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 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)
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