[EM] Fwd: Duncan Proposal Draft

[Kristofer Munsterhjelm]

I'm having some trouble sending mail directly to you - adam.com.au 
bounces my mail. So I'm leaving your mail address off the To field; EM 
should send it to you in turn.

On 2023-10-14 18:10, C.Benham wrote:
> Kristofer,
> 
>> This is not feedback on the draft as such, but the results of my 
>> strategy vulnerability tests with CTE-Borda (which I'm guessing this is).
>>
>> My implementation uses bubble sort, which I understand is the same as 
>> sink sort (see e.g. https://xlinux.nist.gov/dads/HTML/sinkSort.html). 
>> I asked you if it's different, but I didn't got a response. If what 
>> you mean by "sink sort" differs from bubble sort, my results may be off. 
> 
> The definition of "sink sort" includes (from the link you gave):
>> *Definition:*Sort by comparing each adjacent pair of items in a/list/ 
>> <https://xlinux.nist.gov/dads/HTML/list.html>in turn, swapping the 
>> items if necessary...
> 
> As I understand the items in the list are in order of whatever (in this 
> case Borda count) with the highest-ordered at the top of the list.
> 
> Sink sort starts at the top and "sinks" down it, while "bubble" sort 
> starts at the bottom and moves up  (the same direction as bubbles in 
> water) it.

In that case, I am indeed implementing sink sort. My code starts at the 
top and swaps pairs that are out of order, repeating from the top, until 
it finishes a whole pass without swapping anyone.

> The choice of one over the other seems arbitrary to me.
> 
> The concise (i.e. minus the redundant preamble) definition given by 
> Forest of this "Duncan" method suggestion is
>> ..elect the highest score candidate that pairbeats every candidate
>> with lower score.
> I'm not sure of the exact definition of "CTE-Borda" but I don't think 
> Duncan is the same thing.  Nor is it Sink-Sorted Borda  or Bubble-Sorted 
> Borda or Margins-Sorted Borda.

Yeah, I was just going by Forest's previous discussion of the Condorcet 
Takedown Elimination method. Looks like I jumped the gun.

Now that I think about it, mine is ever so slightly different from 
theirs; perhaps it makes a difference. It shouldn't in a three candidate 
case at least. Forest and Mike's is:

1. Elect the undefeated candidate when there is one ... else ...
eliminate any candidate that defeats no other candidate ... and ...
2. List the remaining candidates in order of their Nominal Favorability 
Score" NFS.
3. Update the list by Sink Sorting it pairwise.
4. Let P (for Pivot) be the candidate that has sunk to the bottom of the 
list.
5. Eliminate P along with any candidates defeated by P.
6. While more than one candidate remains, repeat steps 2 through 5.
7. Elect the uneliminated candidate.

And mine is:

1. Elect the CW if there is one.
2. Eliminate the Condorcet loser if there is one. (not every weak CL)
3. List the remaining candidates in order of some base method ranking 
(scores aren't needed for comparison-based sorting).
4. Sink sort this list pairwise.
5. Eliminate the bottom-ranked candidate on the list along with 
everybody he beats pairwise.
6. If more than one candidate remains, go to *step 1* (not step 3!)
7. Otherwise elect the sole remaining candidate.

> Believe it or not, it is simply  "elect the Smith-set member with the 
> lowest Borda score".
> 
> (Someone please correct me if I have that wrong.)

Suppose we have an A>B>C>A cycle and the Borda ranking is A>B>C. The 
Smith set is {A, B, C}. But the highest ranking candidate who beats 
everybody ranked below him would be B, not C, since B beats C pairwise. 
So B would be elected. I think.

But I wouldn't imagine this is monotone? Suppose B wins here. Then let B 
be upranked so that the Borda ranking becomes B>A>C (still an A>B>C>A 
cycle). Then C wins because A doesn't beat C pairwise.

I'll have to check its burial performance with quadelect later.

-km