# [EM] Consociational PR

Raph Frank raphfrk at gmail.com
Wed Sep 5 03:22:34 PDT 2012

```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 :).

> 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.

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

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.

> 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.

It also breaks the secret ballot.

> 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.

> 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.

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

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.

```