[EM] A very simple quota method based on Bucklin

[Kristofer Munsterhjelm]

As the subject says, this is a very simple multiwinner method that's 
based on Bucklin. I referred to it in another post, and so I think I 
should explain how it works:

Inputs are ranked ballots. Each voter starts with a weight of one. The 
quota is Droop (Hare does much worse).

As in Bucklin, start counting first place votes, then second place, and 
so on. Equal ranks may either count as one vote for each, or as a 
fractional vote for each.

At some point, the counts of one candidate will exceed the quota. That 
candidate is elected. If more than one are above quota, pick the one who 
has the most votes. If they're still tied, break by the first round 
where their numbers differed. If they're still tied, break the tie based 
on a single-winner method, or flip a coin, or somesuch.

For all of those voters that voted for the winner, reweight their 
weights by (new weight = old weight * (votes for winner - quota)/(votes 
for winner)).
Don't alter the quota, but in all other respects, restart the election 
with the winner removed from all ballots, as if he never entered. Keep 
on doing this until enough candidates have been elected.

That's it. For the single-winner case, the method reduces to Bucklin, 
which is monotonic. I'm not sure if the method is monotonic in the 
multiwinner case as well, but I think so.

According to my simulation, the method isn't as proportional as STV.