[EM] Elections to cabinets

[David Catchpole]

An interesting subject... A cabinet election system would need the
following features-

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Represents only "one side of the room" (this is the most contentious
feature, so it goes first...)

Proportionately represents that one side of the room

Incorporates these concepts of at-large (at-half?) proportionality while
having different selections for different portfolios (and incorporating
ministers'-to-be preferences).
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It might be easier to begin the exposition with a "caucus" election system
(that used by a party caucus to select a cabinet) which would not
incorporate the minority exclusion feature.

Any ideas?