On Aug 31, 2008, at 15:25 , Raph Frank wrote:
On Sat, Aug 30, 2008 at 5:46 PM, Juho <[EMAIL PROTECTED]> 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 [EMAIL PROTECTED] like effort to find the 'true' best
arrangement (or maybe both party's supporters doing their own version)
[EMAIL PROTECTED] and [EMAIL PROTECTED] :)
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
[EMAIL PROTECTED] 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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