[EM] Condorcet divisor method proportional representation

[Kristofer Munsterhjelm]

Kathy Dopp wrote:
> Thanks Kristofer.  I ignored the "all* in "all others".
> 
> I must say then, I simply do not like the Droop quota as a criteria
> because it elects less popular candidates favored by fewer voters
> overall and eliminates the Condorcet winners some times. The Droop
> quota seems to go hand in hand with IRV and STV methods.

Then the question you should ask is where you want to balance 
proportionality and majoritarianism. When dealing with multiwinner 
elections, there are two objectives that work against each other. On the 
one hand, you'd want proportionality, so that variation in the 
electorate is reflected by variation in the assembly or council. That 
is, you'd like it to have members that some people like a lot. On the 
other, you'd want quality across the board, i.e. candidates that every 
voter can like to some extent.

This, as my simulations show, gives a tradeoff scale (on the Pareto 
frontier). At one end, the only thing that matters is that 
proportionality is accurately reproduced (consider an assembly that's 
elected by lot, and that it's large enough to be representative). At the 
other, the only thing that matters is what the electorate as a whole 
thinks of the council (which would give a majority party, even a 51% 
one, every single seat; or even a well-liked minority party every single 
seat, Range style).

The Droop criterion pulls in the direction of proportionality. Like the 
mutual majority criterion says that a majority can control the single 
outcome in a singlewinner method, the Droop proportionality criterion 
says that, if you consider each seat to have a "majority", each 
"majority" (Droop fraction) should be able to control the winner of that 
seat. In doing so, it can go against the wishes of a larger group: it 
satisfies a proportion of the electorate to a greater extent at the cost 
of satisfying the whole electorate less on average.

(As someone who thinks proportional representation is important, I think 
  the people may actually get a better result, on the whole, by PR. 
However, that kind of additional benefit arises from the dynamics, such 
as minor parties or independents checking major parties. That is quite 
hard to model, so when I mentioned "satisfying the whole electorate" 
above, I was referring to "according to the preferences the voters gave 
in the election".)