[EM] Consociational PR

Kristofer Munsterhjelm km_elmet at lavabit.com
Thu Sep 6 09:34:48 PDT 2012

On 09/05/2012 06:35 PM, Raph Frank wrote:
> On Wed, Sep 5, 2012 at 5:17 PM, Kristofer Munsterhjelm
> <km_elmet at lavabit.com>  wrote:
>> Raph Frank wrote:
>>> It also breaks the secret ballot.
>> Not really. The apportionment is done after the election. So the method
>> would provide the same result whether the ballots were:
> I mean you have to match Mr. A between the 2 votes, or would you use
> the same ballots for both stages?

I'd use the same ballots, or subsets of them. Consider it like this: the 
clustering method gets a bunch of ballots in random order. There's no ID 
on any of the ballots to say "this is Mr. A's ballot; that is Mr. B's 
ballot". Say there are 300 ballots. Then the method moves 100 of them to 
one pile, another 100 to the second pile, and the final 100 in a third 
pile. Which ballots are moved to which piles? The ballots should be 
selected so that the discrepancy between PR and majoritarian rules run 
on the ballots of each pile in isolation is minimized.

Since the arrangement only depends on the contents 
(rankings/ratings/etc) of the ballots, it doesn't matter to the method 
whether misters A and B voted F>G>H and C and D voted X>Y>Z or if it 
were the other way around. In a 2-council arrangement, the optimum would 
in any case be to put the two F>G>H votes in one pile and the two X>Y>Z 
votes in the other pile.

The method is both anonymous and symmetric. It doesn't care about what 
voter submitted what ballot, and it doesn't care about the names of the 

>> How would that work in practice? If you have three House of Reps buildings
>> (or floors in the same building), each of which houses 100, it would be
>> somewhat difficult to house 300 representatives in one of them. I suppose
>> you could have 300 seats in each, but then most of the bodies' seats would
>> be vacant.
> There are clustering algorithms that will give an estimate of the
> number of clusters in the data.
> Basically, as you add more clusters, the average match gets better and
> better, but then it levels off.  You could have a rule that the number
> of clusters is equal to the smallest number that has a match that is
> at least 75% of the match if you assumed 10 (or some large number)
> clusters.

I imagine there are rules that could try to estimate cluster size, but I 
was speaking of how you would set it up in the real world, when you're 
not sure how many seats each assembly needs or how many assembly 
buildings will be in use.

In the US, you know there will always be a Senate and a House of 
Representatives. That's okay. The House meets in the south wing of 
Capitol, the Senate in the north. But now imagine that some years, there 
would be no Senate (as would be the case if they'd use a dynamic 
clustering method). Would you keep the north wing vacant? Would you have 
to keep 541 seats in the room of both wings?

>> However, while PR may have de facto majoritarian rule in this manner some of
>> the time, majoritarian systems have it all the time, so I still favor PR
>> over majoritarian systems.
> Ideally, you want many parties that are willing to go into government
> with each other, but don't end up merging.

Yes, and that may give some information as to what makes PR work. PR 
works when the groups are kept both representative and dynamic. With 
many parties, you can have representativity, but if it isn't dynamic, 
then permanent alliances or outright mergers could subvert the 

It's a somewhat like the idea of competition. If there are many parties 
and they don't collude, then they have to appeal to the voters, but if 
they collude, then they can get by with a majority-of-a-majority logic 
(like corporations can use oligopoly inefficiency to acquire additional 

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