[EM] Consociational PR

Kristofer Munsterhjelm km_elmet at lavabit.com
Wed Sep 5 09:17:40 PDT 2012

On 09/05/2012 12:22 PM, Raph Frank wrote:
> On Tue, Sep 4, 2012 at 10:15 PM, Kristofer Munsterhjelm
> <km_elmet at lavabit.com>  wrote:
>> So here's the system. Say you have k different legislative bodies (n doesn't
>> matter, but should probably be small, and if possible highly composite, so
>> something like 2, 3, or if you're really pushing it, 6).
> 3 isn't technically highly composite :).

Right. 2 and 3 are practical, 6 is the "deluxe" version :-)

>> Furthermore, say
>> there are n voters. After the election, associate to each body, n/k voters
>> so that the difference between the seat allocation to each were one to run a
>> majoritarian election for that body accordng to the associated voters, and
>> were one to run a proportional election for that body, is minimized. Then
>> run the actual elections - one PR election for each body - and you're done.
> So, assuming rankings, you fill the body based on condorcet ordering
> and PR and pick the sets of voters so as to try to match the 2
> assemblies.

You fill the body using PR, but each body is assigned a set of voters, 
or rather ballots, so that the discrepancy between (say) Schulze and 
Schulze STV is minimized. I think Hamming distance would make the most 
sense for the discrepancy measure. If body X has 50 seats, then you take 
the 50 candidates first ranked on Schulze. Call the set of these 
candidates X1. Then you take the 50 candidates first ranked on Schulze 
STV, and call that set X2. The discrepancy measure for body X is the 
Hamming distance (number of candidates in one set but not the other) for 
X1 wrt X2.

As for how to aggregate the discrepancy measure, either mean (sum) or 
minmax seems reasonable, but minmax is more likely to be hard to 
optimize (e.g. minmax Approval vs ordinary Approval).

> It isn't clear how to do that in a systematic way.  Find the maximum
> can often be NP-complete.

True. For Schulze and Schulze STV, it'd probably be impractical. It 
might work better with PR methods that already employ optimization 
(biweight, PAV, etc), or one could use greedy approximations.

> You could also take into account rankings directly.  For example, pick
> the distribution that minimise the sum of the condorcet rankings over
> all PR-assemblies.
> A PR assembly containing candidates ranked at 1-34 and 36 is better
> than one that has candidates 1-34 and candidate 100, even though there
> are 34 matches.

Do you mean measuring the dissimilarity between a Condorcet ranking for 
the whole electorate and each body's PR result? That would encourage 
similarity rather than clustering, I think. If each party runs a bunch 
of clones, the winner's clones will occupy the upper ranks and so these 
clones would be spread throughout all the bodies.

>> If society is divided, then the proportional result becomes like the
>> majoritarian one (or less different) if each group gets its own body -- and
>> we don't have to set ahead of time or have any preconception about what
>> those groups actually are.
> However, it does create an incentive to lie in the first stage and try
> to infiltrate other assemblies.

There would be an incentive to lie, as there is in any system. I'm not 
sure if it would be more serious than in ordinary methods, though.

> 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:

Mr. A: X > Y > Z
Mr. B: F > G > H
Mr. C: X > Y > Z
Mr. D: F > G > H


Mr. A: F > G > H
Mr. B: F > G > H
Mr. C: X > Y > Z
Mr. D: X > Y > Z,

namely populating one body with F, G, and H, and another with X, Y, and Z.

>> The system is not perfect, of course. By enshrining a division into n
>> groups, it may polarize those groups.
> One possible option would be to have the number of assemblies decided
> based on social polarisation.
> There could be a formal clustering algorithm of some kind.  Some of
> them allow you to estimate the number of clusters.
> If the public can be modeled as a single Gaussian, then you would only
> have 1 assembly.

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.

>> Mutual veto or double majority rules
>> could help counter this, but that doesn't make the system elect more
>> compromise candidates.
> In Northern Ireland, they have a mandatory coalition system.
> Basically, the leader of the largest party becomes First Minister and
> leader of the largest party from the other community becomes deputy
> First Minister.  The remaining seats at cabinet are then divided using
> the d'Hondt method between the parties.  When a party is assigned a
> seat, the leader of the party gets to pick which department the
> cabinet member will be responsible for (of the ones remaining).  This
> gives an added bias towards the larger parties, since they get to pick
> first.

So the party composition of the executive is not decided by 
negotiations, but rather ahead of time as the parties are given seats?

> It also means that each assembly member has to declare which community
> they are from (there are cross-community rules for certain bills).
> This means that assembly members who refuse to do that have reduced
> power.  Non-sectarian parties should at minimum have equal power to
> the sectarian parties.  There was a situation where some non-aligned
> tactically declared in order to get a bill passed and break a
> deadlock.
> Majority based democracy doesn't work very well when you have a
> divided society that is near 50-50.  Voters in the larger faction can
> be convinced of the need to vote as a bloc, so both communities end up
> with less democracy (though the minority ends up with none).  If the
> larger faction had a more solid majority, then that fear would be
> reduced and wouldn't end up being the main basis on which voters vote.
> I think if a society was made up of many sub-groups, with none near a
> majority on its own, then standard PR should work reasonably well,
> since each sub-group can negotiate.  That assumes that you don't end
> up with a de-facto bloc of voters with slightly above 50%.  You really
> need to deal with the case where the minority is large enough to be a
> threat, so that the majority feels the need to vote as a bloc.

PR systems may also, in certain situations, become majoritarian through 
mutual strategy. The strategy goes like this: First the governing 
coalition decides to move closer to one another in order to be effective 
(and all the positive properties ascribed to majoritarian systems). They 
construct a sort of "unified exterior" where they in private agree among 
themselves on the position to take and then stick to it in public. The 
opposition then moves closer in order not to stand divided against the 
united majority. After a while of this, you get one majority bloc and 
one minority bloc.

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. Also, I think that candidate-focused 
methods would, all other things equal, be less susceptible to producing 
this kind of strategy than would party lists. In something like STV, the 
voters can elect candidates that prefer to negotiate out in the open 
rather than in private. The voters can do so while still supporting 
parties whose leaders think the strategy is a good idea.

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