[EM] A computationally feasible method

[Juho]

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




		
___________________________________________________________ 
Now you can scan emails quickly with a reading pane. Get the new Yahoo! Mail. http://uk.docs.yahoo.com/nowyoucan.html