From: Ted Stern <[EMAIL PROTECTED]> Subject: Re: [EM] Re: Approval/Condorcet Hybrids To: Jobst Heitzig <[EMAIL PROTECTED]> Cc: election-methods-electorama.com@electorama.com, Ted Stern <[EMAIL PROTECTED]>
On 11 Jan 2005 at 14:40 PST, Jobst Heitzig wrote:
But ... your argument that, if W differs from A, this implies "that W beat every candidate that A beats head to head" does not follow. It only implies that W has highest approval in U(A).
No, Forest is right, he defined:Let U(A) be the set of uncovered candidates that cover the approval winner A.
Hence every member of U(A) not only defeats A but covers A (or is equal to A), so it defeats all candidates A defeats, by definition!
Unless I'm confusing something, "cover" doesn't mean direct defeat. It means there is a beatpath of length 1 or 2.
A beat path of length 1 or 2 to each other candidate means "uncovered."
If A covers B then A beats (in one step) every candidate that B beats (in one step).
Maybe I'm arguing myself in circles. U(A) is the set of candidates that cover A. If this set is of size > 1 and includes at least one candidate besides A, they don't cover each other. If W has highest approval in that set, there might be another candidate that defeats W. I guess I wanted to say that W doesn't have a particularly strong property other than the highest approval one.
BTW, how does one choose the Dutta minimal covering set from the set of uncovered candidates?
I'll let Jobst answer this one.
Forest ---- Election-methods mailing list - see http://electorama.com/em for list info
