| > I thought Gibbard-Satterthwaite (or maybe just Gibbard's version) applied to cardinal systems as well. Correct, but it is also a weaker version of Arrow's (also as Clay points out, Arrow's isn't really about voting[0]...) > This seemed likely to me for some reason, as if an ordinal method could approximate any particular cardinal discretization by just including "ghost" candidates that can be packed (ordinally) between your actual candidates. Okay, but this just adds complexity. Cardinal is already simpler than ordinal systems (both for voters _and_ for those counting the votes). There's absolutely nothing wrong ranking candidates in a cardinal system (it's actually pretty unlikely that you'll have the same preference for multiple candidates so this is going to naturally happen). The difference? In cardinal you can better express your preference of one candidate over another (I give an example here[1]). So now we've added "encoding efficiency" to the added benefit of cardinal systems. Cardinal systems are better than ordinal systems in almost every single way (the only thing I can think of ordinal systems doing better at is that RP and Schulze perform better on maximal VSE, but as I discuss here[2] that is pretty limited as well as unlikely considering strategic voting and the ability to manipulate people exists). [0] https://news.ycombinator.com/item?id=27598975 [1] https://news.ycombinator.com/item?id=27599324 [2] https://news.ycombinator.com/item?id=27600248 |