User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
User:BetterVotingAdvocacy/Big page of ideas (view source)
Revision as of 22:39, 19 June 2020
, 4 years ago→Negative pairwise counting approach
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An interesting thing to note is that vote-counters may already be doing negative counting in their heads when doing the regular counting approach. This is because when, say, a counter marks a voter's preferences for their 2nd choice, they have to remember not to mark any preference for 2nd choice>1st choice or 2nd choice>2nd choice. This may seem easy, but consider that only a moment ago, that same counter was likely marking the voter's 1st>2nd preference, which in a horizontally oriented matrix is a cell that is directly above or below 2nd>2nd. More generally, the counter starts off by marking willy-nilly the voter's preference for 1st choice against each and every other candidate, but then has to remember to reduce the number of marks they make for every sequentially ranked candidate by one, while in the negative approach they increase it by one.
One issue that can pop up in negative pairwise counting is that, for a voter who ranks every candidate, the vote-counter might accidentally count negative votes for the last-ranked candidates. This doesn't hurt the accuracy of the count, but it can make things significantly slower (specifically, it makes negative counting slower than regular counting when voters rank every candidate); there is no need to count negative votes for last-ranked candidates, since they are not ranked above anyone, and thus can be ignored (One way to think about it is that if the voter hadn't ranked those last-rank candidates at all, they'd have the exact same effect on the election, ignoring write-ins, and no marks would be counted for those last-rank candidates in that case). Here are some ways vote-counters can mentally avoid making that mistake:
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). ▼
▲* 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).
* The ballot itself can be made to have one rank less than the number of candidates. For example, if there are 6 candidates, then only allow voters to rank candidates from 1st to 5th. This doesn't functionally change anything, since a voter wishing to rank some candidate last simply needs to rank the other 5 candidates in any order, and then not rank that particular candidate; because they aren't ranked, they will be treated as if they were ranked last. The reason this would help is because the last-ranked candidate(s) wouldn't be marked on the voter's ballot.
** Note that this trick doesn't always work if equal-ranking is allowed; this is because, for example, with 6 candidates, the voter could rank one of them 1st and 5 of them 2nd; the 2nd-ranked candidates would all functionally be ranked last.
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).
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