Trying to sort this out:
Llull never heard of cycles, and did not have enough data to
think of others doing more complex methods centuries later.
River has the data, and Jobst explains, while describing River,
that having defeat data, sorting defeats, and discarding defeats
related to cycles, can result in a system competitive with the best
other Condorcet methods.
When Jobst wrote of "reverse Llull" his big topic was strategy.
I do not see the protection that River included mentioned as attended
to.
Seems to me that cycles can occur even with sincerity - they relate to
conflict among three or more voter views.
Dave Ketchum
On Nov 19, 2009, at 7:55 PM, [email protected] wrote:
Dave,
Jobst, the inventor of River, is well aware of the cycle problem,
and Jobst
would never advocate public use of a Condorcet method that failed
clone loser,
for example, but as near as I know his simple reverse Llull method
is the first
Condorcet method that gives zero incentive for insincere rankings,
even if
complete rankings are required (at least generically). As a
corollary, it
satisfies the Strong FBC. No other extant Condorcet method does
even that.
In other words it is a benchmark method.
It gives us something to shoot for; a clone free version of the
same, for
example. The complicated method you referred to was my crude
attempt at that.
Forest
Dave Ketchum Wrote ...
Took me a while, but hope what I say is useful.
Jobst had good words, except he oversimplified.
Centuries ago Llull had an idea which Condorcet improved a bit -
compare each pair of candidates, and go with whoever wins in each
pair. Works fine when there is a CW for, once the CW is found, it
will win every following comparison.
BUT, in our newer studying, we know that there is sometimes a cycle,
and NO CW. Perhaps useful to take the N*N array from an election and
use its values as a test of Jobst's rules:
There may be some comparisons before the CW wins one. Then the
found CW will win all following comparisons.
BUT, if no CW, you soon find a cycle member and cycle members
win all following comparisons, just as the CW did above.
Summary:
We are into Condorcet with ranking and no approval cutoffs.
Testing the N*N array for CW is easy enough, once you decide
what to do with ties.
Deciding on rules for resolving cycles is a headache, but I
question involving anything for this other than the N*N array - such
as the complications Jobst and fsimmons offer.
Dave Ketchum
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