[EM] electing a variable number of seats

[Kristofer Munsterhjelm]

fsimmons at pcc.edu wrote:
> Andy,
> 
> I like the idea of iterating RRV to infinity to find the weights for a weighted voting system.  
> 
> And of course,interpreted stochastically. it also gives another solution to Jobst's consensus challenge.
> 
> I doubt that it is always the same as the Ultimate Lottery.  Probably an example where sequential PAV 
> differs from PAV would show that.

Do you think the non-sequential version would be equivalent to the 
Ultimate Lottery?

And since I don't recall, how do you measure the quality of a given lottery?

> I suspect that, unlike sequential PAV and RRV, both ordinary PAV and the Ultimate Lottery may be 
> computationally NP-complete.

If you're lucky, the NP-complete problem may still be feasible in 
practice. For instance, I implement both Kemeny and Young's method in 
Quadelect, and in the vast majority of the time, the linear programming 
relaxation is already optimal. In the other few cases (unless you're 
dealing with extreme numbers of candidates and voters), branch-and-bound 
finds a solution in reasonable time.