Ted, I had written:
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."
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"?
You responded (Fri.May6):
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.
Yes, the two definitions may not be exactly equivalent, but they convey the same idea. I would say that normally a method that meets one would meet the other.
Ted:
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.
Yes.
I also wrote: 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.
Ted: "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 ;-)"
CB: The method I had in mind when I wrote that I've since rejected, sorry. Also, sorry list for somehow accidentally sending my last post three times.
Chris Benham
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