I assume Approval or Condorcet would permit n-dimensions, but I wonder about the value of n. Maybe n would be infinite, but with some dimensions "larger" than others. The realities of campaign finance and public attention might limit the value of n, or make it subject to factors other than the voting system. For example, liberal public financing might increase n, while strict limits on campaign advertising might force a fixed number of dimensions to have equal weight (I'm not saying either of these are good or bad).
I've been wondering whether Approval in parliamentary elections would lead into a single dominant party system, a strong central party, with an occasional seat gained by other parties, or with the central party making bargains right and left. With luck that could be a virtual one-party system.
Olli Salmi
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