User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
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Revision as of 18:07, 15 July 2020
, 3 years ago→Negative pairwise counting approach
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=== Rated pairwise preference ballot ===
(See the rated pairwise preference ballot subsection of the vote-counting section below for more information on how to count the votes with this ballot type)
It is possible to treat every pairwise matchup as being a [[Score voting]] match-up where the voter can score both candidates on a scale. In this sense, the traditional pairwise preference idea of a voter giving one vote to their preferred candidate in a match-up is akin to them giving the max score to that candidate, and a min score to the other candidate. This may make it easier to think about the rated support and pairwise support that are both allowed with the [[rated pairwise preference ballot]].
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A basic justification for using some kind of pairwise counting procedure where every candidate a voter ranks 1st can be counted with only one mark each: suppose you use the "rated or ranked preference" implementation of [[Rated pairwise preference ballot]], and a voter does [[min-max voting]] with their scores and casts a rated preference. This voter would only need one mark to count each candidate they gave a max score to, and no marks for the min-scored candidates. And in effect, this voter is giving one set of candidates maximal support against all candidates not in the set, while casting no preference between the candidates in the set, which is equivalent to ranking them 1st and all other candidates last. But, if this voter were to switch to now casting a ranked preference, the vote-counters would have to increase the number of marks they count for the voter's ballot, while not essentially capturing any different information (except that the voter would now be essentially treated as giving 0 votes to both candidates in the matchup between two equally-ranked candidates, rather than potentially giving both of them 1 vote i.e. because they might have max-scored both).
==== Semi-negative counting procedure ====
Technically, the markings required for the negative counting approach can be reduced almost by half in the following manner: when a voter ranks a candidate last, make no marks for them. When a voter ranks a candidate one rank above last, the only mark made is that the voter prefers this candidate over the last-place candidate; this way, rather than marking negative votes in almost all of this candidate's matchups, only one mark has to be made. And so on. For ballots that rank all candidates, the top-ranked half of the candidates would be counted negatively, while the bottom-ranked half would be counted in this way. But this could potentially be more confusing and/or require more data storage (i.e. separately counting the negative and positive pairwise votes for each candidate).
When doing the "semi-negative" counting procedure mentioned in the previous paragraph, some voters will be able to contribute votes to both candidates in a matchup, while other voters won't, purely based on how highly or lowly they ranked them. If this creates legal or procedural issues, it is possible to have each precinct only submit the [[Margins|margin]] they found in every pairwise matchup, rather than the votes on both sides as well. In other words, if, for the A vs B matchup, in Precinct 1 A has 15 votes and B 10, while in P2 A has 7 and B 8, then it is possible for P1 to submit that A has 5 votes more than B, and P2 to submit that B has 1 vote more than A. This can be used to find that A has 4 votes more than B in the combined electorate of the two precincts.
===== Rated pairwise preference ballot =====
For the rated pairwise ballot, semi-negative counting can sometimes be beneficial, but there is some nuance in how to apply it. Take the following two rated pairwise votes for example (on a scale of 0 to 5):
A:5 B:0, B:5 C:0 (so A:5 C:0)
A:5 B:4, B:5 C:3 (transitivity implies something like A:5 C:2)
For the former vote, it'd be easier to assume the voter gave the max score to every candidate in each matchup, and then do negative counting i.e. count it as
{| class="wikitable"
|+
!
!A
!B
!C
|-
|A
|5
|
|
|-
|B
| -5
|5
|
|-
|C
| -5
| -5
|5
|}
Note that with a scale of 0 to 1, this particular example looks exactly like negative pairwise counting as applied to a ranked ballot.
For the latter vote, it'd be easier to assume the voter is somehow constantly scoring the candidates in each matchup, and then only add or subtract points in as necessary i.e.
{| class="wikitable"
|+
!
!A
!B
!C
|-
|A
|5
|
|
|-
|B
|
|4
| +1
|-
|C
| -1
|
|3
|}
So it's as if the voter had filled out a rated ballot, with the only difference being that they gave B 1 more point in the B vs C matchup than would normally be allowed, which then forced the voter to give C 1 less point against A (depending on how you implement the ballot design and transitivity requirements).
==== Examples ====
| |||