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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?


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