On Nov 18, 2009, at 6:25 PM, Dave Ketchum wrote:
BUT, in our newer studying, we know that there is sometimes a
cycle, and NO CW.
there certainly *can* be a cycle. since Condorcet is not yet used in
governmental elections there is no track record there to say
"sometimes". have there been cases in organization elections (like
Wikipedia and those listed in http://en.wikipedia.org/wiki/
Schulze_method#Use_of_the_Schulze_method ) that evidently use a
Condorcet method. are there historical cases where there were cycles
with any of those organizations? or is it only the hypothesizing of
election method scholars and commentators? sure, we can create
pathological cases where there is a cycle, but does it really happen?
i'm not saying it can't be expected to; when i voted for IRV for
Burlington VT in 2005, i thought to myself that it would not likely
ever elect a non-CW when a CW exists because we know that if the CW
would have to be eliminated before the final IRV round. that didn't
happen in 2006, but that is exactly what happened in Burlington in
2009. so pathologies can happen even if we might guess they happen
rarely.
but are there actual elections in some organizations where there was
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.
the outcome of resolving a Condorcet paradox should never depend on
the chronological order that pairs are considered. if the method
does involving starting with a particular pair and proceeding to
another pair (like Tideman would), it should come up with the same
result, no matter which pair you happen to consider first. and if a
CW exists, the method should always pick the CW.
--
r b-j [email protected]
"Imagination is more important than knowledge."
On Nov 17, 2009, at 8:53 PM, [email protected] wrote:
Here's a way to incorporate this idea for large groups:
Ballots are ordinal with approval cutoffs.
After the ballots are counted, list the candidates in order of
approval.
Use just enough randomly chosen ballots to determine the Lull
winner with 90%
confidence: let L(0) be the candidate with least approval. Then
for i = 0, 1,
2, ... move L(i) up the list until some candidate L(i+1) beats L
(i) majority
pairwise (in the random sample). If the majority is so close that
the required
confidence is not attained, then increase the sample size, etc.
Then with the entire ballots set, apply Jobst's Reverse Lull
method: Start with
candidate A at the top of the approval list. If a majority of
the ballots rank
A above the Lull winner (i.e. the presumed winner if A is not
elected) then
elect A. Otherwise, go down the list one candidate to candidate
B. Let L be the
top Lull winner with approval less than B. If a majority of
ballots rank B
above L, then elect B, else continue down the list in the same way.
In each case the comparison is of a candidate C with the L(i) with
the most
approval less than C's approval.
If the decisions are all made in the same direction as in the
sample, then the
Reverse Lull winner is the same as the Lull winner, but
occasionally (about ten
percent of the time) there will be a surprise.
If a voter knew that her ballot was going to be used in the
forward Lull sample,
she would be tempted to vote strategically. But in a large
election, most
voters would not be in the sample, so there would be little point
in them voting
strategically. If sincerity had any positive utility at all, it
would be enough
to result in sincere rankings (in a large enough election).
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