"Since ranks do not allow for the arithmetic operations to do such calculations. As such there are no optimal Ordinal voting systems but only optimal Cardinal voting systems"
Actually there are optimal ordinal methods. They just work a bit differently. Here are two such methods: https://en.wikipedia.org/wiki/Schulze_STV https://en.wikipedia.org/wiki/CPO-STV
While they have STV in the name, they are not types of STV and instead reduce to Condorcet methods in the single winner case. CPOSTV works by comparing possible election outcome to every other possible election outcome and SchulzeSTV works by comparing every possible election outcome to every other possible election outcome that differs by only one candidate. To compute the results, both methods then plug these pairwise comparisons between election outcomes into single Condorcet methods as if the outcomes were individual candidates. They are even more computationally expensive then most optimal methods because instead of just having to consider every possible outcome, you now have to consider either every possible pair of outcomes or all the pairs of outcomes that differ by one candidate.
Also, there is an additional odd ball optimal ordinal system that does use a quality function like the optimal cardinal methods. It's actually Monroe voting. Monroe actually made the blunder of defining his method to work with Borda count such that the cost a result was the sum of the ranks voters have given towards the candidate their ballot is allocated to in the most optimal configuration of voters to candidates. The score version of Monroe's method is actually just a variant of it (a drastically superior variant). Because of this, perhaps we should split up the method into Cardinal Monroe's method and Ordinal Monroe's method to clear up any ambiguity when referring to the two methods.
"Sequential Cardinal Methods elect winners one at a time in sequence using a candidate selection method and a reweighting mechanism."
Not all sequential methods are defined this way. Case in point: sequential Ebert, sequentially shrinking quota (though I guess you could define these methods as the selection algorithm and make the re-weighting mechanism do nothing). Perhaps you should say that this is just a common way that they are defined. ParkerFriedland (talk) 08:28, 9 February 2020 (UTC)
- Hi ParkerFriedland. Well this is the whole point of a wiki page. I did my best writing this page and am not surprised there are some gaps or things needing clarification. I would not call Schulze_STV an optimal system. Optimal is not synonymous with "elects all at once" but classifies based on the fact that it optimizes a quality function. For a quality function to work it has to use real numbers not ranks. Of course you are right that using borda count would be a method to make an ordinal optimal system. But Monroe's method listed in the optimal systems. Maybe we just need a name for the class of systems like Schulze_STV which do not use borda so there is not quality function possible. Maybe there is one already, I have not studied them. I do not think optimal is fitting. You are right about the SSQ systems not fitting my definition of sequential. Of course SSQ did not exist when I wrote that and I did not know of the others which did. Anyway, I have posed on the forum about the "new class" of sequential systems. There are these select/reweight type and then the other. Please help make the page better. Also, the Monroe's method page needs some attention. I would suggest that both the ordinal and cardinal variants are discussed on the same page. Psephomancy has been pushing for a better taxonomy/categorization of systems. It is going to be tricky. Look at this post --Dr. Edmonds (talk) 18:10, 10 February 2020 (UTC)