Let’s say that I want to define the winning sets of an election for n seats in the manner of sequential STV but using the beat paths as defined by Schulze STV, that is I want to define a winning set of n candidates as a set that has a beat path to every other set of n candidates that differ from it by one candidate (instead of to every other set of n candidates with no restriction). Can this be efficiently done?

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. -- Andrew Ross Hyman wrote: > Let’s say that I want to define the winning sets of an election for n seats in the manner of sequential STV but using the beat paths as defined by Schulze STV, that is I want to define a winning set of n candidates as a set that has a beat path to every other set of n candidates that differ from it by one candidate (instead of to every other set of n candidates with no restriction). Can this be efficiently done? >

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.