No voting system can deal with people who have arbitrary preferences. I’ve lost track of the first time I looked into this, but I’m pretty sure that if you map preference space, impose a metric, and say that each candidate and voter choose a location in that space and the votes go in proportion to the distance by that metric, it gets around Arrow by imposing the requirement “voters may only express a preference that their representatives share their preferences”, which is reasonable but still violates the theorem’s preconditions.
No voting system can deal with people who have arbitrary preferences. I’ve lost track of the first time I looked into this, but I’m pretty sure that if you map preference space, impose a metric, and say that each candidate and voter choose a location in that space and the votes go in proportion to the distance by that metric, it gets around Arrow by imposing the requirement “voters may only express a preference that their representatives share their preferences”, which is reasonable but still violates the theorem’s preconditions.