[EM] strategy-free Condorcet method after all!

[robert bristow-johnson]

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                  rbj at audioimagination.com

"Imagination is more important than knowledge."




> On Nov 17, 2009, at 8:53 PM, fsimmons at pcc.edu 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).