[EM] A computationally feasible method

[Juho]

On Aug 31, 2008, at 15:25 , Raph Frank wrote:

> On Sat, Aug 30, 2008 at 5:46 PM, Juho <juho4880 at yahoo.co.uk> wrote:
>> 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.
>
> Brian Olson suggests this approach for his anti-gerrymandering  
> proposals.
>
> http://bolson.org/dist/USIRA.html
> and
> http://bolson.org/dist/
>
> Ofc, he doesn't define "geographic centers of the districts", which
> presumably means the centre of gravity of the district.
>
> Maybe it would be better to define the centre of the district as the
> average position of all the people in the district.
>
> One possible problem is that it would allow people with very powerful
> computers to gain an advantage.  The Republicans and the Democrats
> would probably end up being favoured.
>
> However, the advantage is likely to be slight.  Also, it could end up
> that there was a SETI at Home like effort to find the 'true' best
> arrangement (or maybe both party's supporters doing their own version)
> Democrats at Home and Republicans at Home :)

Yes, this would require better analysis but my feeling is that it  
would be more typical that in computationally complex election  
methods large parties would not have any major advantage over others.  
Already the first results could be very close to optimal, changes  
could be just swapping seats between candidates without changing the  
strength of the parties, and there could be also many others like  
SETI at home interested in finding better solutions than just the  
parties. Also private PCs could be powerful enough to check some  
interesting branches. Maybe some candidate that was not elected would  
try to find solutions where he/she would be elected.

Here's one example where finding the best solution may be more  
complex than just swapping few candidates and checking if one can  
improve the results that way, or when starting from that modified  
scenario. There is a circular atoll with 100 candidates. Everyone  
votes for his/her geographically nearest candidates. Every second of  
the candidates will be elected. When looking at where the candidates  
live on the atoll, every second candidate will be in the proposed  
set. It is however possible that electing those 50 that were not  
elected in the first proposed set is a better solution. And that may  
be quite difficult to find if one just makes small modifications.  
Monte carlo (+ optimization) on the other hand could find that easily.

Most sets are however not good at all and I guess in most cases very  
good results can be achieved although there would be no proof of the  
proposed set being the best one. Other benefits of the complex  
methods may well weigh more than the uncertainty of finding the best  
set.

Juho





		
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