Talk:Ranked voting: Difference between revisions

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:: I would go a step futher to distinguish them. I saw the statement above and condidered changing it just yesterday. There are at least three ways I can think of the statement that "Cardinal ballots are a subset of Ordinal ballots" is wrong. In terms of number /group theory they are distinct and do not share overlapping theory. In terms of information theory Cardinal ballots capture more informaiton so at best an argument that "Ordinal ballots are a subset of Cardinal ballots" could be made but I would not think that was useful. In terms of social choice theory it considered different ballot types. To make a statement like this would at least require a source which uses the terms in this way. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 05:07, 13 April 2020 (UTC)

::: I'd actually argue rated and ranked ballots are a subset of a ballot type where you're allowed to indicate your strength of preference in each and every head-to-head matchup between the candidates i.e. for each pair, how strongly you prefer each candidate. So in essence, a rated ballot but allowing you to indicate the scale anew for every matchup. I've written about this at [[Order theory#Strength of preference]] to try to define what transitivity might look like with such a ballot. But it seems worth documenting, perhaps on its own separate page, since it is a generalization of choose-one, approval, ranked, and rated ballots, and thus it captures the ideal of the amount of information that a voter should be able to provide in a voting method. Condorcet methods are the only type of voting methods that I can think of that can handle the information offered by such a ballot, though. (To further categorize the voting methods, as I've written before at [[Score voting#Connection to Condorcet methods]], Score and Approval are subsets of Condorcet methods where there is a restriction in place such that the voter's preference can be represented by points, rather than needing to be separated out into individual head-to-head matchups (i.e. if you say A is maximally better than B, then you can't say B is better than C on a rated ballot)). [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 06:45, 13 April 2020 (UTC)

::: I'd actually argue rated and ranked ballots are a subset of a ballot type where you're allowed to indicate your strength of preference in each and every head-to-head matchup between the candidates i.e. for each pair, how strongly you prefer each candidate. So in essence, a rated ballot but allowing you to indicate the scale anew for every matchup. I've written about this at [[Order theory#Strength of preference]] to try to define what transitivity might look like with such a ballot. But it seems worth documenting, perhaps on its own separate page, since it is a generalization of choose-one, approval, ranked, and rated ballots, and thus it captures the ideal of the amount of information that a voter should be able to provide in a voting method. Condorcet methods are the only type of voting methods that I can think of that can handle the information offered by such a ballot, though. (To further categorize the voting methods, as I've written before at [[Score voting#Connection to Condorcet methods]], Score and Approval are subsets of Condorcet methods where there is a restriction in place such that the voter's preference can be represented by points, rather than needing to be separated out into individual head-to-head matchups (i.e. if you say A is maximally better than B, then you can't say B is better than C on a rated ballot)). To further elaborate on this, consider that in a matchup between two candidates, putting one at the max score and the other at the min score is equivalent to ranking one above the other i.e. if everyone does this, you just get majority rule. So, with this generalized "cardinal pairwise" ballot, you can indicate ranked preference between every candidate by, for example, "ranking" your 1st choice maximally above every other candidate in matchups, etc. To express rated preference, you just use the same score for a candidate in every matchup they have against another candidate as you would on a rated ballot for them. To express choose-one and Approval preferences, give the candidate(s) you'd mark on those ballots maximal scores in every matchup, and all other candidates minimal scores. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 06:45, 13 April 2020 (UTC)

: I think we conflate many things when we talk about [[election method]]s. This community seems to break up the tabulation strategies for electoral methods into two big categories: ordinal and cardinal. We also have two categories of ballots: ranked and rated. The two categories are orthogonal; that is, it's entirely possible to tabulate an election conducted with rated ballots using an ordinal method. In fact, that was my strategy with [[Electowidget]]. Moreover [[STAR voting]] is a hybrid of ordinal and cardinal tabulation methods. So to answer [[User:BetterVotingAdvocacy|BVA]]'s question: I believe that it would be difficult to tabulate ranked ballots using cardinal methods, though I suppose that's what the [[Borda count]] is. -- [[User:RobLa|RobLa]] ([[User talk:RobLa|talk]]) 05:16, 13 April 2020 (UTC)