Here's a system I thought about some days ago. It's a bit interesting on
its own, but I haven't found out if it has any practical uses, or is
good enough to use in the situations that spring most readily to mind.
Say you have a divided society. In this society, disparate groups of
people vote for "their" parties or candidates, and there's little
overlap between each group's candidates. In ordinary PR, you might get
kingmaker scenarios that provide instability; in majoritarian systems,
the lesser groups might not get any representation at all.
What if one divided the different groups' candidates into different
chambers? Then one could provide each with mutual blocking rules to get
closer to a consensus system rather than a majority system, without
having the system be as brittle as an actual supermajority system.
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).
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.
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.
The system is not perfect, of course. By enshrining a division into n
groups, it may polarize those groups. Mutual veto or double majority
rules could help counter this, but that doesn't make the system elect
more compromise candidates. Furthermore, for the same reason, it could
slow the merging of divided groups, because the existence of n bodies
would reinforce the notion that there are exactly n groups "that matter".
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