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If you're going to use [[:Category:Pairwise counting-based voting methods|Category:Pairwise counting-based voting methods]], I encourage considering using [[Pairwise counting#Negative vote-counting approach]] and [[Rated pairwise preference ballot]].
This page is a loosely organized page for various ideas that might be of interest.
Some ideas:▼
== Description of some common Condorcet methods ==
Here are some how-to guides on using different voting methods for your own elections.
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Find the Smith set. Whoever has the most approvals in it wins.
== Finding the CW faster ==
Some examples of finding the Condorcet winner faster:
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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.
== Miscellaneous ==▼
▲Miscellaneous
One criterion that might be good for PR methods is the "Duplicated Quotas" criterion: if a PR method elects some candidate in the single-winner case, and the ballots are "duplicated" N times, then if N+1 seats are to be filled, the duplicated winner should win. Example for Condorcet PR:
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B and E are the duplicated winners, since they're Condorcet winners when ignoring all of the voters who ranked the other.
Discussion on how to use Approval and Condorcet for legislative votes, including the ideas of "approval threshold" (how many people need to support an action being taken for it to happen; by default, it's a majority) and "concession threshold" (if an idea has a certain significant amount of support, you can indicate that you will switch from opposing to supporting it): https://www.reddit.com/r/EndFPTP/comments/futa9q/comment/fmmfulq?context=1▼
== Condorcet ==
It is arguable whether a voter can have maximal preferences between more than one transitive pair of candidates. Utilitarianism says if you maximally prefer A to B, then you must not prefer B to C, while Condorcet says you can for as many pairs as you like. An interesting method that goes one step away from utilitarianism towards Condorcet is "3-slot/tiered Smith//Approval": the voter may rank each candidate either 1st, 2nd, or last, and may approve either only their 1st choices, or also their 2nd choices. With only 1 tier, this would reduce to regular Approval voting.▼
A basic reason to prefer [[:
It is likely possible that the [[tied at the top rule]] can be made to work with something like Smith//Approval.▼
=== Connection between Condorcet, Smith set, and Asset ===
One way to understand, Condorcet, Smith, and [[Asset voting]]: imagine you're having a discussion where you have to discuss one option at a time. So, one option, at any given point in time, "dominates the discussion". However, people can bring up other options one at a time, and then depending on the mood of the group, the group decides to discuss one option or the other. The group may discuss options for as long as they like, and can discuss the same options multiple times. If you start off with an option that is not in the Smith set, what you'll find is that if everyone is maximally intransigent i.e. doesn't yield any ground, then the majority-preferred option between any two options will always begin to dominate the discussion, resulting eventually in a matchup between a non-Smith option and Smith option where the Smith option must win. Now, because the Smith option is preferred by more people than any non-Smith option, a non-Smith option simply can't return to the discussion i.e. all of the Smith options will beat it any time a non-Smith option comes up for consideration. If people have weaker preferences, or don't vote in all of the matchups, this can bias the Smith set itself to being more utilitarian i.e. a minority can start to win certain matchups, resulting in the group trending closer to preferring the Score winner than the Condorcet winner or the Smith set candidates.▼
=== Condorcet PR ===
Here is an example illustrating the difficulty of creating a Condorcet multiwinner method along the lines of RRV:
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B is the CW, so they'd win the first seat. If their supporters' ballots are reweighted by half, then C pairwise beats A 48.5 to 34 and wins, despite A being bullet voted by a Droop quota. One complicated way of possibly fixing this is to, after electing B, say that if B hadn't been in the election, C would have been the winner, and therefore both B and C voters' ballots should be reweighted by half since they both rank C above all candidates other than B (A), thus allowing A to beat C 34 to 33.
== Negative pairwise counting approach ==
▲It is likely possible that the [[tied at the top rule]] can be made to work with something like Smith//Approval.
▲Discussion on how to use Approval and Condorcet for legislative votes, including the ideas of "approval threshold" (how many people need to support an action being taken for it to happen; by default, it's a majority) and "concession threshold" (if an idea has a certain significant amount of support, you can indicate that you will switch from opposing to supporting it): https://www.reddit.com/r/EndFPTP/comments/futa9q/comment/fmmfulq?context=1
▲One way to understand, Condorcet, Smith, and [[Asset voting]]: imagine you're having a discussion where you have to discuss one option at a time. So, one option, at any given point in time, "dominates the discussion". However, people can bring up other options one at a time, and then depending on the mood of the group, the group decides to discuss one option or the other. The group may discuss options for as long as they like, and can discuss the same options multiple times. If you start off with an option that is not in the Smith set, what you'll find is that if everyone is maximally intransigent i.e. doesn't yield any ground, then the majority-preferred option between any two options will always begin to dominate the discussion, resulting eventually in a matchup between a non-Smith option and Smith option where the Smith option must win. Now, because the Smith option is preferred by more people than any non-Smith option, a non-Smith option simply can't return to the discussion i.e. all of the Smith options will beat it any time a non-Smith option comes up for consideration. If people have weaker preferences, or don't vote in all of the matchups, this can bias the Smith set itself to being more utilitarian i.e. a minority can start to win certain matchups, resulting in the group trending closer to preferring the Score winner than the Condorcet winner or the Smith set candidates.
▲It is arguable whether a voter can have maximal preferences between more than one transitive pair of candidates. Utilitarianism says if you maximally prefer A to B, then you must not prefer B to C, while Condorcet says you can for as many pairs as you like. An interesting method that goes one step away from utilitarianism towards Condorcet is "3-slot/tiered Smith//Approval": the voter may rank each candidate either 1st, 2nd, or last, and may approve either only their 1st choices, or also their 2nd choices. With only 1 tier, this would reduce to regular Approval voting.
Negative counting approaches can be applied to various voting methods. For example, it's possible to reserve a special mark in Score voting that indicates that a voter have every non-write-in candidate the max score, and then count negative scores for the voter in such a way as to reproduce their actual scores. The practicality of this would likely be limited to ballots that max-score nearly all of the candidates, though.▼
▲A basic reason to prefer [[:Category:Condorcet-cardinal hybrid methods|Category:Condorcet-cardinal hybrid methods]] over most other Condorcet methods (or at least, over the [[:Category:Defeat-dropping Condorcet methods|Category:Defeat-dropping Condorcet methods]]) is that they allow the voters who prefer a CW to defend that candidate without needing to do Favorite Betrayal as much (though there may be errors with this analysis). As a general example, suppose there are two main candidates, with one being the CW, and there are some 3rd parties without about half as many pairwise votes in favor of them as the main candidates. The voters who prefer the losing main candidate can bury the CW under the minor candidates, and in the ensuing cycle, the non-CW main faction will win. There isn't anything that voters who prefer the CW as 1st choice can do to fix this, but the voters who rank a 3rd party 1st and the CW above the non-CW main candidate can do FB to prevent their favorite candidate from pairwise beating the CW. This ends the cycle and allows the CW's pairwise victory over the other main candidate to take precedence again. In rated Condorcet methods, however, FB isn't quite as necessary if the CW [[majority-beat]]<nowiki/>s the non-CW main candidate; this is because those who prefer the CW can do [[Min-max voting]] to give the CW maximal points by the majority and the non-CW no support by a majority; this will guaranteeably give CW enough points to win. More specific example of this at <ref>https://www.rangevoting.org/CondStratProb.html</ref> and some explanation of how majorities can force their preference in rated methods in the [[Approval voting]] article.
It's possible to fit both [[Negative vote-counting approach for pairwise counting]] info and rated info in a pairwise matrix by either creating a cell for each candidate that holds both pieces of info, or creating a separate column to contain one of the pieces of info. Example:
{| class="wikitable"
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When doing negative pairwise counting, it's possible to count 1st choices separately from other ranks, with voters who rank multiple candidates 1st potentially being counted separately too. See [[Pairwise counting#Uses for first choice information]].
=== Examples ===
Here's a bit of a farcical example that shows just how much better negative pairwise counting can be than regular pairwise counting (taken from <ref>https://www.reddit.com/r/EndFPTP/comments/fylh2p/how_are_elections_run_under_condorcet_reported/fn1vztw/</ref>): a 2018 election in Washington state involved 28 candidates <ref>https://en.wikipedia.org/wiki/2018_United_States_Senate_election_in_Washington</ref>. For simplicity's sake, suppose there had only been 100 voters in that election, with 80% of them ranking 5 candidates and 20% ranking all 28 candidates. (See the "Formula for number of marks that need to be made" section in the negative counting article for info on the following calculations.)
* Under negative counting, at least '''8,760''' marks would be made.
** Calculation: 378 * 20 + 15 * 80
*** The 378 comes from (1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27). The 15 is from adding the first 5 values in this calculation, 1+2+3+4+5.
* Regular counting would require '''148,600''' marks.
** Calculation: 6930*20+125*80
*** The 6930 comes from 27+53+78+102+125+147+168+188+207+225+242+258+273+287+300+312+323+333+342+350+357+363+368+372+375+377+378
**** This calculation comes from 27+26+25+24+23+22+21+20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1. For example, 78 is the 3rd number in the above calculation, and comes from adding the first 3 values in this calculation, 27+26+25.
*** 125 comes from 27+26+25+24+23 (see previous bullet point).
* Miscellaneous:
** FPTP would've required '''100''' markings.
** Supposing voters scored every and only every candidate they ranked, Score voting would have required '''960''' marks (28*20 + 5*80).
Some caveats are that the work in the regular approach could have been reduced significantly because many of these candidates could have potentially been left off of the ballot if there had been tighter ballot access requirements, and the number of rankings could have been limited (i.e. voters could have been given only 5 ranks to put the candidates into), which would make some voters have to equally rank more candidates. These factors also reduce the amount of work for the negative counting approach to some extent.
=== Negative counting in non-pairwise methods ===
▲Negative counting approaches can be applied to various voting methods. For example, it's possible to reserve a special mark in Score voting that indicates that a voter have every non-write-in candidate the max score, and then count negative scores for the voter in such a way as to reproduce their actual scores. The practicality of this would likely be limited to ballots that max-score nearly all of the candidates, though.
See also <ref>https://forum.electionscience.org/t/possible-trick-for-counting-spav-and-cardinal-pr-faster/657</ref>
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