[EM] My Favorite Deterministic Condorcet Efficient Method: TACC

[Kristofer Munsterhjelm]

Kathy Dopp wrote:

> What does "clone free" mean again please?

It means that if people always vote a certain set of candidates next to 
each other, but not necessarily in the same order, the probability that 
the win comes from that set is independent of how many are in that set. 
It's intended to model resistance against vote-splitting and teaming: if 
a party splits in two or two parties always voted next to each other 
join, and nothing else happens, it won't affect the outcome.

> It is a little tricky to count, not very intuitive, so I wonder how to
> explain it so most people could understand its logic?  The logic seems
> solid.

You might do it by saying that the method admits stronger and stronger 
candidates into the set, according to the base method (Approval in this 
case), until it finds the strongest candidate that is also strong (beats 
the other members) in the pairwise sense.

The problem, however, would be to explain why having a candidate that is 
strong in both respects is desirable, and better than a candidate that 
is stronger in one respect but not strong at all in the other.

> It is precinct-summable with an n x n matrix (n = # candidates) using
> the diagonal for the # approval votes for each candidate.  Not sure
> how to do the sampling mathematics for post-election audits - might be
> a challenge to figure out how to limit the risk of certifying an
> incorrect candidate.
> 
> Do you have a multi-winner version or a proportional representation version?

I imagine you could run CPO-STV on this - as you could with any other 
summable Condorcet method - but it would lose its summability properties 
and would not be polynomial in space or time, nor would it be monotone.

Making a PR method that reduces to a Condorcet method in the 
singlewinner case, yet is polytime, seems to be very hard. For that 
matter, making a PR method that's polytime and monotone (and better than 
SNTV) seems very hard as well.