[EM] Request comments on MMP?

[Neal Finne]

John B. Hodges wrote:

> (JBH) I went with odd numbers because Ireland amended their procedure 
> to specify odd numbers, I presume they had a reason. I suppose it was 
> to avoid ties between two major parties. If you had a lot of four-seat 
> districts and two leading parties you could get a two-party 
> legislature permanently deadlocked. 

I looked at this possibility using Washington State 2002 congressional 
elections. We have nine districts, redistricted by a nonpartisan 
committee, so there should be a natural geographic distribution of 
beliefs. I gave all the Green votes to the Dems and split the 
Libertarian votes evenly between Reps and Dems. This resulted the Dems 
winning the aggregate vote with 53.8%. Hypothetically, if I calculated 
the STV totals (assuming party-line votes) with an even number of seats 
per district, the Dems would be underrepresented. I calculated the 
results for 1-9 seats/district, using Droop and Hare quotas. If you'd 
like to see the graph of this, I can send you a gif.

-- Droop Quota --
Seats/District, Dem% of Seats, Overrepresentation
1, 66.7%, 12.9%
2, 50.0%, (3.8%)
3, 59.3%, 5.5%
4, 50.0%, (3.8%)
5, 53.3%, (0.5%)
6, 52.7%, (1.1%)
7, 54.0%, 0.2%
8, 52.8%, (1.0%)
9, 53.1%, (0.7%)

-- Hare Quota --
Seats/District, Dem% of Seats, Overrepresentation
1, 66.7%, 12.9%
2, 55.6%, 1.8%
3, 55.6%, 1.8%
4, 50.0%, (3.8%)
5, 55.6%, 1.8%
6, 53.7%, (0.1%)
7, 52.4%, (1.8%)
8, 53.4%, (0.4%)
9, 53.1%, (0.7%)

As expected, even numbers cause underrepresentation in this case. There 
is an exception, however, with Hare quotas, which show the exact 
opposite trend from 6 to 9 seats per district. I'd be interested to know 
if this were the same case with another set of data. I'm willing to 
accept the other exception, the tie between 2 and 3 seats in Hare, as a 
fluke, without further analysis. Also, the deadlock problem seems to be 
only a problem with 2 and 4 seats per district, but at 6 and 8 the 
problem is minor. Hmm... I've also read that gerrymandering can be a 
problem with fewer than 7 seats per district.

> (JBH) You've got to give me more details before I can imagine this. We 
> have eighteen three-seat districts holding STV elections for a total 
> of forty-nine seats, and then fill another fifty-one seats by some 
> "additional member" calculation? Use a double-ballot such as in MMP in 
> Germany? (forget the U.S. Senate, assume I'm talking about a state 
> legislature.) Or are you saying the winners of the sub-districts would 
> be determined by the math of the greater district? I'm interested in 
> your idea, but not clear what you are saying.

What if all the sub-district ballots are counted together--for example, 
we take ten 3-seat districts and count them as a 30-seat district with 
an appropriate quota--and we use the rule, "the candidate to be 
eliminated shall be the candidate with the lowest votes from the party 
with the lowest average votes per candidate"? That would ensure party 
PR, and if I'm not mistaken, geographic PR. I suppose that could be 
combined with CPO-STV as well.