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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