thanks, Juho, for this summary.
On May 9, 2010, at 2:24 PM, Juho wrote:
All classical Condorcet methods can handle equal rankings and their
impact has been analyzed quite well.
Usually the discussion focuses on how to measure the strength of the
pairwise preferences. This is the next step after the matrix has
been populated. The two most common approaches are margins and
winning votes.
- Let's define AB = number of votes that rank A above B
- In margins the strength of pairwise comparison of a A against B
is: AB - BA
- In winning votes the strength of pairwise comparison of a A
against B is: AB if AB>BA and 0 otherwise
- Note that in margins ties could be measured either as 0:0 or as
0.5:0.5 since the strength of the pairwise comparison will stay the
same in both approaches
The most common (/classical) Condorcet methods give always the same
winner if there are three candidates and all votes are fully ranked.
If there is no Condorcet winner then the candidate with smallest
defeat will win. The strengths of the defeats (and therefore also
the end result) may differ in margins and winning votes if there are
equal rankings.
do you mean that marginal defeat strength can differ if equal rankings
are allowed compared to if equal rankings are not allowed? that, of
course is true. but if you mean that marginal defeat strength is
different where equal ranks are counted (as votes for both candidates)
vs. if they are not counted (for both candidates), then i think i
disagree. that's one reason why i think that marginal defeat strength
is a more salient measure than simply the number of winning votes in
each pairing (as a metric to be used in resolving a cycle).
--
r b-j [email protected]
"Imagination is more important than knowledge."
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