On Fri, 28 Sep 2007, Timothy Hunt wrote:
I can't think of any legitimate, deliberate, way of expressing one's
preference in the table that one can't express in a ranked list with
the ability to provide for "is equal to"
` A B C D E
A ` + + + +
B - ` + +
C - ` +
D - - ` +
E - - - - `
This table has no contradictions, and it's transitively complete -- you
can't deduce any more entries from those. But you can't express it as a
list.
It's *not* the list "A, BCD, E"; that would be the (different) table
` A B C D E
A ` + + + +
B - ` +
C - ` +
D - ` +
E - - - - `
and misses the fact that I prefer B to D.
Nor is it the list "A, B, C, D, E"; that says that I prefer B to C, and C
to D, which I don't.
You could express my table validly as a *set* of ballots. But you have to
be careful not to double-vote on any particular pair; that would throw off
the outcome.
You could express it as the not-a-list
C,
- A, E -
B,D,
I'm pretty sure you don't want people to mail you ballots that look like
that. :)
--Z
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