[EM] Proportional Representation from Ratings Ballots

[Kristofer Munsterhjelm]

Brian Olson wrote:
> There's been recent discussion of STV and multi-seat methods, and wanted 
> to chime in again with my contribution.
> 
> I have a pet election method which I think is the greatest thing ever 
> and I call it "Instant Runoff Normalized Ratings". It shows favorably in 
> opinion-space diagrams*, simulated expected utility, and strategic 
> voting resistance. (* It has runoff discontinuities, but they're much 
> smaller than IRV due to using ratings, floating point math, and looking 
> at the whole ballot at once instead of just first-choice-votes.)

While we're talking about our own methods, I'd like to note that my 
recent "forced clustering" approach can be applied to Range votes as 
well - or for that matter, any system where the single-winner objective 
is to minimize (or maximize) the sum of some measure.

The bad news is that the approach is not in polytime (well, unless P = 
NP or there's some pattern I've missed). For Kemeny, the runtime is 
horrible, but for Borda/Range/etc, one can use brute force "test all 
councils" - still slow, but not *that* slow.