidates A, B, C, D and E.
If there are five candidates A, B, C, D and E, and two voters submit the ranked ballots A>B>C, this means that they prefer A over B, B over C, and A over C, with (if it is assumed unranked candidates are ranked equally last) all three of these ranked candidates being preferred over either D or E.
 
IfUsing thereranked are five candidates Aballots, B, C, D and E, andsuppose two voters submit the ranked ballots A>B>C, thiswhich means that they prefer A over B, B over C, and A over C, with (if it is assumed unranked candidates are ranked equally last) all three of these ranked candidates being preferred over either D or E. This assumes that unranked candidates are ranked equally last.
If, for the same example, those two voters instead submit [[Rated voting|rated ballots]] of A:5 B:4 C:3 (meaning A is given a score of 5, B a 4, and C a 3, with D and E left blank), pairwise preferences can be inferred from this as well; because A is scored higher than B, and B is scored higher than C, it is known that these ballots indicate that A is preferred to B, B to C, and A to C, and (if blank scores are assumed to mean the lowest score i.e. usually a 0) all 3 over D and E.
 
If,Now forsuppose the same example, those two voters instead submit [[Rated voting|rated ballots]] of A:5 B:4 C:3, which (meaningmeans A is given a score of 5, B a score of 4, and C a score of 3, with D and E left blank),. pairwisePairwise preferences can be inferred from thisthese asballots. well; becauseSpecifically A is scored higher than B, and B is scored higher than C,. itIt is known that these ballots indicate that A is preferred toover B, B toover C, and A toover C,. and (ifIf blank scores are assumed to mean the lowest score, i.e.which is usually a 0), allthen 3A and B and C are preferred over D and E.
 
In a pairwise comparison table, this can be visualized as (organized by [[Copeland]] ranking):
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([https://star.vote star.vote] offers the ability to see the pairwise matrix based off of rated ballots.)
 
PartialPairwise pairwisecounting comparisonsalso can be done using [[Choose-one voting]] ballots and [[Approval voting]] ballots, but such ballots do not supply information to indicate that the voter prefers their 1st choice over their 2nd choice, that the voter prefers their 2nd choice over their 3rd choice, and so on.
 
== Election examples ==
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