On 6 May 2005 at 10:44 UTC-0700, Chris Benham wrote: > Ted, James (and anyone interested), > > In my last post (Thu.May5) I suggested this criterion: > > "If x wins, and afterwards some identical ballots that approve x > are uniformly changed only so that they approve more candidates > than previously; then if there is a new winner it must be one of > the candidates approved on these altered ballots." > > This is supposed to be a simple test for the property that approving > more candidates should never change the winner from an approved (on > the original ballots) candidate to a disapproved (on both sets of > ballots) candidate. > > This is very similar to this monotonicity-like criterion: > > "If x wins, and afterwards some ballots are changed only to > increase the approval scores of some other candidates; then if > there is new winner it must be one of the candidates whose > approval scores have been raised."
I was going to say that I didn't see why these were different. But now I see -- the difference is that in the first, the approval is extended on ballots that approve X, and in the second version, it can be any set of ballots, X-approving or not, and they don't have to be identical. > > Or maybe it is better to put it the other way: > > "If x wins, and afterwards some ballots are changed only to > decrease the approval scores of one or more other candidates; > then x must still win." > > Yes, this seems more succinct. But what to call it, "Mono-reduce > opposition approval"? But you lost me here. I'm don't think the two last definitions are equivalent. In the first mono-like criterion, X is the winner before approval-extension. In the second, X is the winner with expanded approval. Call the second winner Y instead, for clarity. Then if Y is the new winner after the first definition, the only way to go back is to remove approval for Y in the second definition. Also, are you assuming that when approval is extended it is being applied only to lower-ranked candidates than those already approved? That would be normal for ranked ballots with approval cutoff. > > Another criterion that applies to rankings/approval methods > interests me, which I might call "Disapproval Later-no-Harm": > > "Ranking a disapproved candidate must never harm an approved > candidate". > > (A stronger version would add "or a higher-ranked disapproved > candidate"). This is incompatible with Condorcet, and in a future > post I'll suggest a method that meets it. This goes around and around ... If you have such a method, I don't think it will satisfy the Condorcet Criterion. But I'm interested anyway ;-) -- araucaria dot araucana at gmail dot com ---- Election-methods mailing list - see http://electorama.com/em for list info
