[EM] strategy-free Condorcet method after all!

[Dave Ketchum]

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

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).