[EM] Re: Finding the probable best candidate?

[Adam Tarr]

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 beleive 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.

This is not to say that Ranked Pairs is certainly better; only that it is very 
different and I don't see any intuitive reason why the outcomes of the Ranked 
Pairs method of breaking cyclic ties would bear any strong resemblance to the 
BSBS method of breaking cyclic ties.  I would not be surprised to see an example 
where BSBS does a better job than Ranked Pairs of producing an intuitively 
correct result.

Finally, let me add that I don't think Ranked Pairs is the best tie-breaker 
either... I think Mike's Shwartz Sequential Dropping is better.  The only 
differences as far as I can tell are that
1) You only deal with the Smith Set
2) You consider number of voters in favor of the defeat, not the margin of the 
defeat.

Months before I joined this list, I corresponded briefly with Mike Ossipoff and 
Russ Paielli about examples I had cooked up that seemed to create problems for 
Condorcet.  At the time, I did not realize the distinction between Ranked Pairs 
and SSD, and some of my seemigly undesireable results hinged on this.

-Adam