Here's one practical and simple approach to guaranteeing
computational feasibility of some otherwise complex election methods.
The original method might be based e.g. on evaluating all possible
sets of n candidates and then electing the best set. Comparing all
the sets is usually not computationally feasible. But the function
that compares two of these sets is typically computationally feasible.
The solution is to apply some general optimization methods (monte
carlo, following the gradient etc.) to find the best set one can. To
gain even better trust that this set is the best one one could
publish the best found set and then wait for a week and allow other
interested parties to seek for even better sets. Maybe different
parties or candidates try to find alternatives where they would do
better. If nothing is found then the first found set is declared
elected.
In this approach one is typically finds a set that is with high
probability either the best or at least in value close to best. If
better ones can not be found, this set could as well be considered to
be the best ("best known" at least). Other random factors of the
election method may well cause more randomness, so from theoretical
point of view this approach should in most cases be good enough.
This approach should make many complex methods computationally
feasible. The involved randomness may be a bit unpleasant, but from
technical point of view the performance is probably quite good.
Juho
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