Abd ul-Rahman Lomax wrote:
"Demanding" is an odd word to use for "allowing." "Condorcet" doesn't
really refer to ballot form, though it is often assumed to use a
full-ranking ballot. In any case, a ballot that allows full ranking, if
it allows equal ranking and this causes an empty space to open up for
each equal ranking, is a ratings ballot, in fact. It's Borda count
converted to Range by having fixed ranks that assume equal preference
strength. Then the voter assigns the candidates to the ranks. It is
simply set-wise ranking, but the voter may simply rank any way the voter
pleases, and full ranking is a reasonable option, just as is bullet
voting or intermediate options, as fits the opinion of the voter.
If the range is too narrow or too wide, the equivalence fails.
For an example of the former, there's no way to express all possible
Range-4 ballots with a ranked ballot with three candidates, even if you
permit equal rank. To do so, you would have to be able to vote for
"Nothing", e.g.
A > B >> C, which is A > B > {} > C, which is A gets 4 pts, B gets 3, C
gets 1.
It works the other way as well: if you have five candidates, ranked
ballots expressing a full preference ordering cannot be converted to
Range-4.
----
Election-Methods mailing list - see http://electorama.com/em for list info
