[EM] Schulze STV question

[Kristofer Munsterhjelm]

On 01/15/2017 07:19 PM, Andrew Myers wrote:
> CIVS has an (implemented) proportional mode that operates over sets of
> candidates (http://civs.cs.cornell.edu/proportional.html) and it does
> get used. However, in principle it can be much less efficient than
> regular Condorcet for the reasons Markus identified.

An interesting challenge: Find a method that works like Schulze STV or 
proportional CIVS (that is, compares assemblies) but there is some 
convexity or other structure to the assembly scores so that a local 
search (or a polytime search of some other form) is guaranteed to find 
the optimal assembly, while the system as a whole still obeys desired 
properties like Droop proportionality, monotonicity, teaming 
independence, etc.

I suspect that (very handwavy) to achieve a certain type of 
proportionality, you have to solve a set covering problem. Certainly, 
set covering appears in a lot of PR problems (e.g. Monroe). But it might 
be doable to settle for less than perfect proportionality while still 
being Condorcet and obeying the DPC.

STV-ME (the STV version of BTR-IRV) is Condorcet in the single-winner 
case and I think it passes the DPC, but it can't be easily formulated as 
an assembly-vs-assembly method. It's not monotone either.