[EM] Re: Approval/Condorcet Hybrids

[Ted Stern]

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.

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?

Ted
-- 
 Ted Stern                               
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