User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
User:BetterVotingAdvocacy/Big page of ideas (view source)
Revision as of 23:33, 18 June 2020
, 4 years ago→Condorcet-cardinal hybrid methods
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Note that when demonstrating the result of [[Smith//Score]] or similar methods, it isn't necessary to discover the entire Smith set in every case to find the winner. This is because if you confirm that some candidate is in the Smith set, and they have more points than all other candidates (i.e. are the Score winner), then regardless of who else is in the Smith set, this candidate will win.
I'd say Smith//Score can essentially be thought of as "Score except it passes the [[mutual majority]] criterion". This is because, when there isn't a majority faction, [[burying]] is likely to create cycles so large that the election essentially is resolved using Score voting on the major candidates; but when there is one, the minority's burying can't prevent one of the majority-preferred candidates from always winning. In order to reduce the vote-counting work for Smith//Score, the "Rated or ranked preference" implementation of [[Rated pairwise preference ballot]] might be useful.
=== Rated pairwise preference ballot ===
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It might be useful to do negative counting by sequentially counting the ranks of a voter's ballot by starting at the last rank and going upwards. Note that, when a voter doesn't skip ranks, for them to have ranked a candidate last, they must have given that candidate a ranking number equivalent to the number of candidates (if equal ranking isn't allowed) or less than that (i.e. a "higher" rank).
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).
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