User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
User:BetterVotingAdvocacy/Big page of ideas (view source)
Revision as of 08:20, 30 June 2020
, 4 years ago→Miscellaneous
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A quick note: It can be seen that the top two lines rank only S or K above MB, and the top two lines are a majority. So one way to quickly figure out who won would've been to compare S and K to MB, and if MB pairwise beats them, then it is guaranteed that MB won, because when ignoring S and K, a majority prefer MB over all others. This is a demonstration of how Condorcet methods' attempts to make majority rule maximally comply with [[IIA]] helps in analyzing election scenarios.
== Score voting ==
One way to explain [[normalization]] for scored ballots is that a voter attempts to put the maximal margin between every pair of candidates, while still preserving their relative strength of preference between each pair of candidates. Specifically, this means that you try to give your favorite the maximal margin (1 vote i.e. [max score - min score] points) against your least favorite.▼
One way to understand why a voter should give maximal support to their lesser evil if their favorite isn't viable: if, whenever a candidate is very unlikely to win, the voter pretends they aren't in the election i.e. got eliminated, then eventually the voter will have a candidate who is their "favorite of the remaining candidates". If they are normalizing, then they ought to give this candidate the max score, and likewise give their least favorite of the remaining candidates (i.e. the greater evils) a 0.▼
It might help when thinking about using negative scores in [[Score voting]] to imagine a Score scale of -1 to 0. This would be equivalent to Approval voting, essentially.▼
== Miscellaneous ==
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One way to think about how large the difference in required markings can be between pairwise counting and IRV is to consider an election scenario with a candidate who is a majority's 1st choice, where voters rank every candidate. In both Condorcet and RCV, the majority's 1st choice will win, but in RCV, only the 1st choices of each voter need be counted, resulting in one mark per ballot, while with pairwise counting, supposing there are 10 candidates, at a minimum 25 marks will need to be made per ballot (see [[Negative vote-counting approach for pairwise counting#Semi-negative counting procedure]]). However, pairwise counting will give more detailed information as to how much support each candidate has overall.
When designing a digital interface for the rated pairwise ballot, it's possible to use various software features to highlight the constraints on how a voter can vote. For example, if the voter submits an incorrect A>C preference, then their A>B and B>C preferences could be highlighted on the screen, with an indicator to show why the three preferences don't line up. Similarly, if the voter indicates a maximal margin for A>B and prefers B>=C, then the software can "fill out" the voter's ballot to put a maximal margin in favor of A in every matchup where the voter prefers B to the other candidate (For clarity purposes, the software should probably indicate, perhaps with colors or something, which matchups the voter filled out and which ones were auto-filled).▼
▲One way to explain [[normalization]] for scored ballots is that a voter attempts to put the maximal margin between every pair of candidates, while still preserving their relative strength of preference between each pair of candidates. Specifically, this means that you try to give your favorite the maximal margin (1 vote i.e. [max score - min score] points) against your least favorite.
For rated pairwise, when there are 7 candidates, at least 21 lines are required on the ballot where the voters can score each matchup. When there are more than 7 candidates, it can be more practical to have the voters rank/score each candidate individually (like in Score voting) with only up to 6 [[slot]]<nowiki/>s offered, and then below that, allow the voter to indicate how they'd score the candidates in a matchup between their 1st choice and 2nd choice, 2nd choice and 3rd choice, etc. This is because with 8 candidates, at least 28 lines would be needed for each and every matchup, but with this compression trick, instead 8 lines are needed for each candidate's score/rank, and then 15 lines are offered to allow the voter to indicate their pairwise preference between candidates in each of the 6 gradations, for a total of 23 lines. From here, one line is added for each additional candidate i.e. 24 lines would be needed for 9 candidates, etc. As a bonus, voters who only fill out the ranked/scored section of the ballot and not the pairwise part can simply have their rankings/scores counted directly as their pairwise preferences (see the "Ranked or rated preference" implementation of the rated pairwise ballot). Also see <ref>https://www.reddit.com/r/EndFPTP/comments/fcexg4/score_but_for_every_pairwise_matchup/fvxnqmj/?context=3</ref>.▼
▲One way to understand why a voter should give maximal support to their lesser evil if their favorite isn't viable: if, whenever a candidate is very unlikely to win, the voter pretends they aren't in the election i.e. got eliminated, then eventually the voter will have a candidate who is their "favorite of the remaining candidates". If they are normalizing, then they ought to give this candidate the max score, and likewise give their least favorite of the remaining candidates (i.e. the greater evils) a 0.
With rated pairwise, if a candidate receives a score from the voter in some matchups but not all, the highest score they got in any matchup could be considered the voter's score for them in every matchup involving that candidate where the voter indicated no preference. Alternatively, it could be the highest score the candidate gets in any matchup where the voter prefers them in the matchup more than or at least equally as the other candidate in the matchup. In other words, if there are 4 candidates and the voter votes A:5 B:4, B:1 C:0, A:5 C:0, then it could be assumed the voter would vote B:1 D:0 rather than B:4.<blockquote>Is it possible to do FPTP and IRV with rated pairwise? Fundamentally, you'd have to be limited to giving only your 1st choice(s) any rated pairwise support at a given point, and the main question is whether or not, with such a constraint, Condorcet cycles can still occur. Cycles can't occur when voters are assumed to give their 1st choices maximum pairwise preference over all other candidates (and no support to any other candidates), but could that change if voters give weak preferences in some matchups in favor of their 1st choice? Also, supposing no intransitivity, how should a voter's vote change, if at all, between rounds in IRV? </blockquote>The answer to the above appears to be no. Here's an example:▼
▲It might help when thinking about using negative scores in [[Score voting]] to imagine a Score scale of -1 to 0. This would be equivalent to Approval voting, essentially.
1 voter: A>B 60%, A>C 70% (A>B>C)
▲When designing a digital interface for the rated pairwise ballot, it's possible to use various software features to highlight the constraints on how a voter can vote. For example, if the voter submits an incorrect A>C preference, then their A>B and B>C preferences could be highlighted on the screen, with an indicator to show why the three preferences don't line up. Similarly, if the voter indicates a maximal margin for A>B and prefers B>=C, then the software can "fill out" the voter's ballot to put a maximal margin in favor of A in every matchup where the voter prefers B to the other candidate (For clarity purposes, the software should probably indicate, perhaps with colors or something, which matchups the voter filled out and which ones were auto-filled).
1: B>A 40% B>C 100% (B>A>C)
▲For rated pairwise, when there are 7 candidates, at least 21 lines are required on the ballot where the voters can score each matchup. When there are more than 7 candidates, it can be more practical to have the voters rank/score each candidate individually (like in Score voting) with only up to 6 [[slot]]<nowiki/>s offered, and then below that, allow the voter to indicate how they'd score the candidates in a matchup between their 1st choice and 2nd choice, 2nd choice and 3rd choice, etc. This is because with 8 candidates, at least 28 lines would be needed for each and every matchup, but with this compression trick, instead 8 lines are needed for each candidate's score/rank, and then 15 lines are offered to allow the voter to indicate their pairwise preference between candidates in each of the 6 gradations, for a total of 23 lines. From here, one line is added for each additional candidate i.e. 24 lines would be needed for 9 candidates, etc. As a bonus, voters who only fill out the ranked/scored section of the ballot and not the pairwise part can simply have their rankings/scores counted directly as their pairwise preferences (see the "Ranked or rated preference" implementation of the rated pairwise ballot). Also see <ref>https://www.reddit.com/r/EndFPTP/comments/fcexg4/score_but_for_every_pairwise_matchup/fvxnqmj/?context=3</ref>.
1: C>A 80% C>B 60% (C>B>A)
The result is that A>B (A pairwise beats B) with 0.6 votes to 0.4, B>C 1 to 0.6, and C>A 0.8 to 0.7. So there's a cycle, with all of the voters each only supporting one candidate.
▲Is it possible to do FPTP and IRV with rated pairwise? Fundamentally, you'd have to be limited to giving only your 1st choice(s) any rated pairwise support at a given point, and the main question is whether or not, with such a constraint, Condorcet cycles can still occur. Cycles can't occur when voters are assumed to give their 1st choices maximum pairwise preference over all other candidates (and no support to any other candidates), but could that change if voters give weak preferences in some matchups in favor of their 1st choice? Also, supposing no intransitivity, how should a voter's vote change, if at all, between rounds in IRV?
Here is an example of a situation where, if voters are assumed to normalize their scores, it is possible to justify a non-majoritarian winner even with only ranked preferences: suppose there are very many voters, with there being a majority faction only one voter larger than an opposing minority faction. The majority's preference is A>B>C>etc. while the minority bullet votes B. In this case, B would almost guaranteeably win in Score under the above assumptions, even if decimal scores were allowed, so long as the majority's preference for B was non-infinitesimal, since this would cut into their ability to express their A>B preference.
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