[EM] Re: Finding the probable best candidate?

[Forest Simmons]

On Wed, 20 Feb 2002, Adam Tarr wrote:

> Forest wrote:
> 
> >(1) Bubble sort starts from the top and works down: If the Borda order is 
> >    A > B > C , then Bubble compares A and B first, and then advances C as
> >    far up as possible, one comparison at a time. So in circular ties
> >    Bubble can alter the Borda order if the Borda order is opposite to the
> >    cyclic order.
> 
> My mistake.  So my examples were wrong.  In a three way cyclic tie, 3rd in Borda 
> can never win; whoever wins the first vs. second matchup wins.  For more 
> complicated cyclic ties, the lowest candidate who beats every candidate above 
> them wins.  This seems reasonable, I suppose.
> 
> >(2) Borda's strategic problems are no worse than those of Ranked Pairs
> >    when it comes to three way circular ties.  In other words, Black is as
> >    good as Ranked Pairs in three way races.
> 
> I believe this is not the case.  Ranked Pairs is (at least in some
> cases) more 
> clone independent.  Adding a candidate to the race that is listed just after one 
> of the leaders on every ballot will boost that leading candidate's Borda count, 
> while not changing anything in the pairwise matchups.  If this boost brings the 
> candidate from third to first in a three-way cyclic tie, they will win the 
> election where they would have lost it.

But adding a candidate changes the race from three way to four way. Note
that I didn't claim that Black was as good as Ranked Pairs in four way
races.

In three way races Black, Ranked Pairs, and SSD all give the same answer
if there are no truncations, so none has any possible advantage over the
others in three way races without truncations.

It seems to me that SSD's advantages are mostly due to truncation serving
as an Approval cutoff detector, although the winning vote aspect, and the
"chain is no stronger than the weakest link" idea probably contribute. I'm
not an expert on the fine points of SSD and Ranked Pairs.

I certainly don't consider Borda Seeded Bubble Sort to be in the same
league as the big boys. 

As I said before, I don't believe in pure preference ballot methods. Like
Demorep I think we have to look at both the pairwise preferences and the
Approval scores to get good results in the gamut of cases that are likely
to happen.

And (as I said before) the only reason I proposed Bubble Sorted Borda was
to find a simple method that would beat Black along the same lines as
Black.  After I forgot about it Rob LeGrand reminded me of the unfinished
business. 

I thought it would be a good way of introducing the idea of Bubble
sorting, which can be applied to other seedings (Bubble Sorted Approval,
Bubble Sorted CR, etc.) and make use of pairwise matrices from other
style ballots such as Five Slot Grade Ballots and Dyadic Ballots.

To set the record straight I owe an apology to Tom Ruen.  As I remember,
his proposal of "Inverse Nanson" was the impetus for my suggestion of
Borda Seeded Single Elimination, later modified to Bubble Sorted Borda.

After experience with all of these four (and other closely related) 
methods I believe that Inverse Nanson (an iterated form of Borda Runoff)
is the best of these four methods based on Borda. 

Forest