Re: Another draft of A.6
On Fri, Nov 15, 2002 at 09:48:55PM -0500, Branden Robinson wrote:
> I am sorry if this tries your patience, but I do not understand this
> statement. Can you give an example with numbers? Specifically, I don't
> understand what would distinguish a "weak" pairwise tie from a non-weak
> one.
Well.. I'm not actually sure how to cook up a set of ballots which
gives me a non-weak tie.
However, consider the following propositions:
125:29 D:E
117:37 B:C
117:37 A:B
116:38 F:A
116:20 E:F
107:47 C:D
105:49 D:F
98:56 A:C
96:58 E:A
96:58 C:E
88:66 F:B
88:66 B:D
85:69 D:A
78:76 F:C
77:77 E:B
77:77 B:E
77:77 is a weak proposition since every other proposition has more
than 77 votes on one side of the comparison.
77:77 is also the weakest proposition since no proposition with 77
votes has more than 77 opposing votes. Obviously, if a tie is a weak
proposition, it has to be the weakest proposition.
If there had been a proposition like 76:75, then 77:77 wouldn't
be a weak proposition, because 76 is less than 77.
Does that help any?
--
Raul
Reply to: