On May 16, 2010, at 9:50 AM, Kristofer Munsterhjelm <[email protected]
> wrote:
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.
Of course not. The equivalent Range ballot is Range 2, not Range 4.
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.
Incorrect. To allow full ranking, for N possible candidates, you
need Range(N-1). Number of ratings = number of ranks. With 5
candidates, the Range ballot needed for full ranking is indeed Range
4. If the voter does not equal rank, the ballot is a Borda ballot.
Borda works as a method to the extent that preference strength
between adjacent ranks is equal, or averages to equal. Borda breaks
down when this assumption breaks down. True clones with pure Borda
cause ratings to fall for all lower-rated (ranked) candidates,
whereas with Range (Borda with equal ranking and thus empty ranked
allowed) ratings are independent.
Borda is a Range method with a peculiar restriction. That
restriction made sense when it was assumed that the only relevant
information was rank order. It is really the same error as vote-for-
one, which works fine when a majority is required....
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