[EM] Non-PR multiwinner election methods

[David CATCHPOLE]

Non-PR multiwinner election methods - this subject has fascinated me ever
since I started considering the possibility of separate executive
assemblies as an alternative to Westminster and presidential institutional
forms. It's also an interesting topic given the contemporary
situation in Australia with majoritarian houses and with minor parties
whose coalition plans don't necessarily reflect the preferred government of
their supporters. I'd say it would be better for the choice of governing
coalition to be made by _voters_.

Here's one idea I've had for such a method. It's somewhat like a cross
between an FPP/Cumulative type system and single winner STV (AV).

Let n be some integer. 2n-1 is the number of candidates to be elected.
Votes are preference-based and counted so that the n highest
preferences, not excluded, on each vote are counted equally as votes for
relevant candidates. So for instance given n is equal to 2 (3 to be
elected) and no-one is excluded yet, the vote-

A>B>C>D>E>F

means one vote for A and one for B. The candidate with the lowest number
of such votes is excluded and this continues until there are only as many
non-excluded candidates as there are places to be filled.

Ties for exclusion could be broken by first preference votes.

In the sense of interparty competition, the system aggregates toward a
"quasi-quota" of 1/3 to begin with (two major groups) and then decides who gets
the one seat that means a majority of the assembly. For instance, in a
heavily strict party competition,

A1>A2>B1>B2>C1>C2 x 3
B1>B2>A1>A2>C1>C2 x 2
C1>C2>B1>B2>A1>A2 x 4

scores would be A1 3, A2 3, B1 2, B2 2, C1 4, C2 4. B1 and B2 are tied for
exclusion but B1 has more first-preference votes so B2 is excluded. The
votes are now

A1>A2>B1>C1>C2 x 3
B1>A1>A2>C1>C2 x 2
C1>C2>B1>A1>A2 x 4

and scores are A1 5, A2 3, B1 2, C1 4, C2 4. B1 is excluded.

A1>A2>C1>C2 x 3
A1>A2>C1>C2 x 2
C1>C2>A1>A2 x 4

and scores are A1 5, A2 5, C1 4, C2 4. C1 and C2 are tied for exclusion.
C1 has more first preferences so C2 is excluded.

A1,A2, and C1 are elected.

A variation on the majoritarian theme would be to make the number to be
elected 3n-1. This would have a tendency to elect 3 groups, instead of 2.
The basic formula is pn-1 where p is the expected number of groups
elected.

PS Is anyone interested in methods of election for various roles
at once, for instance a party room election for government ministers etc.?
I've been trying to think of how to introduce PR principles so various
factions receive a particular number in cabinet, etc.

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