Rated pairwise preference ballot: Difference between revisions
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==Implementations ==
These are ways to use the rated pairwise ballot that limit expressiveness, but still collect more information than other ballot types. They are mostly listed in order of simplicity for vote-counting.
===Rated or ranked preference===
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|8.4
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|}Note that if every voter indicates rated preferences, the [[Smith set]] of the collected pairwise preferences will be the Score winner (or the candidates tied with the most points), while if every voter indicates ranked preferences, it will be the regular Smith set.
|}If using [[:Category:Condorcet-cardinal hybrid methods]], or any voting method where you want to store both the candidate's actual score and their support in head-to-head matchups, it is likely best to store the scores of each voter in one of two separate data values in each candidate's cells i.e. if a voter expressed a rated preference, put their score for a candidate only in the "rated preference" value, but if they expressed a ranked preference, put the score only in the "score for candidate" value. So, for example, a voter expressing a ranked preference who scored candidate A a 5 would be treated as giving A 0 points in the "rated preference" data value but 5 points in the "score for candidate" data value (which could be read as "0, 5" in the A>A cell). This would then be tabulated by giving each candidate as many points as they have in the rated preference data value i.e. a candidate with 51 points in the rated preference value and 37 in the score value would have those values treated such that, supposing a max score of 5, 51/5=10.2 votes would be added to all of their pairwise matchups in favor of them, and 51 points would be added to their score value to find that they have 88 points overall. This actually is easier to count than having to do pairwise counting with only ranked ballots, because for each voter who expresses a rated rather than a ranked preference, their support for a candidate in a head-to-head matchup can be summarized as one data value (the score for the candidate) rather than up to (number of candidates - 1) data values (i.e. the fact that they give that candidate 1 vote in each head-to-head matchup against a lower-ranked candidate).▼
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===Preference threshold===
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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).
A voter who sets their preference threshold at the same score they gave their favorite candidate or higher is essentially casting a rated-preference ballot, while if they set it at the lowest score, they are casting a ranked ballot.
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. ▼
▲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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A:5 B:3 C:2 at 60% optimization
This would become an optimized preference of 76% or 0.76 votes for A>B, 68% for B>C, and 84% for A>C. This is derived by looking at how far apart the rated preference and maximal preference values are, applying the % of optimization to this difference, and adding the resulting value to the rated value. So for example, A>B is a rated preference of (5-3)/5=2/5ths or 40% strength. That is 60% shy of 100%, and 60% optimization multiplied by this 60% difference is 36%, which added back to the rated preference of 40% yields 76%.
0% optimization is equivalent to a rated ballot, while 100% is equivalent to a ranked preference. <blockquote>Note that when designing a ballot to allow voters to indicate strength of preference in pairwise matchups, it could be done by allowing the voters to rank or score the candidates themselves, and then indicate "between your 1st choice(s) and 2nd choice(s), what scores would you give to each in a pairwise matchup?" or "between the candidates you scored (max score) and the candidates you scored (max score - 1), what scores would you give in their pairwise matchups?", etc. Here is an example of one such setup: <ref>{{Cite web|url=https://www.reddit.com/r/EndFPTP/comments/fcz3xd/poll_for_2020_dem_primary_using_scored_pairwise/|title=r/EndFPTP - Poll for 2020 Dem primary using Scored Pairwise Matchups|website=reddit|language=en-US|access-date=2020-04-28}}</ref> and some discussion: <ref>{{Cite web|url=https://www.reddit.com/r/EndFPTP/comments/fimqpv/adjusting_pairwise_matchup_margins_to_favor/fkkldcl|title=r/EndFPTP - Comment by u/Chackoony on ”Adjusting pairwise matchup margins to favor higher-utility candidates”|website=reddit|language=en-US|access-date=2020-04-28}}</ref></blockquote>
==Notes ==
The idea of the rated pairwise ballot is to allow voters to indicate their strength of preference, while not being limited to expressing only one
There is most likely no simple way to create a PR method using rated pairwise ballots, partially because there are no good summary statistics to describe voters' preferences with these ballots (i.e. one voter's 1st choice may be given a different strength of preference in some matchups than another voter's, etc.) Possibly such a thing could be aided by, when some number of winners are desired, allowing voters to express preferences between [[winner set]]<nowiki/>s rather than only pairs of candidates, though this is likely much less practical.
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]].
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