Rated pairwise preference ballot: Difference between revisions
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The matchup between A and B is treated as weak because both candidates come before the threshold (i.e. the voter only gives 0.2 more votes to A than B, which is their scored preference of (5-4)/5=1/5th or 0.2 votes; keep in mind that when changing the scale from 0 to 5 to 0 to 1, the scores of 5 and 4 become 1 and 0.8 respectively, which is what you see in the pairwise table. It is also possible to put 0.2 and 0 instead, which captures only the margin and not the winning votes for the matchup), while all other matchups are treated as maximal (despite, for example, A>C only having a scored preference of (5-2)/5=3/5th or 0.6 votes, it is instead treated as a maximal preference of 1 vote).
It is possible to allow for multiple preference thresholds on a single ballot, such that the matchups between candidates in between thresholds aren't maximized, but all other matchups are. For example, a voter voting A:5 B:4 | C:3 D:2 | E:1 | could have the A vs B and C vs D matchups treated as weak, but the A>C and D>E preferences, for example, treated as strong. Fractional preference thresholds can even be applied; see fractional optimization below.
=== Fractional optimization ===
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The main voting methods with which this ballot type can be used in the single-winner case are the [[:Category:Pairwise counting-based voting methods]].
If using an implementation of this ballot type involving a single rated ballot, with the additional goal of using the rated information in its direct form as well (i.e. you're using the pairwise information to find the Smith set and the rated information to find the Score winner in [[Smith//Score]]), then it may be useful to include an [[approval threshold]] so that a voter trying to express a pairwise preference without expressing rated support for a given candidate can do so.
== References ==
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