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
